How fast must a 56.5-g tennis ball travel to have a de Broglie wavelength equal to that

In what ways are microwave and ultraviolet radiation the same? In what ways are they different?

Consider the following types of electromagnetic radiation: (1) Microwave (2) Ultraviolet (3) Radio waves (4) Infrared (5) X-ray (6) Visible (a) Arrange them in order of increasing wavelength. (b) Arrange them in order of increasing frequency. (c) Arrange them in order of increasing energy.

Define each of the following wave phenomena, and give an example of where each occurs: (a) refraction; (b) diffraction; (c) dispersion; (d) interference.

In the 17th century, Newton proposed that light was a stream of particles. The wave-particle debate continued for over 250 years until Planck and Einstein presented their ideas. Give two pieces of evidence for the wave model and two for the particle model.

Portions of electromagnetic waves A, B, and C are represented by the following (not drawn to scale): +1 A B C Rank them in order of (a) increasing frequency; (b) increasing energy; (c) increasing amplitude. (d) If wave B just barely fails to cause a current when shining on a metal, is wave A or C more likely to do so? (e) If wave B represents visible radiation, is wave A or C more likely to be IR radiation?

What new idea about light did Einstein use to explain the photoelectric effect? Why does the photoelectric effect exhibit a threshold frequency but not a time lag?

An AM station broadcasts rock music at 950 on your radio dial. Units for AM frequencies are given in kilohertz (kHz). Find the wavelength of the stations radio waves in meters (m), nanometers (nm), and angstroms ().

An FM station broadcasts music at 93.5 MHz (megahertz, or 106 Hz). Find the wavelength (in m, nm, and ) of these waves.

A radio wave has a frequency of 3.831010 Hz. What is the energy (in J) of one photon of this radiation?

An x-ray has a wavelength of 1.3 . Calculate the energy (in J) of one photon of this radiation.

Rank these photons in terms of increasing energy: (a) blue (l 5 453 nm); (b) red (l 5 660 nm); (c) yellow (l 5 595 nm).

Rank these photons in terms of decreasing energy: (a) IR (n 5 6.531013 s21); (b) microwave (n 5 9.831011 s21); (c) UV (n 5 8.031015 s21).

Police often monitor traffic with K-band radar guns, which operate in the microwave region at 22.235 GHz (1 GHz 5 109 Hz). Find the wavelength (in nm and ) of this radiation.

Covalent bonds in a molecule absorb radiation in the IR region and vibrate at characteristic frequencies. (a) The CiO bond absorbs radiation of wavelength 9.6 mm. What frequency (in s21) corresponds to that wavelength? (b) The HiCl bond has a frequency of vibration of 8.65231013 Hz. What wavelength (in mm) corresponds to that frequency?

Cobalt-60 is a radioactive isotope used to treat cancers. A gamma ray emitted by this isotope has an energy of 1.33 MeV (million electron volts; 1 eV 5 1.602310219 J). What is the frequency (in Hz) and the wavelength (in m) of this gamma ray?

(a) Ozone formation in the upper atmosphere starts when oxygen molecules absorb UV radiation of wavelengths # 242 nm. Find the frequency and energy of the least energetic of these photons. (b) Ozone absorbs radiation of wavelengths 22002900 , thus protecting organisms from this radiation. Find the frequency and energy of the most energetic of these photons.

How is n1 in the Rydberg equation (Equation 7.4) related to the quantum number n in the Bohr model?

What key assumption of Bohrs model would a Solar System model of the atom violate? What was the theoretical basis for this assumption?

Distinguish between an absorption spectrum and an emission spectrum. With which did Bohr work?

Which of these electron transitions correspond to absorption of energy and which to emission? (a) n 5 2 to n 5 4 (b) n 5 3 to n 5 1 (c) n 5 5 to n 5 2 (d) n 5 3 to n 5 4

Why couldnt the Bohr model predict spectra for atoms other than hydrogen?

