All answers have been checked against the answer key, and should be presumed to be correct. You should ask for help in the recitations if you are unable to obtain these results.
2. v = 4.76 x 106 m/s, r = 9.34 nm.
8. 5.4 x 10-20 J = 0.34 eV
12. 1.77 eV < E < 3.10 eV
24. 1.88 eV, 43.3 kcal/mole
28. maximum wavelength = 6.62 x 10-16 m
30. E = 1.71 MeV, wavelength 7.24 x 10-13 m
32. (a) 7.12 x 10-13 m, (b) 2.43 x 10-12 m, (c) 4.86 x 10-12 m
38. 29 V
42. KEe / KEp = 1.84 x 103
50. transition from level 6 to level 3
52. Evaluating the expression for the Rydberg constant gives 1.0974 x 107 m-1
54. (a) 486 nm, (b) 102 nm, (c) 434 nm
56. 91.2 nm
2. The blackbody radiation of objects at normal temperatures is in the infrared, and not visible, so we can't see their radiation. Infrared cameras can, which is why they are useful in the dark.
3. No. The peak wavelength of light produced by the sun at 6000 K is in the middle of our visual sensitivity range, so sunlight appears white. The peak wavelength of a 2500K lightbulb is much lower, so the light appears to be lacking blue frequencies.
4. An ideal blackbody absorbs any radiation that strikes it. A small hole in an otherwise closed body has the same effect, since light going in is unlikely to come out again.
5. Daylight has its peak intensity near the center of human vision, so that objects appear whiter and more natural in daylight than in artificial light, which is peaked at different frequencies.
6. Black and white film is sensitive primarily to blue light, so red light does not expose it. Color film is sensitive to red light, so a red light cannot be used in that case. The darkroom must be dark.
7. The material with the longer threshhold wavelength has a lower threshhold frequency, and therefore a lower threshhold energy. That means the electrons are less tightly bound, and has a lower work function.
8. Waves do not have a minimum amount of energy they can impart to an electron. More intense light would stimulate the electron more. In the particle picture, it is unlikely for an electron to be simultaneously stimulated by more than one photon, so there is a cutoff energy equal to the amount of energy carried by a single photon.
9. The photons of UV light carry more energy than the photons of visible light. The energy carried by a photon is the amount it can impart to an electron in the skin, possibly causing a chemical change or other damage. UV photons have enough energy for this, but visible photons do not, even if the light is very bright, since the energy per photon is unaffected by intensity.
10. The Compton effect predicts that the energy of the photon will decrease when it is scattered from an electron, since some of the energy is transferred to the electron. This means that the wavelength will increase.
11. In the photoelectric effect, the energy of the photon is completely absorbed by the electron ejected from the atom. In the Compton effect, the photon is deflected and reduced in energy, but not completely absorbed.
12. (a) If a burglar interrupts the beam of light, no current flows.
This could be detected and used to sound an alarm.
(b) If a beam of light is shines perpendicular to a photodetector,
any smoke entering the beam would cause light to shine onto the photodetector,
and could signal an alarm to sound. (At low densities, the amount of light
the smoke blocks is negligible, so it is better to measure the light reflected
to the side.)
(c) In a photographic light meter, the fact that the current flowing
depends on the amount of light hitting the phototube could be used to tell
the intensity of the light.
(d) The tube can be moved at different angles to see where the
brightest intensity of the spectral lines are, and measure their locations.
13. Light has wave properties because it can diffract and be polarized. Light has particle properties because its energy is quantized in minimal units which depend on the frequency, and it can only transfer energy in multiples of those units (hf).
14. Electrons have wave properties because they diffract when scattered through metals. They have particle properties because we can isolate individual electrons and measure their mass, velocity, and other kinematic properties.
15.
Photons are massless, electrons have mass.
Photons move at the speed of light (in a vacuum),
electrons cannot move that fast.
Photons are electrically neutral, electrons carry charge.
Photons do not obey an exclusion principle, electrons do (Chapter 28).
Photons have spin 1, electrons have spin 1/2 (Chapter 28).
16. The wavelength of the electron depends on the mass of the electron and its velocity, while the wavelength of the photon depends both on the frequency and velocity (which may be less than c in a material). This question does not have an answer unless the frequency of the light is given.
17. The Coulomb attraction between the positive nucleus and the negative electron holds the electron in orbit.
18. Only rareified gasses emit a line spectrum. Otherwise, the spectrum is dominated by interactions between the atoms, which are not quantized in general. Dense gasses, liquids, and solids have continuous spectra.
19. There is not enough average kinetic energy in the air at room temperature (only about 0.04 eV) to excite any of the higher energy levels in oxygen.
20. You could look for spectral lines unique to oxygen to tell if any were present in the sun.
21. The Lyman series contains transitions to the ground state of Hydrogen. At room temperature, almost all hydrogen is in its ground state, so these are the transitions that are observed.
22. Closely spaced lines have small energy differences, which correspond to small differences in wavelength.
23. Rutherford's atom had electrons in any possible energy level, at any possible radius. In Bohr's model, both of these are quantized. Rutherford's atom had no minimum energy level, so there was nothing to prevent an electron from radiating away all of its energy and spiraling down into the nucleus.
24. The electrons would repel each other, so they may be expected to stay further from the nucleus than in the hydrogen atom.
25. The different lines are all different possible energy levels for a single electron.
26. The Balmer series was discovered first because it is visible. The Lyman series is in the UV range, so it was not detected immediately.
27. Yes. If light at a shorter wavelength is absorbed, the atom becomes ionized, and the electron ends up in an unbound continuum state. Actually, some light from the sun would be absorbed at that frequency. It is an example of the photoelectric effect. There would not be any sharp line in the spectrum, however, since the final state is in the continuum, not quantized.
28. Conservation of momentum shows that the proton must recoil (at a velocity much less than the electron) when an electron is emitted. Therefore, some of the kinetic energy will be carried away by the nucleus, not just by the electron. This makes the electron's energy somewhat less than predicted by Eq. 27-10, since nuclear recoil was neglected.
| Physics 222 | Department of Physics | University of Tennessee |