Before quantum mechanics was developed, Johannes Rydberg developed an equation that

Problem 16E What is the de Broglie wavelength of an electron? What determines the value of the de Broglie wavelength for an electron?

Problem 17E What are complementary properties? How does electron diffraction demonstrate the complementarity of the wave nature and particle nature of the electron?

Problem 18E Explain Heisenberg's uncertainty principle. What paradox is at least partially solved by the uncertainty principle?

Problem 19E What is a trajectory? What kind of information do you need to predict the trajectory of a particle?

Problem 20E Why does the uncertainty principle make it impossible to predict a trajectory for the electron?

Problem 21E Newton's laws of motion are deterministic. Explain this statement.

Problem 22E An electron behaves in ways that are at least partially indeterminate Explain this statement.

Problem 23E What is a probability distribution map?

Problem 24E For each solution to the Schrodinger equation, what can be precisely specified: the electron s energy or its position? Explain.

Problem 25E What is a quantum-mechanical orbital?

Problem 26E What is the Schrodinger equation? What is a wave function? How is a wave function related to an orbital?

Problem 27E What are the possible values of the principal quantum number n ? What does the principal quantum number determine?

What are the possible values of the angular momentum quantum number ? What does the angular momentum quantum number determine?

What are the possible values of the magnetic quantum number m? What does the magnetic quantum number determine?

Problem 30E List all the orbitals in each principal level. Specify the three quantum numbers for each orbital. a. n = 1 b. n = 2 c. n = 3 d. n = 4

Problem 31E Explain the difference between a plot showing the probability density for an orbital and one showing the radial distribution function.

Problem 32E Make sketches of the general shapes of the s, p, and d orbitals.

Problem 33E List the four different sublevels. Given that only a maximum of two electrons can occupy orbital, determine the maximum number of electrons that can exist in each sublevel.

Problem 34E Why are atoms usually portrayed as spheres when most orbitals are not spherically shaped?

Problem 1E Why is the quantum-mechanical model of the atom important for understanding chemistry?

Problem 1SAQ Which wavelength of light has the highest frequency? a) 10 nm b) 10 mm c) 1 nm d) 1 mm

Problem 2E What is light? How fast does it travel in a vacuum?

Problem 2SAQ Which kind of electromagnetic radiation contains the greatest energy per photon? a) microwaves b) gamma rays c) X-rays d) visible light

Problem 3E Define the wavelength and amplitude of a wave. How are these related to the energy of the wave?

How much energy (in J) is contained in 1.00 mole of 552 nm photons? a) 3.60 x 10-19 J b) 2.17 x 105 J c) 3.60 x 10-28 J d) 5.98 x 10-43 J

Problem 4E Define the frequency of electromagnetic radiation. How is frequency related to wavelength?

Problem 4SAQ Light from three different lasers (A. B. and C), each with a different wavelength, was shined onto the same metal surface. Laser A produced no photoelectrons. Lasers B and C both produced photoelectrons, but the photoelectrons produced by laser B had a greater velocity than those produced by laser C. Arrange the lasers in order of increasing wavelength. a) A < B < C b) B < C < A c) C < B < A d) A < C < B

Problem 5E What determines the color of light? Describe the difference between red light and blue light.

Calculate the wavelength of an electron traveling at 1.85 x 107 m/s. a) 2.54 x 1013 m b) 3.93 x 10-14 m c) 2.54 x 1010 m d) 3.93 x 10-11 m

Problem 6E What determines the color of a colored object? Explain why grass appears green.

Which set of three quantum numbers does not specify an orbital in the hydrogen atom? a) n = 2; = 1; m = -1 b) n = 3; = 3; m = -2 c) n = 2; = 0; m = 0 d) n = 3; = 2; m = 2

Problem 7SAQ Calculate the wavelength of light emitted when an electron in the hydrogen atom makes a transition from an orbital with n = 5 to an orbital with n = 3. a) 1.28 x 10-6 m b) 6.04 xi0-7m c) 2.28 x 10-6 m d) 1.55 x 10-19 m

Calculate the wavelength of light emitted when an electron in the hydrogen atom makes a transition from an orbital with n = 5 to an orbital with n = 3. a) 1.28 x 10-6 m b) 6.04 x 10-7 m c) 2.28 x 10-6 m d) 1.55 x 10-19 m

Problem 8E Explain the wave behavior known as interference. Explain the difference between constructive and destructive interference.

Problem 8SAQ Which electron transition produces light of the highest frequency in the hydrogen atom? a) 5p ? ls b) 4p ? ls c) 3p ? ls d) 2p ? ls

Problem 9E Explain the wave behavior known as diffraction. Draw the diffraction pattern that occurs when light travels through two slits comparable in size and separation to the light’s wavelength.

How much time (in seconds) does it take light to travel 1.00 billion km? a) 3.00 x 1017 s b) 3.33 s c) 3.33 x 103 s d) 3.00 x 1020 s

Problem 10E Describe the photoelectric effect. How did experimental observations of this phenomenon differ from the predictions of classical electromagnetic theory?

Which orbital is a d orbital?

Problem 15E Explain electron diffraction.

An electron traveling at 3.7 x 105 m/s has an uncertainty in its velocity of 1.88 x 105 m/s. What is the uncertainty in its position?

Problem 71E An electron in the n = 7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 397 nm. What is the value of n for the level to which the electron relaxed?

Problem 87AE Elements in group 7 A in the periodic table are called the halogens; elements in group 6A are called the chalcogens (a) What is the most common oxidation state of the chalcogens compared to the halogens? (b) For each of the following periodic properties, state whether the halogens or the chalcogens have larger values: atomic radii, ionic radii of the most common oxidation state, first ionization energy, second ionization energy.

Problem 108AE We will see in Chapter that semiconductors are materials that conduct electricity better than nonmetals but not as well as metals. The only two elements in the periodic table that are technologically useful semiconductors are silicon and germanium. Integrated circuits in computer chips today are based on silicon. Compound semiconductors are also used in the electronics industry. Examples are gallium arsenide. GaAs: gallium phosphide, GaP; cadmium sulfide. CdS; and cadmium selenide. CdSe. (a) What is the relationship between the compound semiconductors' compositions and the positions of their elements on the periodic table relative to Si and Ge? (b) Workers in the semiconductor industry refer to “II—VI” and “III—V” materials, using Roman numerals. Can you identify which compound semiconductors are II—VI and which are III—V? (c) Suggest other compositions of compound semiconductors based on the positions of their elements in the periodic table.

Problem 110IE

Problem 111IE One way to measure ionization energies is ultraviolet photoelectron spectroscopy (PES), a technique based on the photoelectric effect. =*» (Section) In PES, monochromatic light is directed onto a sample, causing electrons to be emitted. The kinetic energy of the emitted electrons is measured. The difference between the energy of the photons and the kinetic energy of the electrons corresponds to the energy needed to remove the electrons (that is. the ionization energy). Suppose that a PES experiment is performed in which mercury vapor is irradiated with ultraviolet light of wavelength 58.4 nm. (a) What is the energyof a photon of this light, in eV? (b) Write an equation that shows the process corresponding to the first ionization energy of Hg. (c) The kinetic energy of the emitted electrons is measured to be 10.75 eV. What is the first ionization energy of Hg. in kJ/mol? (d) Using Figure determine which of the halogen elements has a first ionization energy closest to that of mercury. A Figure Trends in first ionization energies of the elements. The value for astatine. At, is missing in this figure. To the nearest 100 kJ/mol, what estimate would you make for the first ionization energy of At?

Problem 11E How did the photoelectric effect lead Einstein to propose that light is quantized?

Problem 12E What is a photon? How is the energy of a photon related to its wavelength? Its frequency?

Problem 13E What is an emission spectrum? How does an emission spectrum of a gas in a discharge tube differ from a white light spectrum?

Problem 14E Describe the Bohr model for the atom. How did the Bohr model account for the emission spectra of atoms?

Problem 37E List these types of electromagnetic radiation in order of (i) increasing wavelength and (ii) increasing energy per photon: a. radio waves b. microwaves c. infrared radiation d. ultraviolet radiation

Problem 38E List these types of electromagnetic radiation in order of (i) increasing frequency and (ii) decreasing energy per photon: a. gamma rays b. radio waves c. microwaves d. visible light

Which electron is, on average, closer to the nucleus: an electron in a 2s orbital or an electron in a 3s orbital?

Which electron is, on average, further from the nucleus: an electron in a 3p orbital or an electron in a 4p orbital?

What are the possible values of for each value of n? a. 1 b. 2 c. 3 d. 4

What are the possible values of ml for each value of ? a. 0 b. 1 c. 2 d. 3

Which set of quantum numbers cannot occur together to specify an orbital? a. n = 2, = 1, m = -1 b. n = 3, = 2, m = 0 c. n = 3, = 3, m = 2 d. n = 4, = 3, m = 0

Which combinations of n and represent real orbitals and which do not exist? a. 1s b. 2p c. 4s d. 2d

Sketch the 1s and 2p orbitals. How would the 2s and 3p orbitals differ from the 1s and 2p orbitals?

Sketch the 3d orbitals. How would the 4d orbitals differ from the 3d orbitals?

Problem 65E An electron in a hydrogen atom is excited with electrical energy to an excited state with n = 2. The atom then emits a photon. What is the value of n for the electron following the emission?

Problem 66E Determine whether each transition in the hydrogen atom corresponds to absorption or emission of energy. a. n = 3 ? n = 1 b. n = 2 ? n = 4 c. n = 4 ? n = 3

Problem 67E According to the quantum-mechanical model for the hydrogen atom, which electron transitions would produce light with the longer wavelength: 2p ? 1s or 3p ? 1s?