The H atom and the Be31 ion each have one electron. Would you expect the Bohr model to predict their spectra accurately? Would you expect their spectra to be identical? Explain.

Use the Rydberg equation to find the wavelength (in nm) of the photon emitted when an electron in an H atom undergoes a transition from n 5 5 to n 5 2.

Use the Rydberg equation to find the wavelength (in ) of the photon absorbed when an electron in an H atom undergoes a transition from n 5 1 to n 5 3.

What is the wavelength (in nm) of the least energetic spectral line in the infrared series of the H atom?

What is the wavelength (in nm) of the least energetic spectral line in the visible series of the H atom?

Calculate the energy difference (DE) for the transition in Problem 7.23 for 1 mol of H atoms.

Calculate the energy difference (DE) for the transition in Problem 7.24 for 1 mol of H atoms.

Arrange the following H atom electron transitions in order of increasing frequency of the photon absorbed or emitted: (a) n 5 2 to n 5 4 (b) n 5 2 to n 5 1 (c) n 5 2 to n 5 5 (d) n 5 4 to n 5 3

Arrange the following H atom electron transitions in order of decreasing wavelength of the photon absorbed or emitted: (a) n 5 2 to n 5 ` (b) n 5 4 to n 5 20 (c) n 5 3 to n 5 10 (d) n 5 2 to n 5 1

The electron in a ground-state H atom absorbs a photon of wavelength 97.20 nm. To what energy level does it move?

An electron in the n 5 5 level of an H atom emits a photon of wavelength 1281 nm. To what energy level does it move?

In addition to continuous radiation, fluorescent lamps emit some visible lines from mercury. A prominent line has a wavelength of 436 nm. What is the energy (in J) of one photon of it?

A Bohr-model representation of the H atom is shown below with several electron transitions depicted by arrows: n = 1 2 3 A B C D E F 4 5 6 (a) Which transitions are absorptions and which are emissions? (b) Rank the emissions in terms of increasing energy. (c) Rank the absorptions in terms of increasing wavelength of light absorbed.

In what sense is the wave motion of a guitar string analogous to the motion of an electron in an atom?

What experimental support did de Broglies concept receive?

If particles have wavelike motion, why dont we observe that motion in the macroscopic world?

Why cant we overcome the uncertainty predicted by Heisenbergs principle by building more precise instruments to reduce the error in measurements below the h/4p limit?

A 232-lb fullback runs 40 yd at 19.8 6 0.1 mi/h. (a) What is his de Broglie wavelength (in meters)? (b) What is the uncertainty in his position?

An alpha particle (mass 5 6.6310224 g) emitted by a radium isotope travels at 3.43107 6 0.13107 mi/h. (a) What is its de Broglie wavelength (in meters)? (b) What is the uncertainty in its position?

How fast must a 56.5-g tennis ball travel to have a de Broglie wavelength equal to that of a photon of green light (5400 )?

How fast must a 142-g baseball travel to have a de Broglie wavelength equal to that of an x-ray photon with l 5 100. pm?

A sodium flame has a characteristic yellow color due to emissions of wavelength 589 nm. What is the mass equivalence of one photon with this wavelength (1 J 5 1 kg?m2/s2)?

A lithium flame has a characteristic red color due to emissions of wavelength 671 nm. What is the mass equivalence of 1 mol of photons with this wavelength (1 J 5 1 kg?m2/s2)?

What physical meaning is attributed to c2?

What does electron density in a tiny volume of space mean?

Explain what it means for the peak in the radial probability distribution plot for the n 5 1 level of an H atom to be at 0.529 . Is the probability of finding an electron at 0.529 from the nucleus greater for the 1s or the 2s orbital?

What feature of an orbital is related to each of the following? (a) Principal quantum number (n) (b) Angular momentum quantum number (l) (c) Magnetic quantum number (ml )

How many orbitals in an atom can have each of the following designations: (a) 1s; (b) 4d; (c) 3p; (d) n 5 3?

