Solution: An electron in a hydrogen atom is excited from the

What is a wave? Explain the following terms associated with waves: wavelength, frequency, amplitude.

What are the units for wavelength and frequency of electromagnetic waves? What is the speed of light in meters per second and miles per hour?

List the types of electromagnetic radiation, starting with the radiation having the longest wavelength and ending with the radiation having the shortest wavelength.

Give the high and low wavelength values that define the visible region of the electromagnetic spectrum.

Briefly explain Plancks quantum theory and explain what a quantum is. What are the units for Plancks constant?

Give two everyday examples that illustrate the concept of quantization.

(a) What is the wavelength (in nanometers) of light having a frequency of 8.6 3 1013 Hz? (b) What is the frequency (in Hz) of light having a wavelength of 566 nm?

(a) What is the frequency of light having a wavelength of 456 nm? (b) What is the wavelength (in nanometers) of radiation having a frequency of 2.45 3 109 Hz? (This is the type of radiation used in microwave ovens.)

The average distance between Mars and Earth is about 1.3 3 108 miles. How long would it take TV pictures transmitted from the Viking space vehicle on Mars surface to reach Earth? (1 mile 5 1.61 km.)

How many minutes would it take a radio wave to travel from the planet Venus to Earth? (Average distance from Venus to Earth is 28 million miles.)

The SI unit of time is the second, which is defined as 9,192,631,770 cycles of radiation associated with a certain emission process in the cesium atom. Calculate the wavelength of this radiation (to three significant figures). In which region of the electromagnetic spectrum is this wavelength found?

The SI unit of length is the meter, which is defined as the length equal to 1,650,763.73 wavelengths of the light emitted by a particular energy transition in krypton atoms. Calculate the frequency of the light to three significant figures.

What are photons? What role did Einsteins explanation of the photoelectric effect play in the development of the particle-wave interpretation of the nature of electromagnetic radiation?

Consider the plots shown here for the photoelectric effect of two different metals A (green line) and B (red line). (a) Which metal has a greater work function? (b) What does the slope of the lines tell us? Kinetic energy

A photon has a wavelength of 624 nm. Calculate the energy of the photon in joules.

The blue color of the sky results from the scattering of sunlight by air molecules. The blue light has a frequency of about 7.5 3 1014 Hz. (a) Calculate the wavelength, in nm, associated with this radiation, and (b) calculate the energy, in joules, of a single photon associated with this frequency.

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