Problem 69E Calculate the wavelength of the light emitted when an electron in a hydrogen atom makes each transition and indicate the region of the electromagnetic spectrum (infrared, visible, ultraviolet, etc.) where the light is found. a. n = 2 ? n = 1 b. n = 3 ? n = 1 c. n = 4 ? n = 2 d. n = 5 ? n = 2

Problem 70E Calculate the frequency of the light emitted when an electron in a hydrogen atom makes each transition: a. n = 4 ? n = 3 b. n = 5 ? n = 1 c. n = 5 ? n = 4 d. n = 6 ? n = 5

Problem 72E An electron in a hydrogen atom relaxes to the n = 4 level, emitting light of 114 THz. What is the value of n for the level in which the electron originated?

Problem 74E The human eye contains a molecule called 11- cis -retinal that changes shape when struck with light of sufficient energy. The change in shape triggers a series of events that results in an electrical signal being sent to the brain. The minimum energy required to change the conformation of 11- cis -retinal within the eye is about 164 kJ/mol. Calculate the longest wavelength visible to the human eye.

Problem 75E An argon ion laser puts out 5.0 W of continuous power at a wavelength of 532 nm. The diameter of the laser beam is 5.5 mm. If the laser is pointed toward a pinhole with a diameter of 1.2 mm, how many photons will travel through the pinhole per second? Assume that the light intensity is equally distributed throughout the entire cross-sectional area of the beam. (1 W = 1 J/s)

A green leaf has a surface area of 2.50 cm2. If solar radiation is 1000 W/m2, how many photons strike the leaf every second? Assume three significant figures and an average wavelength of 504 nm for solar radiation.

An X-ray photon of wavelength 0.989 nm strikes a surface. The emitted electron has a kinetic energy of 969 eV. What is the binding energy of the electron in kJ/mol?

In a technique used for surface analysis called Auger electron spectroscopy (AES), electrons are accelerated toward a metal surface. These electrons cause the emissions of secondary electrons— called auger electrons—from the metal surface. The kinetic energy of the auger electrons depends on the composition of the surface. The presence of oxygen atoms on the surface results in auger electrons with a kinetic energy of approximately 506 eV. What is the de Broglie wavelength of one of these electrons?

Problem 79AE Group Trends in Metals and Nonmetals (Sections) Write a balanced equation for the reaction that occurs in each of the following cases:(a) Chlorine reacts with water, (b) Barium metal is heated in an atmosphere of hydrogen gas. (c) Lithium reacts with sulfur, (d) Fluorine reacts with magnesium metal.

Problem 80AE Consider the stable elements through lead (Z = 82). In how many instances are the atomic weights of the elements out of order relative to the atomic numbers of the elements?

Problem 81AE Figure shows the radial probability distribution functions for the 2s orbitals and 2p orbitals, (a) Which orbital. 2s or 2p, has more electron density close to the nucleus? (b) How would you modify Slater's rules to adjust for the difference in electronic penetration of the nucleus for the 2s and 2p orbitals? A Figure Comparison of 1s. 2s. and 2p radial probability functions. Based on this figure, is it possible for an electron in a 2s orbital to be closer to the nucleus than an electron in a 1 s orbital? (a) If the core electrons were totally effective at screening the valence electrons and the valence electrons provided no screening for each other, what would be the effective nuclear charge acting on the 3s and 3p valence electrons in P? (b) Repeat these calculations using Slater's rules, (c) Detailed calculations indicate that the effective nuclear charge is 5.6+ for the 3s electrons and 4.9+ for the 3p electrons. Why are the values for the 3s and 3p electrons different? (d) If you remove a single electron from a P atom, which orbital will it come from?

Problem 82AE As we move across a period of the periodic table, why do the sizes of the transition elements change more gradually than those of the representative elements?

Problem 86AE The following observations are made about two hypothetical elements A and B: The A—A and B—B bond lengths in elemental A and B are 2.36 and 1.94 A. respectively. A and B react to form the binary compound AB2. which has a linear structure (that is^B-A-B = 180°). Based on these statements, predict the separation between the two B nuclei in amolecule of AB2.

Problem 83AE In the series of group 5A hydrides, of general formula MH3, the measured bond distances are P—H. 1.419 A; As—H. 1.519 A; Sb—H. 1.707 A. (a) Compare these values with those estimated by use of the atomic radii in Figure, (b) Explain the steady increase in M—H bond distance in this series in terms of the electron configurations of the M atoms. A Figure Trends in bonding atomic radii for periods 1 through 5. Which part of the periodic table (top/bottom. left/right) has the elements with the largest atoms?

Problem 84AE In Table the bonding atomic radius of neon is listed as 0.58 A. whereas that for xenon is listed as 1.40 A. A classmate of yours states that the value for Xe is more realistic than the one for Ne. Is she correct? If so. what is the basis for her statement? Table Some Properties of the Noble Gases

Problem 85AE The As—As bond length in elemental arsenic is 2.48 A. The Cl—Cl bond length in CI2 is 1.99 A. (a) Based on these data, what is the predicted As—Cl bond length in arsenic trichloride.AsCI3, in which each of the three Cl atoms is bonded to the As atom? (b) What bond length is predicted for AsCI3, using the atomic radii in Figure. A Figure Trends in bonding atomic radii for periods 1 through 5. Which part of the periodic table (top/bottom. left/right) has the elements with the largest atoms?

Problem 88AE Note from the following table that there is a significant increase in atomic radius upon moving from Y to La whereas the radii of Zr to Hf are the same. Suggest an explanation for this effect.

The iodine molecule can be photodissociated into iodine atoms in the gas phase with light of wavelengths shorter than about \(792 \mathrm{~nm}\). A \(100.0 \mathrm{~mL}\) glass tube contains \(55.7 \mathrm{mtorr}\) of gaseous iodine at \(25.0^{\circ} \mathrm{C}\). What minimum amount of light energy must be absorbed by the iodine in the tube to dissociate \(15.0 \%\) of the molecules?

Problem 55E An electron has an uncertainty in its position of 552 pm. What is the uncertainty in its velocity?

The distance from the sun to Earth is 1.496 x 108 km. How long does it take light to travel from the sun to Earth?

Problem 39E Calculate the frequency of each wavelength of electromagnetic radiation: a. 632.8 nm (wavelength of red light from helium-neon laser) b. 503 nm (wavelength of maximum solar radiation) c. 0.052 nm (a wavelength contained in medical X-rays)

Problem 40E Calculate the wavelength of each frequency of electromagnetic radiation: a. 100.2 MHz (typical frequency for FM radio broadcasting) b. 1070 kHz (typical frequency for AM radio broadcasting) (assume four significant figures) c. 835.6 MHz (common frequency used for cell phone communication)

Problem 41E Calculate the energy of a photon of electromagnetic radiation at each of the wavelengths indicated in Problem 39. REFERENCE PROBLEM: Calculate the frequency of each wavelength of electromagnetic radiation: a. 632.8 nm (wavelength of red light from helium-neon laser) b. 503 nm (wavelength of maximum solar radiation) c. 0.052 nm (a wavelength contained in medical X-rays)

Problem 42E Calculate the energy of a photon of electromagnetic radiation at each of the frequencies indicated in Problem 40. REFERENCE PROBLEM: Calculate the wavelength of each frequency of electromagnetic radiation: a. 100.2 MHz (typical frequency for FM radio broadcasting) b. 1070 KHz (typical frequency for AM radio broadcasting) (assume four significant figures) c. 835.6 MHz (common frequency used for cell phone communication)

Problem 43E A laser pulse with wavelength 532 nm contains 3.85 mJ of energy. How many photons are in the laser pulse?

A heat lamp produces 32.8 watts of power at a wavelength of 6.5 m. How many photons are emitted per second? (1 watt = 1 J/s)

Problem 45E Determine the energy of 1 mol of photons for each kind of light. (Assume three significant figures.) a. infrared radiation (1500 nm) b. visible light (500 nm) c. ultraviolet radiation (150 nm)

Problem 46E How much energy is contained in 1 mol of each? a. X-ray photons with a wavelength of 0.135 nm b. y -ray photons with a wavelength of 2.15 x 10-5 nm.

Problem 47E Sketch the interference pattern that results from the diffraction of electrons passing through two closely spaced slits.

What happens to the interference pattern described in Problem 47 if the rate of electrons going through the slits is decreased to one electron per hour? What happens to the pattern if we try to determine which slit the electron goes through by using a laser placed directly behind the slits?

Problem 49E The resolution limit of a microscope is roughly equal to the wavelength of light used in producing the image. Electron microscopes use an electron beam (in place of photons) to produce much higher resolution images, about 0.20 nm in modern instruments. Assuming that the resolution of an electron microscope is equal to the de Broglie wavelength of the electrons used, to what speed must the electrons be accelerated to obtain a resolution of 0.20 nm?

Problem 50E The smallest atoms can themselves exhibit quantum- mechanical behavior Calculate the c Broglie wavelength (in pm) of a hydrogen atom traveling at 475 m/s.

What is the de Broglie wavelength of an electron traveling at 1.35 x 105 m/s?

Problem 52E A proton in a linear accelerator has a de Broglie wavelength of 122 pm. What is the speed of the proton?

Problem 53E Calculate the de Broglie wavelength of a 143 g baseball traveling at 95 mph. Why is the wave nature of matter not important for a baseball?

Problem 54E A 0.22-caliber handgun fires a 27 g bullet at a velocity of 765 m/s. Calculate the de Broglie wavelength of the bullet. Is the wave nature of matter significant for bullets?

A photon has a frequency of 6.0 3 104 Hz. (a) Convert this frequency into wavelength (nm). Does this frequency fall in the visible region? (b) Calculate the energy (in joules) of this photon. (c) Calculate the energy (in joules) of 1 mole of photons all with this frequency

What is the wavelength, in nm, of radiation that has an energy content of 1.0 3 103 kJ/mol? In which region of the electromagnetic spectrum is this radiation found?

When copper is bombarded with high-energy electrons, X rays are emitted. Calculate the energy (in joules) associated with the photons if the wavelength of the X rays is 0.154 nm

A particular form of electromagnetic radiation has a frequency of 8.11 3 1014 Hz. (a) What is its wavelength in nanometers? In meters? (b) To what region of the electromagnetic spectrum would you assign it? (c) What is the energy (in joules) of one quantum of this radiation?