How many orbitals in an atom can have each of the following designations: (a) 5f; (b) 4p; (c) 5d; (d) n 5 2?

Give all possible ml values for orbitals that have each of the following: (a) l 5 2; (b) n 5 1; (c) n 5 4, l 5 3.

Give all possible ml values for orbitals that have each of the following: (a) l 5 3; (b) n 5 2; (c) n 5 6, l 5 1.

Draw 90% probability contours (with axes) for each of the following orbitals: (a) s; (b) px.

Draw 90% probability contours (with axes) for each of the following orbitals: (a) pz; (b) dxy.

For each of the following, give the sublevel designation, the allowable ml values, and the number of orbitals: (a) n 5 4, l 5 2 (b) n 5 5, l 5 1 (c) n 5 6, l 5 3

For each of the following, give the sublevel designation, the allowable ml values, and the number of orbitals: (a) n 5 2, l 5 0 (b) n 5 3, l 5 2 (c) n 5 5, l 5 1

For each of the following sublevels, give the n and l values and the number of orbitals: (a) 5s; (b) 3p; (c) 4f

For each of the following sublevels, give the n and l values and the number of orbitals: (a) 6g; (b) 4s; (c) 3d.

Are the following combinations allowed? If not, show two ways to correct them: (a) n 5 2; l 5 0; ml 5 21 (b) n 5 4; l 5 3; ml 5 21 (c) n 5 3; l 5 1; ml 5 0 (d) n 5 5; l 5 2; ml 5 13

Are the following combinations allowed? If not, show two ways to correct them: (a) n 5 1; l 5 0; ml 5 0 (b) n 5 2; l 5 2; ml 5 11 (c) n 5 7; l 5 1; ml 5 12 (d) n 5 3; l 5 1; ml 5 22

The orange color of carrots and orange peel is due mostly to b-carotene, an organic compound insoluble in water but soluble in benzene and chloroform. Describe an experiment to determine the concentration of b-carotene in the oil from orange peel.

The quantum-mechanical treatment of the H atom gives the energy, E, of the electron as a function of n: E 5 2 h2 8p2 mea0 2 n2 (n 5 1, 2, 3, . . .) where h is Plancks constant, me is the electron mass, and a0 is 52.92310212 m. (a) Write the expression in the form E 5 2(constant)(1/n2), evaluate the constant (in J), and compare it with the corresponding expression from Bohrs theory. (b) Use the expression from part (a) to find DE between n 5 2 and n 5 3. (c) Calculate the wavelength of the photon that corresponds to this energy change.

The photoelectric effect is illustrated in a plot of the kinetic energies of electrons ejected from the surface of potassium metal or silver metal at different frequencies of incident light. Kinetic energy Frequency K Ag (a) Why dont the lines begin at the origin? (b) Why dont the lines begin at the same point? (c) From which metal will light of shorter wavelength eject an electron? (d) Why are the slopes equal?

The optic nerve needs a minimum of 2.0310217 J of energy to trigger a series of impulses that eventually reach the brain. (a) How many photons of red light (700. nm) are needed? (b) How many photons of blue light (475 nm)?

One reason carbon monoxide (CO) is toxic is that it binds to the blood protein hemoglobin more strongly than oxygen does. The bond between hemoglobin and CO absorbs radiation of 1953 cm21. (The units are the reciprocal of the wavelength in centimeters.) Calculate the wavelength (in nm and ) and the frequency (in Hz) of the absorbed radiation.

A metal ion Mn1 has a single electron. The highest energy line in its emission spectrum has a frequency of 2.96131016 Hz. Identify the ion

Compare the wavelengths of an electron (mass 5 9.11310231 kg) and a proton (mass 5 1.67310227 kg), each having (a) a speed of 3.43106 m/s; (b) a kinetic energy of 2.7310215 J.

Five lines in the H atom spectrum have these wavelengths (in ): (a) 1212.7; (b) 4340.5; (c) 4861.3; (d) 6562.8; (e) 10,938. Three lines result from transitions to nfinal 5 2 (visible series). The other two result from transitions in different series, one with nfinal 5 1 and the other with nfinal 5 3. Identify ninitial for each line.

In his explanation of the threshold frequency in the photoelectric effect, Einstein reasoned that the absorbed photon must have a minimum energy to dislodge an electron from the metal surface. This energy is called the work function (f) of the metal. What is the longest wavelength of radiation (in nm) that could cause the photoelectric effect in each of these metals: (a) calcium, f 5 4.60310219 J; (b) titanium, f 5 6.94310219 J; (c) sodium, f 5 4.41310219 J?

Refractometry is based on the difference in the speed of light through a substance (v) and through a vacuum (c). In the procedure, light of known wavelength passes through a fixed thickness of the substance at a known temperature. The index of refraction equals c/v. Using yellow light (l 5 589 nm) at 208C, for example, the index of refraction of water is 1.33 and that of diamond is 2.42. Calculate the speed of light in (a) water and (b) diamond.

A laser (light amplification by stimulated emission of radiation) provides nearly monochromatic high-intensity light. Lasers are used in eye surgery, CD/DVD players, basic research, and many other areas. Some dye lasers can be tuned to emit a desired wavelength. Fill in the blanks in the following table of the properties of some common types of lasers: Type l (nm) n (s21) E (J) Color He-Ne 632.8 ? ? ? Ar ? 6.14831014 ? ? Ar-Kr ? ? 3.499310219 ? Dye 663.7 ? ? ?

The following combinations are not allowed. If n and ml are correct, change the l value to create an allowable combination: (a) n 5 3; l 5 0; ml 5 21 (b) n 5 3; l 5 3; ml 5 11 (c) n 5 7; l 5 2; ml 5 13 (d) n 5 4; l 5 1; ml 5 22

A ground-state H atom absorbs a photon of wavelength 94.91 nm, and its electron attains a higher energy level. The atom then emits two photons: one of wavelength 1281 nm to reach an intermediate energy level, and a second to return to the ground state. (a) What higher level did the electron reach? (b) What intermediate level did the electron reach? (c) What was the wavelength of the second photon emitted?

Ground-state ionization energies of some one-electron species are H 5 1.313103 kJ/mol He1 5 5.243103 kJ/mol Li21 5 1.183104 kJ/mol (a) Write a general expression for the ionization energy of any one-electron species. (b) Use your expression to calculate the ionization energy of B41. (c) What is the minimum wavelength required to remove the electron from the n 5 3 level of He1? (d) What is the minimum wavelength required to remove the electron from the n 5 2 level of Be31?

Use the relative size of the 3s orbital below to answer the following questions about orbitals AD. 3s A B C D (a) Which orbital has the highest value of n? (b) Which orbital(s) have a value of l 5 1? l 5 2? (c) How many other orbitals with the same value of n have the same shape as orbital B? Orbital C? (d) Which orbital has the highest energy? Lowest energy?

In the course of developing his model, Bohr arrived at the following formula for the radius of the electrons orbit: rn 5 n2h2e0/pmee2, where me is the electron mass, e is its charge, and e0 is a constant related to charge attraction in a vacuum. Given that me 5 9.109310231 kg, e 5 1.602310219 C, and e0 5 8.854310212 C2/J?m, calculate the following: (a) The radius of the first (n 5 1) orbit in the H atom (b) The radius of the tenth (n 5 10) orbit in the H atom

(a) Find the Bohr radius of an electron in the n 5 3 orbit of an H atom (see Problem 7.76). (b) What is the energy (in J) of the atom in (a)? (c) What is the energy of an Li21 ion with its electron in the n 5 3 orbit? (d) Why are the answers to (b) and (c) different?