The work function of potassium is 3.68 3 10219 J. (a) What is the minimum frequency of light needed to eject electrons from the metal? (b) Calculate the kinetic energy of the ejected electrons when light of frequency equal to 8.62 3 1014 s21 is used for irradiation

When light of frequency equal to 2.11 3 1015 s21 shines on the surface of gold metal, the kinetic energy of ejected electrons is found to be 5.83 3 10219 J. What is the work function of gold?

(a) What is an energy level? Explain the difference between ground state and excited state. (b) What are emission spectra? How do line spectra differ from continuous spectra?

(a) Briefly describe Bohrs theory of the hydrogen atom and how it explains the appearance of an emission spectrum. How does Bohrs theory differ from concepts of classical physics? (b) Explain the meaning of the negative sign in Equation (7.5).

Explain why elements produce their own characteristic colors when they emit photons?

Some copper compounds emit green light when they are heated in a flame. How would you determine whether the light is of one wavelength or a mixture of two or more wavelengths?

Is it possible for a fluorescent material to emit radiation in the ultraviolet region after absorbing visible light? Explain your answer.

Explain how astronomers are able to tell which elements are present in distant stars by analyzing the electromagnetic radiation emitted by the stars

Consider the following energy levels of a hypothetical atom: E4 __________ 21.0 3 10219 J E3 __________ 25.0 3 10219 J E2 __________ 210 3 10219 J E1 __________ 215 3 10219 J (a) What is the wavelength of the photon needed to excite an electron from E1 to E4? (b) What is the energy (in joules) a photon must have in order to excite an electron from E2 to E3? (c) When an electron drops from the E3 level to the E1 level, the atom is said to undergo emission. Calculate the wavelength of the photon emitted in this process

The first line of the Balmer series occurs at a wavelength of 656.3 nm. What is the energy difference between the two energy levels involved in the emission that results in this spectral line?

Calculate the wavelength (in nanometers) of a photon emitted by a hydrogen atom when its electron drops from the n 5 5 state to the n 5 3 state

Calculate the frequency (Hz) and wavelength (nm) of the emitted photon when an electron drops from the n 5 4 to the n 5 2 level in a hydrogen atom.

Careful spectral analysis shows that the familiar yellow light of sodium lamps (such as street lamps) is made up of photons of two wavelengths, 589.0 nm and 589.6 nm. What is the difference in energy (in joules) between photons with these wavelengths?

An electron in the hydrogen atom makes a transition from an energy state of principal quantum numbers ni to the n 5 2 state. If the photon emitted has a wavelength of 434 nm, what is the value of ni?

Explain the statement, Matter and radiation have a dual nature.

How does de Broglies hypothesis account for the fact that the energies of the electron in a hydrogen atom are quantized?

Why is Equation (7.8) meaningful only for submicroscopic particles, such as electrons and atoms, and not for macroscopic objects?

(a) If a H atom and a He atom are traveling at the same speed, what will be the relative wavelengths of the two atoms? (b) If a H atom and a He atom have the same kinetic energy, what will be the relative wavelengths of the two atoms?

Thermal neutrons are neutrons that move at speeds comparable to those of air molecules at room temperature. These neutrons are most effective in initiating a nuclear chain reaction among 235U isotopes. Calculate the wavelength (in nm) associated with a beam of neutrons moving at 7.00 3 102 m/s. (Mass of a neutron 5 1.675 3 10227 kg.)

Protons can be accelerated to speeds near that of light in particle accelerators. Estimate the wavelength (in nm) of such a proton moving at 2.90 3 108 m/s. (Mass of a proton 5 1.673 3 10227 kg.)

What is the de Broglie wavelength, in cm, of a 12.4-g hummingbird flying at 1.20 3 102 mph? (1 mile 5 1.61 km.)

What is the de Broglie wavelength (in nm) associated with a 2.5-g Ping-Pong ball traveling 35 mph?

What are the inadequacies of Bohrs theory?

What is the Heisenberg uncertainty principle? What is the Schrdinger equation?

What is the physical significance of the wave function?

How is the concept of electron density used to describe the position of an electron in the quantum mechanical treatment of an atom?

What is an atomic orbital? How does an atomic orbital differ from an orbit?

Describe the shapes of s, p, and d orbitals. How are these orbitals related to the quantum numbers n, /, and m/?

List the hydrogen orbitals in increasing order of energy

Describe the characteristics of an s orbital, a p orbital, and a d orbital. Which of the following orbitals do not exist: 1p, 2s, 2d, 3p, 3d, 3f, 4g?

Why is a boundary surface diagram useful in representing an atomic orbital?

Describe the four quantum numbers used to characterize an electron in an atom.

Which quantum number defines a shell? Which quantum numbers define a subshell?

Which of the four quantum numbers (n, /, m/, ms) determine (a) the energy of an electron in a hydrogen atom and in a many-electron atom, (b) the size of an orbital, (c) the shape of an orbital, (d) the orientation of an orbital in space?

An electron in a certain atom is in the n 5 2 quantum level. List the possible values of / and m/ that it can have.

An electron in an atom is in the n 5 3 quantum level. List the possible values of / and m/ that it can have.

Give the values of the quantum numbers associated with the following orbitals: (a) 2p, (b) 3s, (c) 5d

Give the values of the four quantum numbers of an electron in the following orbitals: (a) 3s, (b) 4p, (c) 3d.

Discuss the similarities and differences between a 1s and a 2s orbital

What is the difference between a 2px and a 2py orbital?

List all the possible subshells and orbitals associated with the principal quantum number n, if n 5 5.

List all the possible subshells and orbitals associated with the principal quantum number n, if n 5 6.

Calculate the total number of electrons that can occupy (a) one s orbital, (b) three p orbitals, (c) five d orbitals, (d) seven f orbitals.

What is the total number of electrons that can be held in all orbitals having the same principal quantum number n?

Determine the maximum number of electrons that can be found in each of the following subshells: 3s, 3d, 4p, 4f, 5f.

Indicate the total number of (a) p electrons in N (Z 5 7); (b) s electrons in Si (Z 5 14); and (c) 3d electrons in S (Z 5 16)

Make a chart of all allowable orbitals in the first four principal energy levels of the hydrogen atom. Designate each by type (for example, s, p) and indicate how many orbitals of each type there are.

Why do the 3s, 3p, and 3d orbitals have the same energy in a hydrogen atom but different energies in a many-electron atom?

For each of the following pairs of hydrogen orbitals, indicate which is higher in energy: (a) 1s, 2s; (b) 2p, 3p; (c) 3dxy, 3dyz; (d) 3s, 3d; (e) 4f, 5s.

Which orbital in each of the following pairs is lower in energy in a many-electron atom? (a) 2s, 2p; (b) 3p, 3d; (c) 3s, 4s; (d) 4d, 5f

What is electron configuration? Describe the roles that the Pauli exclusion principle and Hunds rule play in writing the electron configuration of elements.

Explain the meaning of the symbol 4d6 .

Explain the meaning of diamagnetic and paramagnetic. Give an example of an element that is diamagnetic and one that is paramagnetic. What does it mean when we say that electrons are paired?

What is meant by the term shielding of electrons in an atom? Using the Li atom as an example, describe the effect of shielding on the energy of electrons in an atom.

Indicate which of the following sets of quantum numbers in an atom are unacceptable and explain why: (a) (1, 0, 1 2, 1 2), (b) (3, 0, 0, 11 2), (c) (2, 2, 1, 11 2), (d) (4, 3, 22, 11 2), (e) (3, 2, 1, 1).

The ground-state electron configurations listed here are incorrect. Explain what mistakes have been made in each and write the correct electron configurations. Al: 1s 2 2s 2 2p4 3s 2 3p3 B: 1s 2 2s 2 2p5 F: 1s 2 2s 2 2p6

The atomic number of an element is 73. Is this element diamagnetic or paramagnetic?

Indicate the number of unpaired electrons present in each of the following atoms: B, Ne, P, Sc, Mn, Se, Kr, Fe, Cd, I, Pb.

State the Aufbau principle and explain the role it plays in classifying the elements in the periodic table.

Describe the characteristics of the following groups of elements: transition metals, lanthanides, actinides.

What is the noble gas core? How does it simplify the writing of electron configurations?

What are the group and period of the element osmium?

Define the following terms and give an example of each: transition metals, lanthanides, actinides.

Explain why the ground-state electron configurations of Cr and Cu are different from what we might expect

Explain what is meant by a noble gas core. Write the electron configuration of a xenon core

Comment on the correctness of the following statement: The probability of finding two electrons with the same four quantum numbers in an atom is zero.

Use the Aufbau principle to obtain the ground-state electron configuration of selenium.

Use the Aufbau principle to obtain the ground-state electron configuration of technetium.

Write the ground-state electron configurations for the following elements: B, V, Ni, As, I, Au.

Write the ground-state electron configurations for the following elements: Ge, Fe, Zn, Ni, W, Tl.

The electron configuration of a neutral atom is 1s 2 2s 2 2p6 3s 2 . Write a complete set of quantum numbers for each of the electrons. Name the element

Which of the following species has the most unpaired electrons? S1, S, or S2. Explain how you arrive at your answer.

A sample tube consisted of atomic hydrogens in their ground state. A student illuminated the atoms with monochromatic light, that is, light of a single wavelength. If only two spectral emission lines in the visible region are observed, what is the wavelength (or wavelengths) of the incident radiation?

A laser produces a beam of light with a wavelength of 532 nm. If the power output is 25.0 mW, how many photons does the laser emit per second? (1 W 5 1 J/s.)

When a compound containing cesium ion is heated in a Bunsen burner flame, photons with an energy of 4.30 3 10219 J are emitted. What color is the cesium flame?

Discuss the current view of the correctness of the following statements. (a) The electron in the hydrogen atom is in an orbit that never brings it closer than 100 pm to the nucleus. (b) Atomic absorption spectra result from transitions of electrons from lower to higher energy levels. (c) A many- electron atom behaves somewhat like a solar system that has a number of planets

What is the basis for thinking that atoms are spherical in shape even though the atomic orbitals p, d, . . . have distinctly nonspherical shapes?

What is the maximum number of electrons in an atom that can have the following quantum numbers? Specify the orbitals in which the electrons would be found. (a) n 5 2, ms 5 11 2; (b) n 5 4, m/ 5 11; (c) n 5 3, / 5 2; (d) n 5 2, / 5 0, ms 5 21 2; (e) n 5 4, / 5 3, m/ 5 22

Identify the following individuals and their contributions to the development of quantum theory: Bohr, de Broglie, Einstein, Planck, Heisenberg, Schrdinger.

What properties of electrons are used in the operation of an electron microscope?

In a photoelectric experiment a student uses a light source whose frequency is greater than that needed to eject electrons from a certain metal. However, after continuously shining the light on the same area of the metal for a long period of time the student notices that the maximum kinetic energy of ejected electrons begins to decrease, even though the frequency of the light is held constant. How would you account for this behavior?

A certain pitchers fastballs have been clocked at about 100 mph. (a) Calculate the wavelength of a 0.141-kg baseball (in nm) at this speed. (b) What is the wavelength of a hydrogen atom at the same speed? (1 mile 5 1609 m.)

A student carried out a photoelectric experiment by shining visible light on a clean piece of cesium metal. The table here shows the kinetic energies (KE) of the ejected electrons as a function of wavelengths (). Determine graphically the work function and the Planck constant. (nm) 405 435.8 480 520 577.7 KE (J) 2.360 3 2.029 3 1.643 3 1.417 3 1.067 3 10219 10219 10219 10219 10219

(a) What is the lowest possible value of the principal quantum number (n) when the angular momentum quantum number (/) is 1? (b) What are the possible values of the angular momentum quantum number (/) when the magnetic quantum number (m/) is 0, given than n # 4?

Considering only the ground-state electron configuration, are there more diamagnetic or paramagnetic elements? Explain

A ruby laser produces radiation of wavelength 633 nm in pulses whose duration is 1.00 3 1029 s. (a) If the laser produces 0.376 J of energy per pulse, how many photons are produced in each pulse? (b) Calculate the power (in watts) delivered by the laser per pulse. (1 W 5 1 J/s.)

A 368-g sample of water absorbs infrared radiation at 1.06 3 104 nm from a carbon dioxide laser. Suppose all the absorbed radiation is converted to heat. Calculate the number of photons at this wavelength required to raise the temperature of the water by 5.008C.

Photodissociation of water H2O(l) 1 hn H2(g) 1 1 2O2(g) has been suggested as a source of hydrogen. The Hrxn for the reaction, calculated from thermochemical data, is 285.8 kJ per mole of water decomposed. Calculate the maximum wavelength (in nm) that would provide the necessary energy. In principle, is it feasible to use sunlight as a source of energy for this process?

Spectral lines of the Lyman and Balmer series do not overlap. Verify this statement by calculating the longest wavelength associated with the Lyman series and the shortest wavelength associated with the Balmer series (in nm)

An atom moving at its root-mean-square speed at 208C has a wavelength of 3.28 3 10211 m. Identify the atom.

Certain sunglasses have small crystals of silver chloride (AgCl) incorporated in the lenses. When the lenses are exposed to light of the appropriate wavelength, the following reaction occurs: AgCl Ag 1 Cl The Ag atoms formed produce a uniform gray color that reduces the glare. If DH for the preceding reaction is 248 kJ/mol, calculate the maximum wavelength of light that can induce this process.

The He1 ion contains only one electron and is therefore a hydrogenlike ion. Calculate the wavelengths, in increasing order, of the first four transitions in the Balmer series of the He1 ion. Compare these wavelengths with the same transitions in a H atom. Comment on the differences. (The Rydberg constant for He1 is 8.72 3 10218 J.)

Ozone (O3) in the stratosphere absorbs the harmful radiation from the sun by undergoing decomposition: O3 O 1 O2. (a) Referring to Table 6.4, calculate the DH8 for this process. (b) Calculate the maximum wavelength of photons (in nm) that possess this energy to cause the decomposition of ozone photochemically

The retina of a human eye can detect light when radiant energy incident on it is at least 4.0 3 10217 J. For light of 600-nm wavelength, how many photons does this correspond to?

A helium atom and a xenon atom have the same kinetic energy. Calculate the ratio of the de Broglie wavelength of the helium atom to that of the xenon atom

A laser is used in treating retina detachment. The wavelength of the laser beam is 514 nm and the power is 1.6 W. If the laser is turned on for 0.060 s during surgery, calculate the number of photons emitted by the laser. (1 W 5 1 J/s.)

An electron in an excited state in a hydrogen atom can return to the ground state in two different ways: (a) via a direct transition in which a photon of wavelength 1 is emitted and (b) via an intermediate excited state reached by the emission of a photon of wavelength 2. This intermediate excited state then decays to the ground state by emitting another photon of wavelength 3. Derive an equation that relates 1 to 2 and 3.

A photoelectric experiment was performed by separately shining a laser at 450 nm (blue light) and a laser at 560 nm (yellow light) on a clean metal surface and measuring the number and kinetic energy of the ejected electrons. Which light would generate more electrons? Which light would eject electrons with greater kinetic energy? Assume that the same amount of energy is delivered to the metal surface by each laser and that the frequencies of the laser lights exceed the threshold frequency.

Draw the shapes (boundary surfaces) of the following orbitals: (a) 2py, (b) 3dz 2, (c) 3dx2 2y2. (Show coordinate axes in your sketches.)

The electron configurations described in this chapter all refer to gaseous atoms in their ground states. An atom may absorb a quantum of energy and promote one of its electrons to a higher-energy orbital. When this happens, we say that the atom is in an excited state. The electron configurations of some excited atoms are given. Identify these atoms and write their ground-state configurations: (a) 1s 1 2s 1 (b) 1s 2 2s 2 2p2 3d1 (c) 1s 2 2s 2 2p6 4s 1 (d) [Ar]4s 1 3d104p4 (e) [Ne]3s 2 3p4 3d1

Draw orbital diagrams for atoms with the following electron configurations: (a) 1s 2 2s 2 2p5 (b) 1s 2 2s 2 2p6 3s 2 3p3 (c) 1s 2 2s 2 2p6 3s 2 3p6 4s 2 3d7

If Rutherford and his coworkers had used electrons instead of alpha particles to probe the structure of the nucleus as described in Section 2.2, what might they have discovered?

Scientists have found interstellar hydrogen atoms with quantum number n in the hundreds. Calculate the wavelength of light emitted when a hydrogen atom undergoes a transition from n 5 236 to n 5 235. In what region of the electromagnetic spectrum does this wavelength fall?

Calculate the wavelength of a helium atom whose speed is equal to the root-mean-square speed at 208C.

Ionization energy is the minimum energy required to remove an electron from an atom. It is usually expressed in units of kJ/mol, that is, the energy in kilojoules required to remove one mole of electrons from one mole of atoms. (a) Calculate the ionization energy for the hydrogen atom. (b) Repeat the calculation, assuming in this second case that the electrons are removed from the n 5 2 state.

An electron in a hydrogen atom is excited from the ground state to the n 5 4 state. Comment on the correctness of the following statements (true or false). (a) n 5 4 is the first excited state. (b) It takes more energy to ionize (remove) the electron from n 5 4 than from the ground state. (c) The electron is farther from the nucleus (on average) in n 5 4 than in the ground state. (d) The wavelength of light emitted when the electron drops from n 5 4 to n 5 1 is longer than that from n 5 4 to n 5 2. (e) The wavelength the atom absorbs in going from n 5 1 to n 5 4 is the same as that emitted as it goes from n 5 4 to n 5 1

The ionization energy of a certain element is 412 kJ/mol (see Problem 7.125). However, when the atoms of this element are in the first excited state, the ionization energy is only 126 kJ/mol. Based on this information, calculate the wavelength of light emitted in a transition from the first excited state to the ground state

Alveoli are the tiny sacs of air in the lungs (see Problem 5.136) whose average diameter is 5.0 3 1025 m. Consider an oxygen molecule (5.3 3 10226 kg) trapped within a sac. Calculate the uncertainty in the velocity of the oxygen molecule. (Hint: The maximum uncertainty in the position of the molecule is given by the diameter of the sac.)

How many photons at 660 nm must be absorbed to melt 5.0 3 102 g of ice? On average, how many H2O molecules does one photon convert from ice to water? (Hint: It takes 334 J to melt 1 g of ice at 08C.)

Shown are portions of orbital diagrams representing the ground-state electron configurations of certain elements. Which of them violate the Pauli exclusion principle? Hunds rule? (a) (b) (c) (d) (e) (f) hg hg gg hg hg hg h h h h h h g hg h h hh h hg g h hg h

The UV light that is responsible for tanning the skin falls in the 320- to 400-nm region. Calculate the total energy (in joules) absorbed by a person exposed to this radiation for 2.0 h, given that there are 2.0 3 1016 photons hitting Earths surface per square centimeter per second over a 80-nm (320 nm to 400 nm) range and that the exposed body area is 0.45 m2 . Assume that only half of the radiation is absorbed and the other half is reflected by the body. (Hint: Use an average wavelength of 360 nm in calculating the en

The sun is surrounded by a white circle of gaseous material called the corona, which becomes visible during a total eclipse of the sun. The temperature of the corona is in the millions of degrees Celsius, which is high enough to break up molecules and remove some or all of the electrons from atoms. One way astronomers have been able to estimate the temperature of the corona is by studying the emission lines of ions of certain elements. For example, the emission spectrum of Fe141 ions has been recorded and analyzed. Knowing that it takes 3.5 3 104 kJ/mol to convert Fe131 to Fe141, estimate the temperature of the suns corona. (Hint: The average kinetic energy of one mole of a gas is 3 2RT .)