Enormous numbers of microwave photons are needed to warm macroscopic samples of matter. A portion of soup containing 252 g of water is heated in a microwave oven from 20.8C to 988C, with radiation of wavelength 1.5531022 m. How many photons are absorbed by the water in the soup?

The quantum-mechanical treatment of the hydrogen atom gives this expression for the wave function, c, of the 1s orbital: 5 1 "p a 1 a0 b 3/2 e2r/a0 where r is the distance from the nucleus and a0 is 52.92 pm. The probability of finding the electron in a tiny volume at distance r from the nucleus is proportional to c2. The total probability of finding the electron at all points at distance r from the nucleus is proportional to 4pr2 c2 . Calculate the values (to three significant figures) of c, c2, and 4pr2c2 to fill in the following table and sketch a plot of each set of values versus r. Compare the latter two plots with those in Figure 7.17A, p. 311: r(pm) (pm23/2) 2 (pm23) 4r 22 (pm21) 0 50 100 200

Lines in one spectral series can overlap lines in another. (a) Does the range of wavelengths in the n1 5 1 series for the H atom overlap the range in the n1 5 2 series? (b) Does the range in the n1 5 3 series overlap the range in the n1 5 4 series? (c) How many lines in the n1 5 4 series lie in the range of the n1 5 5 series? (d) What does this overlap imply about the H atom line spectrum at longer wavelengths?

The following values are the only energy levels of a hypothetical one-electron atom: E6 5 22310219 J E5 5 27310219 J E4 5 211310219 J E3 5 215310219 J E2 5 217310219 J E1 5 220310219 J (a) If the electron were in the n 5 3 level, what would be the highest frequency (and minimum wavelength) of radiation that could be emitted? (b) What is the ionization energy (in kJ/mol) of the atom in its ground state? (c) If the electron were in the n 5 4 level, what would be the shortest wavelength (in nm) of radiation that could be absorbed without causing ionization?

Photoelectron spectroscopy applies the principle of the photoelectric effect to study orbital energies of atoms and molecules. High-energy radiation (usually UV or x-ray) is absorbed by a sample and an electron is ejected. The orbital energy can be calculated from the known energy of the radiation and the measured energy of the electron lost. The following energy differences were determined for several electron transitions: DE2-1 5 4.098310217 J DE3-1 5 4.854310217 J DE5-1 5 5.242310217 J DE4-2 5 1.024310217 J Calculate DE and l of a photon emitted in the following transitions: (a) level 3 - 2; (b) level 4 - 1; (c) level 5 - 4.

Horticulturists know that, for many plants, dark green leaves are associated with low light levels and pale green with high levels. (a) Use the photon theory to explain this behavior. (b) What change in leaf composition might account for this difference?

In order to comply with the requirement that energy be conserved, Einstein showed in the photoelectric effect that the energy of a photon (hn) absorbed by a metal is the sum of the work function (f), the minimum energy needed to dislodge an electron from the metals surface, and the kinetic energy (Ek) of the electron: hn 5 f 1 Ek. When light of wavelength 358.1 nm falls on the surface of potassium metal, the speed (u) of the dislodged electron is 6.403105 m/s. (a) What is Ek (1 2mu2 ) of the dislodged electron? (b) What is f (in J) of potassium?

For any microscope, the size of the smallest observable object is one-half the wavelength of the radiation used. For example, the smallest object observable with 400-nm light is 231027 m. (a) What is the smallest observable object for an electron microscope using electrons moving at 5.53104 m/s? (b) At 3.03107 m/s?

In fireworks, the heat of the reaction of an oxidizing agent, such as KClO4, with an organic compound excites certain salts, which emit specific colors. Strontium salts have an intense emission at 641 nm, and barium salts have one at 493 nm. (a) What colors do these emissions produce? (b) What is the energy (in kJ) of these emissions for 5.00g each of the chloride salts of Sr and Ba? (Assume that all the heat produced is converted to emitted light.)