In 1996 physicists created an anti-atom of hydrogen. In such an atom, which is the antimatter equivalent of an ordinary atom, the electrical charges of all the component particles are reversed. Thus, the nucleus of an anti-atom is made of an anti-proton, which has the same mass as a proton but bears a negative charge, while the electron is replaced by an antielectron (also called positron) with the same mass as an electron, but bearing a positive charge. Would you expect the energy levels, emission spectra, and atomic orbitals of an antihydrogen atom to be different from those of a hydrogen atom? What would happen if an anti-atom of hydrogen collided with a hydrogen atom?

Use Equation (5.16) to calculate the de Broglie wavelength of a N2 molecule at 300 K.

When an electron makes a transition between energy levels of a hydrogen atom, there are no restrictions on the initial and final values of the principal quantum number n. However, there is a quantum mechanical rule that restricts the initial and final values of the orbital angular momentum /. This is the selection rule, which states that / 5 61; that is, in a transition, the value of / can only increase or decrease by one. According to this rule, which of the following transitions are allowed: (a) 2s 1s, (b) 3p 1s, (c) 3d 4f , (d) 4d 3s? In view of this selection rule, explain why it is possible to observe the various emission series shown in Figure 7.11

In an electron microscope, electrons are accelerated by passing them through a voltage difference. The kinetic energy thus acquired by the electrons is equal to the voltage times the charge on the electron. Thus, a voltage difference of 1 V imparts a kinetic energy of 1.602 3 10219 C 3 V or 1.602 3 10219 J. Calculate the wavelength associated with electrons accelerated by 5.00 3 103 V.

A microwave oven operating at 1.22 3 108 nm is used to heat 150 mL of water (roughly the volume of a tea cup) from 208C to 1008C. Calculate the number of photons needed if 92.0 percent of microwave energy is converted to the thermal energy of water

The radioactive Co-60 isotope is used in nuclear medicine to treat certain types of cancer. Calculate the wavelength and frequency of an emitted gamma photon having the energy of 1.29 3 1011 J/mol.

(a) An electron in the ground state of the hydrogen atom moves at an average speed of 5 3 106 m/s. If the speed is known to an uncertainty of 1 percent, what is the uncertainty in knowing its position? Given that the radius of the hydrogen atom in the ground state is 5.29 3 10211 m, comment on your result. The mass of an electron is 9.1094 3 10231 kg. (b) A 3.2-g Ping-Pong ball moving at 50 mph has a momentum of 0.073 kg ? m/s. If the uncertainty in measuring the momentum is 1.0 3 1027 of the momentum, calculate the uncertainty in the Ping-Pong balls position.

One wavelength in the hydrogen emission spectrum is 1280 nm. What are the initial and final states of the transition responsible for this emission?

Owls have good night vision because their eyes can detect a light intensity as low as 5.0 3 10213 W/m2 . Calculate the number of photons per second that an owls eye can detect if its pupil has a diameter of 9.0 mm and the light has a wavelength of 500 nm. (1 W 5 1 J/s.)

For hydrogenlike ions, that is, ions containing only one electron, Equation (7.5) is modified as follows: En 5 2RHZ2 (1yn2 ), where Z is the atomic number of the parent atom. The figure here represents the emission spectrum of such a hydrogenlike ion in the gas phase. All the lines result from the electronic transitions from the excited states to the n 5 2 state. (a) What electronic transitions correspond to lines B and C? (b) If the wavelength of line C is 27.1 nm, calculate the wavelengths of lines A and B. (c) Calculate the energy needed to remove the electron from the ion in the n 5 4 state. (d) What is the physical significance of the continuum? C B A Continuum

When two atoms collide, some of their kinetic energy may be converted into electronic energy in one or both atoms. If the average kinetic energy is about equal to the energy for some allowed electronic transition, an appreciable number of atoms can absorb enough energy through an inelastic collision to be raised to an excited electronic state. (a) Calculate the average kinetic energy per atom in a gas sample at 298 K. (b) Calculate the energy difference between the n 5 1 and n 5 2 levels in hydrogen. (c) At what temperature is it possible to excite a hydrogen atom from the n 5 1 level to n 5 2 level by collision? [The average kinetic energy of 1 mole of an ideal gas is (3 2)RT.]

Calculate the energies needed to remove an electron from the n 5 1 state and the n 5 5 state in the Li21 ion. What is the wavelength (in nm) of the emitted photon in a transition from n 5 5 to n 5 1? The Rydberg constant for hydrogenlike ions is (2.18 3 10218 J)Z2 , where Z is the atomic number.

The de Broglie wavelength of an accelerating proton in the Large Hadron Collider is 2.5 3 10214 m. What is the kinetic energy (in joules) of the proton?

The minimum uncertainty in the position of a certain moving particle is equal to its de Broglie wavelength. If the speed of the particle is 1.2 3 105 m/s, what is the minimum uncertainty in its speed?

According to Einsteins special theory of relativity, the mass of a moving particle, mmoving, is related to its mass at rest, mrest, by the following equation mmoving 5 mrest B1 2 a u c b 2 where u and c are the speeds of the particle and light, respectively. (a) In particle accelerators, protons, electrons, and other charged particles are often accelerated to speeds close to the speed of light. Calculate the wavelength (in nm) of a proton moving at 50.0 percent the speed of light. The mass of a proton is 1.673 3 10227 kg. (b) Calculate the mass of a 6.0 3 1022 kg tennis ball moving at 63 m/s. Comment on your results.

The mathematical equation for studying the photoelectric effect is hn 5 W 1 1 2meu2 where n is the frequency of light shining on the metal, W is the work function, and me and u are the mass and speed of the ejected electron. In an experiment, a student found that a maximum wavelength of 351 nm is needed to just dislodge electrons from a zinc metal surface. Calculate the speed (in m/s) of an ejected electron when she employed light with a wavelength of 313 nm.

In the beginning of the twentieth century, some scientists thought that a nucleus may contain both electrons and protons. Use the Heisenberg uncertainty principle to show that an electron cannot be confined within a nucleus. Repeat the calculation for a proton. Comment on your results. Assume the radius of a nucleus to be 1.0 3 10215 m. The masses of an electron and a proton are 9.109 3 10231 kg and 1.673 3 10227 kg, respectively. (Hint: Treat the diameter of the nucleus as the uncertainty in position.)

Blackbody radiation is the term used to describe the dependence of the radiation energy emitted by an object on wavelength at a certain temperature. Planck proposed the quantum theory to account for this dependence. Shown in the figure is a plot of the radiation energy emitted by our sun versus wavelength. This curve is characteristic of the temperature at the surface of the sun. At a higher temperature, the curve has a similar shape but the maximum will shift to a shorter wavelength. What does this curve reveal about two consequences of great biological significance on Earth? Solar radiation energy (nm) 0 500 1000

All molecules undergo vibrational motions. Quantum mechanical treatment shows that the vibrational energy, Evib, of a diatomic molecule like HCl is given by Evib 5 an 1 1 2 b hn where n is a quantum number given by n 5 0, 1, 2, 3, . . . and n is the fundamental frequency of vibration. (a) Sketch the first three vibrational energy levels for HCl. (b) Calculate the energy required to excite a HCl molecule from the ground level to the first excited level. The fundamental frequency of vibration for HCl is 8.66 3 1013 s21 . (c) The fact that the lowest vibrational energy in the ground level is not zero but equal to 1 2hn means that molecules will vibrate at all temperatures, including the absolute zero. Use the Heisenberg uncertainty principle to justify this prediction. (Hint: Consider a nonvibrating molecule and predict the uncertainty in the momentum and hence the uncertainty in the position.)

The wave function for the 2s orbital in the hydrogen atom is 2s 5 1 22a3 0 a1 2 2 be2y2 where a0 is the value of the radius of the first Bohr orbit, equal to 0.529 nm, is Z(r/a0), and r is the distance from the nucleus in meters. Calculate the location of the node of the 2s wave function from the nucleus.

A student placed a large unwrapped chocolate bar in a microwave oven without a rotating glass plate. After turning the oven on for less than a minute, she noticed there were evenly spaced dents (due to melting) about 6 cm apart. Based on her observations, calculate the speed of light given that the microwave frequency is 2.45 GHz. (Hint: The energy of a wave is proportional to the square of its amplitude.)

The wave properties of matter can generally be ignored for macroscopic objects such as tennis balls; however, wave properties have been measured at the fringe of detection for some very large molecules. For example, wave patterns were detected for C60(C12F25)8 molecules moving at a velocity of 63 m/s. (a) Calculate the wavelength of a C60(C12F25)8 molecule moving at this velocity. (b) How does the wavelength compare to the size of the molecule given that its diameter is roughly 3000 pm?

Atoms of an element have only two accessible excited states. In an emission experiment, however, three spectral lines were observed. Explain. Write an equation relating the shortest wavelength to the other two wavelengths.

According to Wiens law, the wavelength of maximum intensity in blackbody radiation, max, is given by max 5 b T where b is a constant (2.898 3 106 nm ? K) and T is the temperature of the radiating body in kelvins. (a) Estimate the temperature at the surface of the sun. (b) How are astronomers able to determine the temperature of stars in general? (See Problem 7.150 for a definition of blackbody radiation.)

Only a fraction of the electrical energy supplied to an incandescent-tungsten lightbulb is converted to visible light. The rest of the energy shows up as infrared radiation (that is, heat). A 60-W lightbulb converts about 15.0 percent of the energy supplied to it into visible light. Roughly how many photons are emitted by the lightbulb per second? (1 W 5 1 J/s.)

Photosynthesis makes use of photons of visible light to bring about chemical changes. Explain why heat energy in the form of infrared photons is ineffective for photosynthesis. (Hint: Typical chemical bond energies are 200 kJ/mol or greater.)

A typical red laser pointer has a power of 5 mW. How long would it take a red laser pointer to emit the same number of photons emitted by a 1-W blue laser in 1 s? (1 W 5 1 J/s.)