Atomic hydrogen produces several series of spectral lines. Each series fits the Rydberg equation with its own particular n1 value. Calculate the value of n1 (by trial and error if necessary) that would produce a series of lines in which: (a) The highest energy line has a wavelength of 3282 nm. (b) The lowest energy line has a wavelength of 7460 nm

Fish-liver oil is a good source of vitamin A, whose concentration is measured spectrometrically at a wavelength of 329 nm. (a) Suggest a reason for using this wavelength. (b) In what region of the spectrum does this wavelength lie? (c) When 0.1232 g of fish-liver oil is dissolved in 500. mL of solvent, the absorbance is 0.724 units. When 1.6731023 g of vitamin A is dissolved in 250. mL of solvent, the absorbance is 1.018 units. Calculate the vitamin A concentration in the fish-liver oil.

Many calculators use photocells as their energy source. Find the maximum wavelength needed to remove an electron from silver (f 5 7.59310219 J). Is silver a good choice for a photocell that uses visible light? [The concept of the work function (f) is explained in Problem 7.69.]

In a game of Clue, Ms. White is killed in the conservatory. A spectrometer in each room records who is present to help find the murderer. For example, if someone wearing yellow is in a room, light at 580 nm is reflected. The suspects are Col. Mustard, Prof. Plum, Mr. Green, Ms. Peacock (blue), and Ms. Scarlet. At the time of the murder, the spectrometer in the dining room shows a reflection at 520 nm, those in the lounge and the study record lower frequencies, and the one in the library records the shortest possible wavelength. Who killed Ms. White? Explain.

Technetium (Tc; Z 5 43) is a synthetic element used as a radioactive tracer in medical studies. A Tc atom emits a beta particle (electron) with a kinetic energy (Ek 5 1 2mv2 ) of 4.71310215 J. What is the de Broglie wavelength of this electron?

Electric power is measured in watts (1 W 5 1 J/s). About 95% of the power output of an incandescent bulb is converted to heat and 5% to light. If 10% of that light shines on your chemistry textbook, how many photons per second shine on the book from a 75-W bulb? (Assume that the photons have a wavelength of 550 nm.)

The flame tests for sodium and potassium are based on the emissions at 589 nm and 404 nm, respectively. When both elements are present, the Na1 emission is so strong that the K1 emission can be seen only by looking through a cobalt-glass filter. (a) What are the colors of these Na1 and K1 emissions? (b) What does the cobalt-glass filter do? (c) Why is KClO4 used as an oxidizing agent in fireworks rather than NaClO4?

The net change during photosynthesis involves CO2 and H2O forming glucose (C6H12O6) and O2. Chlorophyll absorbs light in the 600700 nm region. (a) Write a balanced thermochemical equation for formation of 1.00 mol of glucose. (b) What is the minimum number of photons with l 5 680. nm needed to form 1.00 mol of glucose?

Only certain transitions are allowed from one energy level to another. In one-electron species, the change in l of an allowed transition is 61. For example, a 3p electron can move to a 2s orbital but not to a 2p. Thus, in the UV series, where nfinal 5 1, allowed transitions can start in a p orbital (l 5 1) of n 5 2 or higher, not in an s (l 5 0) or d (l 5 2) orbital of n 5 2 or higher. From what orbital do each of the allowed transitions start for the first four emission lines in the visible series (nfinal 5 2)?

The discharge of phosphate in detergents to the environment has led to imbalances in the life cycle of freshwater lakes. A chemist uses a spectrometric method to measure total phosphate and obtains the following data for known standards: Absorbance (880 nm) Concentration (mol/L) 0 0.031025 0.10 2.531025 0.16 3.231025 0.20 4.431025 0.25 5.631025 0.38 8.431025 0.48 10.531025 0.62 13.831025 0.76 17.031025 0.88 19.431025 (a) Draw a curve of absorbance vs. phosphate concentration. (b) If a sample of lake water has an absorbance of 0.55, what is its phosphate concentration?