Referring to the Chemistry in Action essay on p. 312, estimate the wavelength of light that would be emitted by a cadmium selenide (CdSe) quantum dot with a diameter of 10 nm. Would the emitted light be visible to the human eye? The diameter and emission wavelength for a series of quantum dots are given here. Diameter (nm) 2.2 2.5 3.3 4.2 4.9 6.3 Wavelength (nm) 462 503 528 560 583 626

Problem 36E The nearest star to our sun is Proxima Centauri. at a distance of 4.3 light-years from the sun. A light-year is the distance that light travels in one year (365 days). How far away, in km. is Proxima Centauri from the sun?

Problem 68E According to the quantum-mechanical model for the hydrogen atom, which electron transition would produce light with the longer wavelength: 3p ? 2s or 4p ? 3p?

Problem 73E Ultraviolet radiation and radiation of shorter wavelengths can damage biological molecules because they carry enough energy to break bonds within the molecules. A typical carbon-carbon bond requires 348 kJ/mol to break. What is the longest wavelength of radiation with enough energy to break carbon-carbon bonds?

Problem 79E Ionization involves completely removing an electron from an atom. How much energy is required to ionize a hydrogen atom in its ground (or lowest energy) state? What wavelength of light contains enough energy in a single photon to ionize a hydrogen atom?

Problem 80E The energy required to ionize sodium is 496 kJ/mol. What minimum frequency of light is required to ionize sodium?

Suppose that in an alternate universe, the possible values of were the integer values from 0 to n (instead of 0 to n - 1 ). Assuming no other differences between this imaginary universe and ours, how many orbitals would exist in each level? a. n = 1 b. n = 2 c. n = 3

Suppose that, in an alternate universe, the possible values of ml are the integer values including 0 ranging from - -1 to + 1 (instead of simply - to + ). How many orbitals exist in each sublevel? a. s sublevel b. p sublevel c. d sublevel

Problem 83E An atomic emission spectrum of hydrogen shows three wavelengths: 1875 nm, 1282 nm. and 1093 nm. Assign these wavelengths to transitions in the hydrogen atom.

Problem 84E An atomic emission spectrum of hydrogen shows three wavelengths: 121.5 nm. 102.6 nm. and 97.23 nm. Assign these wavelengths to transitions in the hydrogen atom.

Problem 85E The binding energy of electrons in a metal is 193 kJ/mol. Find the threshold frequency of the metal.

In order for a thermonuclear fusion reaction of two deuterons (H+) to take place, the deuterons must collide each with a velocity of about 1 x 106 m/s. Find the wavelength of such a deuteron.

The speed of sound in air is 344 m/s at room temperature. The lowest frequency of a large organ pipe is \(30 \mathrm{\ s}^{-1}\) and the highest frequency of a piccolo is \(1.5 \times 10^{4} \mathrm{\ s}^{-1}\). Find the difference in wavelength between these two sounds.

The distance from Earth to the sun is 1.5 x 108 km. Find the number of crests in a light wave of frequency 1.0 x 1014 s-1 traveling from the sun to the Earth.

The iodine molecule can be photodissociated into iodine atoms in the gas phase with light of wavelengths shorter than about 792 nm. A 100.0 mL glass tube contains 55.7 mtorr of gaseous iodine at 25.0 °C . What minimum amount of light energy must be absorbed by the iodine in the tube to dissociate 15.0% of the molecules?

A laser produces 20.0 mW of red light. In 1.00 hr, the laser emits 2.29 x 1020 photons. What is the wavelength of the laser?

Problem 90E A 5.00 mL ampule of a 0.100 M solution of naphthalene in hexane is excited with a flash of light. The naphthalene emits 15.5 J of energy at an average wavelength of 349 nm. What percentage of the naphthalene molecules emitted a photon?

A particular laser consumes 150.0 watts of electrical power and produces a stream of 1.33 x 1019 1064 nm photons per second. What is the percent efficiency of the laser in converting electrical power to light?

An electron confined to a one-dimensional box has energy levels given by the equation En = n2h2 / 8 mL2 where n is a quantum number with possible values of 1, 2, 3,c , m is the mass of the particle, and L is the length of the box. a. Calculate the energies of the n = 1, n = 2, and n = 3 levels for an electron in a box with a length of 155 pm. b. Calculate the wavelength of light required to make a transition from n = 1 ? n = 2 and from n = 2 ? n = 3. In what region of the electromagnetic spectrum do these wavelengths lie?

The energy of a vibrating molecule is quantized much like the energy of an electron in the hydrogen atom. The energy levels of a vibrating molecule are given by the equation where n is a quantum number with possible values of 1, 2, ... , and v is the frequency of vibration. The vibration frequency of HCl is approximately 8.85 x 1013 s-1 . What minimum energy is required to excite a vibration in HCl? What wavelength of light is required to excite this vibration?

The wave functions for the 1s and 2s orbitals are as follows: \(1 s \quad \psi=(1 / \pi)^{1 / 2}\left(1 / a_{0}^{3 / 2}\right) \exp \left(-r / a_{0}\right)\) \(2 s \quad \psi=(1 / 32 \pi)^{1 / 2}\left(1 / a_{0}^{3 / 2}\right)\left(2-r / a_{0}\right) \exp \left(-r / a_{0}\right)\) where \(a_{0}\) is a constant (\(a_{0}=53 \ \mathrm{pm}\)) and r is the distance from the nucleus. Use a spreadsheet to make a plot of each of these wave functions for values of r ranging from 0 pm to 200 pm. Describe the differences in the plots and identify the node in the 2s wave function.

Before quantum mechanics was developed, Johannes Rydberg developed an equation that predicted the wavelengths () in the atomic spectrum of hydrogen: In this equation R is a constant and m and n are integers. Use the quantum-mechanical model for the hydrogen atom to derive the Rydberg equation.

Find the velocity of an electron emitted by a metal whose threshold frequency is \(2.25\times10^{14}\mathrm{\ s}^{-1}\) when it is exposed to visible light of wavelength \(5.00\times10^{-7}\mathrm{\ m}\).

Water is exposed to infrared radiation of wavelength 2.8 x 10-4 cm. Assume that all the radiation is absorbed and converted to heat. How many photons are required to raise the temperature of 2.0 g of water by 2.0 K?

The 2005 Nobel Prize in physics was given, in part, to scientists who had made ultrashort pulses of light. These pulses are important in making measurements involving very short time periods. One challenge in making such pulses is the uncertainty principle, which can be stated with respect to energy and time as h/4. What is the energy uncertainty () associated with a short pulse of laser light that lasts for only 5.0 femtoseconds (fs)? Suppose the low energy end of the pulse had a wavelength of 722 nm. What is the wavelength of the high energy end of the pulse that is limited only by the uncertainty principle?

A metal whose threshold frequency is 6.71 x 1014 s-1 emits an electron with a velocity of 6.95 x 105 m/s when radiation of 1.01 x 1015 s-1 strikes the metal. Calculate the mass of the electron.

Problem 101E Find the longest wavelength of a wave that can travel around in a circular orbit of radius 1.8 m.

The heat of fusion of ice is 6.00 kJ/mol. Find the number of photons of wavelength = 6.42 x 10-6m that must be absorbed to melt 1.00 g of ice.

Problem 103E Explain the difference between the Bohr model for the hydrogen atom and the quantum-mechanical model. Is the Bohr model consistent with Heisenberg s uncertainty principle?

Problem 104E The light emitted from one of the following electronic transitions ( n = 4 ? n = 3 or n = 3 ? n = 2) in the hydrogen atom causes the photoelectric effect in a particular metal while light from the other transition does not. Which transition causes the photoelectric effect and why?

Problem 106E Which transition in the hydrogen atom will result in emitted light with the longest wavelength? a. n = 4 ? n = 3 b. n = 2 ? n = 1 c. n = 3 ? n = 2

Problem 105E Determine whether an interference pattern is observed on the other side of the slits in each experiment. a. An electron beam is aimed at two closely spaced slits. The beam is attenuated to produce only one electron per minute. b. An electron beam is aimed at two closely spaced slits. A light beam is placed at each slit to determine when an electron goes through the slit. c. A high-intensity light beam is aimed at two closely spaced slits. d. A gun is fired at a solid wall containing two closely spaced slits. (Will the bullets that pass through the slits form an interference pattern on the other side of the solid wall?)

Does Barbara Ehrenreich seem to be exaggerating the workplace as she describes it in this selection? If you have worked in a restaurant, does her description of the environment match your experience?

What is Ehrenreichs attitude toward her coworkers? Does she appreciate them? Is she condescending? How do you react to her observations?

Early in the selection, as Ehrenreich pays bills left over from her real life, she reflects, [My] old life is beginning to look exceedingly strange (para. 8). At the end, she asks, So why didnt I intervene [with George]? (para. 18). Does the experience of serving in Florida change Ehrenreich? Cite specific passages to support your response.

According to Ehrenreich, who is to blame for the situation of those who work at low-paying jobs in restaurants? Are there heroes and villains, or does the workplace itself change the people who are part of it?

Overall, what is your attitude toward Ehrenreich and her method of research? Does choosing to live as one of the working poor for a short time as a kind of visitor or tourist give her an accurate picture of their lives? Explain whether you find her presentation of them respectful, convincing, sympathetic, patronizing, superficial, or some combination of these. Cite specific passages.

Ehrenreichs essay delivers strong implications about the U.S. economy. What is the relationship between the macroeconomy and the microeconomy in the essay? Which is more prominent? Identify places where she addresses each. What implications does her essay make about each?

Discuss specific instances of humor in this selection. Is it primarily ironic humor? Aggressively sarcastic? Affectionately amusing? Cite specific passages in your response

What elements of fiction does Ehrenreich employ? Consider such elements as figurative language, dialogue, narrative commentary, and description of people and settings

In this selection, Ehrenreich does not state a thesis or indicate directly what her purpose is; instead, she works by inference and implication. What is her purpose? State it directly in a sentence that begins, In this selection, Ehrenreich . . .

How does Ehrenreich establish her ethos in this selection? What part does her relationship with George play in her appeal to ethos?

Who is Ehrenreichs audience? Base your answer on the tone you detect in specific passages.

Paragraph 30 concludes, But none of this damage touches the best part of yourself. What, as implied by Crawford, is the best part of yourself? Do you agree?

How effective is the rhetorical question that concludes paragraph 36?

Crawford concludes that the economy will be improved by enlightened selfinterest (para. 39). Do you agree with his assessment?

In an interview about his book Shop Class as Soulcraft: An Inquiry into the Value of Work, Crawford has said,

Identify the simple sentences in the following selection from In the Strawberry Fields by Eric Schlosser. The few remaining labor camps for single men are grim places. I toured one that was a group of whitewashed buildings surrounded by chain-link fences and barbed wire. Desolate except for a rosebush in front of the managers office, it looked like a holding pen or an old minimum-security prison. A nearby camp was reputed to be one of the best of its kind. Inside the barracks, the walls were freshly painted and the concrete floor was clean. A typical room was roughly twelve feet by ten feet, unheated, and occupied by four men. Sheets of plywood separated the steel cots. For $80 a week, a price far too high for most migrants, you got a bed and two meals a day. Ive seen nicer horse barns. Nevertheless, the labor camps are often preferable to the alternatives. When migrants stay in residential neighborhoods, they must pool their resources. In Watsonville three to four families will share a small house, seven or eight people to a room. Migrants routinely pay $100 to $200 a month to sleep in a garage with anywhere from four to ten other people. A survey of garages in Soledad found 1,500 inhabitants a number roughly equal to one-eighth of the towns official population. At the peak of the harvest the housing shortage becomes acute. Migrants at the labor camps sometimes pay to sleep in parked cars. The newest migrant workers, who lack family in the area and havent yet learned the ropes, often sleep outdoors in the wooded sections of Prunedale, trespassing, moving to a different hiding place each night. On hillsides above the Salinas Valley, hundreds of strawberry pickers have been found living in caves.

Revise the selection in Exercise 1 by turning it into a series of short simple sentences. Then revise it again to eliminate the simple sentences entirely by turning every sentence into a compound, complex, or compound-complex sentence. How do your revisions change the effect? Read the original excerpt; then read your revisions aloud, and listen to the difference.

Identify the short simple sentences and fragments in the following passage from Shopping and Other Spiritual Adventures in America Today by Phyllis Rose. Discuss their effect. Someone told me about a Soviet migr who practices English by declaiming, at random, sentences that catch his fancy. One of his favorites is, Fifty percent off all items today only. Refugees from Communist countries appreciate our supermarkets and discount department stores for the wonders they are. An Eastern European scientist visiting Middletown wept when she first saw the meat counter at Waldbaums. On the other hand, before her year in America was up, her pleasure turned sour. She wanted everything she saw. Her approach to consumer goods was insufficiently abstract, too materialistic. We Americans are beyond a simple, possessive materialism. Were used to abundance and the possibility of possessing things. The things, and the possibility of possessing them, will still be there next week, next year. So today we can walk the aisles calmly. It is a misunderstanding of the American retail store to think we go there necessarily to buy. Some of us shop. Theres a difference. Shopping has many purposes, the least interesting of which is to acquire new articles. We shop to cheer ourselves up. We shop to practice decision-making. We shop to be useful and productive members of our class and society. We shop to remind ourselves how much is available to us. We shop to remind ourselves how much is to be striven for. We shop to assert our superiority to the material objects that spread themselves before us. Shoppings function as a form of therapy is widely appreciated. You dont really need, lets say, another sweater. You need the feeling of power that comes with buying or not buying it. You need the feeling that someone wants something you have even if its just your money. To get the bene fit of shopping, you neednt actually purchase the sweater, any more than you have to marry every man you flirt with. In fact, window-shopping, like flirting, can be more rewarding, the same high without the distressing commitment, the material encumbrance. The purest form of shopping is provided by garage sales. A connoisseur goes out with no goal in mind, open to whatever may come his or her way, secure that it will cost very little. Minimum expense, maximum experience. Perfect shopping.

Find six examples of short simple sentences or fragments in the selections presented in this chapter. Explain their effect in the context of the paragraphs in which you find them.

What are complementary properties? How does electron diffraction demonstrate the complementarity of the wave nature and particle nature of the electron?

Explain Heisenbergs uncertainty principle. What paradox is at least partially solved by the uncertainty principle?

What is a trajectory? What kind of information do you need to predict the trajectory of a particle?

Why does the uncertainty principle make it impossible to predict a trajectory for the electron?

Newtons laws of motion are deterministic . Explain this statement.

An electron behaves in ways that are at least partially indeterminate. Explain this statement.

What is a probability distribution map?

For each solution to the Schrdinger equation, what can be precisely specified: the electrons energy or its position? Explain.

What is a quantum-mechanical orbital?

What is the Schrodinger equation? What is a wave function? How is a wave function related to an orbital?

What are the possible values of the principal quantum number n ? What does the principal quantum number determine?

What are the possible values of the angular momentum quantum number l ? What does the angular momentum quantum number determine?

What are the possible values of the magnetic quantum number m l ? What does the magnetic quantum number determine?

List all the orbitals in each principal level. Specify the three quantum numbers for each orbital. a. n = 1 b. n = 2 c. n = 3 d. n = 4

Explain the difference between a plot showing the probability density for an orbital and one showing the radial distribution function.

Make sketches of the general shapes of the s, p, and d orbitals.

List the four different sublevels. Given that only a maximum of two electrons can occupy an orbital, determine the maximum number of electrons that can exist in each sublevel.

Why are atoms usually portrayed as spheres when most orbitals are not spherically shaped?

The distance from the sun to Earth is 1.496 * 108 km. How long does it take light to travel from the sun to Earth?

The nearest star to our sun is Proxima Centauri, at a distance of 4.3 light-years from the sun. A light-year is the distance that light travels in one year (365 days). How far away, in km, is Proxima Centauri from the sun?

List these types of electromagnetic radiation in order of (i) increasing wavelength and (ii) increasing energy per photon: a. radio waves b. microwaves c. infrared radiation d. ultraviolet radiation

List these types of electromagnetic radiation in order of (i) increasing frequency and (ii) decreasing energy per photon: a. gamma rays b. radio waves c. microwaves d. visible light

Calculate the frequency of each wavelength of electromagnetic radiation: a. 632.8 nm (wavelength of red light from heliumneon laser) b. 503 nm (wavelength of maximum solar radiation) c. 0.052 nm (a wavelength contained in medical X-rays)

Calculate the wavelength of each frequency of electromagnetic radiation: a. 100.2 MHz (typical frequency for FM radio broadcasting) b. 1070 kHz (typical frequency for AM radio broadcasting) (assume four signifi cant fi gures) c. 835.6 MHz (common frequency used for cell phone communication)

Calculate the energy of a photon of electromagnetic radiation at each of the wavelengths indicated in Problem 39

Calculate the energy of a photon of electromagnetic radiation at each of the wavelengths indicated in Problem 39

A laser pulse with wavelength 532 nm contains 3.85 mJ of energy. How many photons are in the laser pulse?

A heat lamp produces 32.8 watts of power at a wavelength of 6.5 mm. How many photons are emitted per second? 11 watt = 1 J>s2

Determine the energy of 1 mol of photons for each kind of light. (Assume three significant figures.) a. infrared radiation (1500 nm) b. visible light (500 nm) c. ultraviolet radiation (150 nm)

How much energy is contained in 1 mol of each? a. X-ray photons with a wavelength of 0.135 nm b. g -ray photons with a wavelength of 2.15 * 10-5 nm.

Sketch the interference pattern that results from the diffraction of electrons passing through two closely spaced slits.

What happens to the interference pattern described in Problem 47 if the rate of electrons going through the slits is decreased to one electron per hour? What happens to the pattern if we try to determine which slit the electron goes through by using a laser placed directly behind the slits?

The resolution limit of a microscope is roughly equal to the wavelength of light used in producing the image. Electron microscopes use an electron beam (in place of photons) to produce much higher resolution images, about 0.20 nm in modern instruments. Assuming that the resolution of an electron microscope is equal to the de Broglie wavelength of the electrons used, to what speed must the electrons be accelerated to obtain a resolution of 0.20 nm?

The smallest atoms can themselves exhibit quantum- mechanical behavior. Calculate the de Broglie wavelength (in pm) of a hydrogen atom traveling at 475 m>s.

What is the de Broglie wavelength of an electron traveling at 1.35 * 105 m>s?

A proton in a linear accelerator has a de Broglie wavelength of 122 pm. What is the speed of the proton?

Calculate the de Broglie wavelength of a 143 g baseball traveling at 95 mph. Why is the wave nature of matter not important for a baseball?

A 0.22-caliber handgun fires a 27 g bullet at a velocity of 765 m>s. Calculate the de Broglie wavelength of the bullet. Is the wave nature of matter significant for bullets?

An electron has an uncertainty in its position of 552 pm. What is the uncertainty in its velocity?

An electron traveling at 3.7 * 105 m>s has an uncertainty in its velocity of 1.88 * 105 m>s. What is the uncertainty in its position?

Which electron is, on average, closer to the nucleus: an electron in a 2 s orbital or an electron in a 3 s orbital?

Which electron is, on average, further from the nucleus: an electron in a 3p orbital or an electron in a 4 p orbital?

What are the possible values of l for each value of n ? a. 1 b. 2 c. 3 d. 4

What are the possible values of ml for each value of l ? a. 0 b. 1 c. 2 d. 3

Which set of quantum numbers cannot occur together to specify an orbital? a. n = 2, l = 1, ml = -1 b. n = 3, l = 2, ml = 0 c. n = 3, l = 3, ml = 2 d. n = 4, l = 3, ml = 0

Which combinations of n and l represent real orbitals and which do not exist? (a) 1s (b) 2p (c) 4s (d) 2d

Sketch the 1s and 2p orbitals. How would the 2s and 3p orbitals differ from the 1s and 2p orbitals?

Sketch the 3 d orbitals. How would the 4 d orbitals differ from the 3 d orbitals?

An electron in a hydrogen atom is excited with electrical energy to an excited state with n = 2. The atom then emits a photon. What is the value of n for the electron following the emission?

Determine whether each transition in the hydrogen atom corresponds to absorption or emission of energy. a. n = 3 h n = 1 b. n = 2 h n = 4 c. n = 4 h n = 3

According to the quantum-mechanical model for the hydrogen atom, which electron transitions would produce light with the longer wavelength: 2p h 1s or 3p h 1s?

According to the quantum-mechanical model for the hydrogen atom, which electron transition would produce light with the longer wavelength: 3p h 2s or 4p h 3p?

Calculate the wavelength of the light emitted when an electron in a hydrogen atom makes each transition and indicate the region of the electromagnetic spectrum (infrared, visible, ultraviolet, etc.) where the light is found. a. n = 2 h n = 1 b. n = 3 h n = 1 c. n = 4 h n = 2 d. n = 5 h n = 2

Calculate the frequency of the light emitted when an electron in a hydrogen atom makes each transition: a. n = 4 h n = 3 b. n = 5 h n = 1 c. n = 5 h n = 4 d. n = 6 h n = 5

An electron in the n = 7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 397 nm. What is the value of n for the level to which the electron relaxed?

An electron in a hydrogen atom relaxes to the n = 4 level, emitting light of 114 THz. What is the value of n for the level in which the electron originated?

Ultraviolet radiation and radiation of shorter wavelengths can damage biological molecules because they carry enough energy to break bonds within the molecules. A typical carboncarbon bond requires 348 kJ>mol to break. What is the longest wavelength of radiation with enough energy to break carboncarbon bonds?

The human eye contains a molecule called 11- cis -retinal that changes shape when struck with light of sufficient energy. The change in shape triggers a series of events that results in an electrical signal being sent to the brain. The minimum energy required to change the conformation of 11- cis -retinal within the eye is about 164 kJ>mol. Calculate the longest wavelength visible to the human eye.

An argon ion laser puts out 5.0 W of continuous power at a wavelength of 532 nm. The diameter of the laser beam is 5.5 mm. If the laser is pointed toward a pinhole with a diameter of 1.2 mm, how many photons will travel through the pinhole per second? Assume that the light intensity is equally distributed throughout the entire cross-sectional area of the beam. ( 1 W = 1 J>s )

A green leaf has a surface area of 2.50 cm2 . If solar radiation is 1000 W>m2 , how many photons strike the leaf every second? Assume three significant figures and an average wavelength of 504 nm for solar radiation.

In a technique used for surface analysis called Auger electron spectroscopy (AES), electrons are accelerated toward a metal surface. These electrons cause the emissions of secondary electrons called auger electronsfrom the metal surface. The kinetic energy of the auger electrons depends on the composition of the surface. The presence of oxygen atoms on the surface results in auger electrons with a kinetic energy of approximately 506 eV. What is the de Broglie wavelength of one of these electrons? 3KE = 1 2mv2 ; 1 electron volt 1eV2 = 1.602 * 10-19 J4

An X-ray photon of wavelength 0.989 nm strikes a surface. The emitted electron has a kinetic energy of 969 eV. What is the binding energy of the electron in kJ>mol? 3KE = 1 2 mv2 ; 1 electron volt 1eV2 = 1.602 * 10-19 J4

Ionization involves completely removing an electron from an atom. How much energy is required to ionize a hydrogen atom in its ground (or lowest energy) state? What wavelength of light contains enough energy in a single photon to ionize a hydrogen atom?

The energy required to ionize sodium is 496 kJ>mol. What minimum frequency of light is required to ionize sodium?

Suppose that in an alternate universe, the possible values of l were the integer values from 0 to n (instead of 0 to n - 1 ). Assuming no other differences between this imaginary universe and ours, how many orbitals would exist in each level? a. n = 1 b. n = 2 c. n = 3

Suppose that, in an alternate universe, the possible values of ml are the integer values including 0 ranging from -l -1 to l + 1 (instead of simply -l to +l ). How many orbitals exist in each sublevel? a. s sublevel b. p sublevel c. d sublevel

An atomic emission spectrum of hydrogen shows three wavelengths: 1875 nm, 1282 nm, and 1093 nm. Assign these wavelengths to transitions in the hydrogen atom.

An atomic emission spectrum of hydrogen shows three wavelengths: 121.5 nm, 102.6 nm, and 97.23 nm. Assign these wavelengths to transitions in the hydrogen atom.

The binding energy of electrons in a metal is 193 kJ>mol. Find the threshold frequency of the metal.

In order for a thermonuclear fusion reaction of two deuterons 12 1H+ 2 to take place, the deuterons must collide each with a velocity of about 1 * 106 m>s. Find the wavelength of such a deuteron.

The speed of sound in air is 344 m>s at room temperature. The lowest frequency of a large organ pipe is 30 s-1 and the highest frequency of a piccolo is 1.5 * 104 s-1 . Find the difference in wavelength between these two sounds.

The distance from Earth to the sun is 1.5 * 108 km. Find the number of crests in a light wave of frequency 1.0 * 1014 s-1 traveling from the sun to the Earth.

The iodine molecule can be photodissociated into iodine atoms in the gas phase with light of wavelengths shorter than about 792 nm. A 100.0 mL glass tube contains 55.7 mtorr of gaseous iodine at 25.0 C . What minimum amount of light energy must be absorbed by the iodine in the tube to dissociate 15.0% of the molecules?

A 5.00 mL ampule of a 0.100 M solution of naphthalene in hexane is excited with a flash of light. The naphthalene emits 15.5 J of energy at an average wavelength of 349 nm. What percentage of the naphthalene molecules emitted a photon?

A laser produces 20.0 mW of red light. In 1.00 hr, the laser emits 2.29 * 1020 photons. What is the wavelength of the laser?

A particular laser consumes 150.0 watts of electrical power and produces a stream of 1.33 * 1019 1064 nm photons per second. What is the percent efficiency of the laser in converting electrical power to light.

An electron confined to a one-dimensional box has energy levels given by the equation En = n2 h2 > 8 mL2 where n is a quantum number with possible values of 1, 2, 3,c , m is the mass of the particle, and L is the length of the box. a. Calculate the energies of the n = 1, n = 2, and n = 3 levels for an electron in a box with a length of 155 pm. b. Calculate the wavelength of light required to make a transition from n = 1 h n = 2 and from n = 2 h n = 3. In what region of the electromagnetic spectrum do these wavelengths lie?

The energy of a vibrating molecule is quantized much like the energy of an electron in the hydrogen atom. The energy levels of a vibrating molecule are given by the equation En = an + 1 2 bhn where n is a quantum number with possible values of 1, 2,c , and n is the frequency of vibration. The vibration frequency of HCl is approximately 8.85 * 1013 s-1 . What minimum energy is required to excite a vibration in HCl? What wavelength of light is required to excite this vibration?

The wave functions for the 1 s and 2 s orbitals are as follows: 1s c = 11>p21>2 11 > a3>2 0 2 exp1 -r> a02 2s c = 11 > 32p21>2 11 > a3>2 0 2 12-r> a02 exp1 -r> a02 where a0 is a constant 1a0 = 53 pm2 and r is the distance from the nucleus. Use a spreadsheet to make a plot of each of these wave functions for values of r ranging from 0 pm to 200 pm. Describe the differences in the plots and identify the node in the 2 s wave function.

Before quantum mechanics was developed, Johannes Rydberg developed an equation that predicted the wavelengths 1l2 in the atomic spectrum of hydrogen: 1>l = R11 >m2 - 1 > n2 2 In this equation R is a constant and m and n are integers. Use the quantum-mechanical model for the hydrogen atom to derive the Rydberg equation.

Find the velocity of an electron emitted by a metal whose threshold frequency is \(2.25\times10^{14}\mathrm{\ s}^{-1}\) when it is exposed to visible light of wavelength \(5.00 \times 10^{-7} \mathrm{\ m}\).

Water is exposed to infrared radiation of wavelength 2.8 * 10-4 cm. Assume that all the radiation is absorbed and converted to heat. How many photons are required to raise the temperature of 2.0 g of water by 2.0 K?

The 2005 Nobel Prize in physics was given, in part, to scientists who had made ultrashort pulses of light. These pulses are important in making measurements involving very short time periods. One challenge in making such pulses is the uncertainty principle, which can be stated with respect to energy and time as E # t h>4p. What is the energy uncertainty ( E ) associated with a short pulse of laser light that lasts for only 5.0 femtoseconds (fs)? Suppose the low energy end of the pulse had a wavelength of 722 nm. What is the wavelength of the high energy end of the pulse that is limited only by the uncertainty principle? 1

A metal whose threshold frequency is 6.71 * 1014 s-1 emits an electron with a velocity of 6.95 * 105 m>s when radiation of 1.01 * 1015 s-1 strikes the metal. Calculate the mass of the electron.

Find the longest wavelength of a wave that can travel around in a circular orbit of radius 1.8 m.

The heat of fusion of ice is 6.00 kJ>mol. Find the number of photons of wavelength = 6.42 * 10-6m that must be absorbed to melt 1.00 g of ice.

Explain the difference between the Bohr model for the hydrogen atom and the quantum-mechanical model. Is the Bohr model consistent with Heisenbergs uncertainty principle?

The light emitted from one of the following electronic transitions ( n = 4 h n = 3 or n = 3 h n = 2 ) in the hydrogen atom causes the photoelectric effect in a particular metal while light from the other transition does not. Which transition causes the photoelectric effect and why?

Determine whether an interference pattern is observed on the other side of the slits in each experiment. a. An electron beam is aimed at two closely spaced slits. The beam is attenuated to produce only one electron per minute. b. An electron beam is aimed at two closely spaced slits. A light beam is placed at each slit to determine when an electron goes through the slit. c. A high-intensity light beam is aimed at two closely spaced slits. d. A gun is fi red at a solid wall containing two closely spaced slits. (Will the bullets that pass through the slits form an interference pattern on the other side of the solid wall?)

Which transition in the hydrogen atom will result in emitted light with the longest wavelength? a. n = 4 h n = 3 b. n = 2 h n = 1 c. n = 3 h n = 2