Download Physical Chemistry by Ball: Diffusion

Physical Chemistry by Ball: Diffusion
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End-of-Chapter questions 19.30 through 19.43
Chapter 30: Quantum Physics
Answers to Even-Numbered Conceptual Questions
2.
If energy is quantized, as suggested by Planck, the amount of energy for even a single high-frequency photon
can be arbitrarily large. The finite energy in a blackbody simply can’t produce such high-frequency photons,
and therefore the infinite energy implied by the “ultraviolet catastrophe” cannot occur. In classical physics,
any amount of energy can be in the form of high-frequency light—the energy does not have to be supplied in
discrete, large lumps as in Planck’s theory. Therefore, classical physics implies that all frequencies of light
have the same amount of energy, no matter how high the frequency. This is what leads to the “catastrophe.”
4.
Planck’s theory of blackbody radiation implies a one-to-one relationship between the absolute temperature of
a blackbody and the frequency of light at the peak of its radiated energy spectrum. This relationship is given
by Wien’s displacement law (equation 30-1). Therefore, by measuring the peak in the radiated energy from a
star, we can tell its temperature. In broad terms, a blue star is very hot, a red star much less so, and a yellowish
star like our Sun is intermediate in temperature.
6.
A monochromatic source of light means—literally—that it emits light of a single color. This means that all the
photons emitted by the source have the same frequency, and hence they also have the same energy.
8.
(a) A photon from a green light source always has less energy than a photon from a blue light source. (b) A
photon from a green light source always has more energy than a photon from a red light source. The reason for
these results is that the energy of a photon depends linearly on the frequency of light; that is, E = hƒ.
10.
Classically, it should be possible to eject electrons with light of any frequency—all that is required is to
increase the intensity of the beam of light sufficiently. The fact that this is not the case means that the classical
picture is incorrect. In addition, the fact that there is a lowest frequency that will eject electrons implies that
the energy of the photon is proportional to its frequency, in agreement with E = hƒ.
12.
Yes. An electron and a proton have the same de Broglie wavelength
momentum.
  h p
if they have the same
Chapter 31: Atomic Physics
Answers to Even-Numbered Conceptual Questions
2.
There are many such reasons, but perhaps the most important is that orbiting electrons in Rutherford’s model
would radiate energy in the form of electromagnetic waves, with the result that atoms would collapse in a very
small amount of time.
4.
The observation that alpha particles are sometimes reversed in direction when they strike a thin gold foil led to
the idea that there must be a great concentration of positive charge and mass within an atom. This became the
nucleus in Rutherford’s model.
6.
In principle, there are an infinite number of spectral lines in any given series. The lines become more closely
spaced as one moves higher in the series, which makes them hard to distinguish in practice.
8.
(a) There is no upper limit to the wavelength of lines in the spectrum of hydrogen. The reason is that the
wavelength is inversely proportional to the energy difference between successive energy levels. The spacing
between these levels goes to zero as one moves to higher levels, and therefore the corresponding wavelengths
go to infinity. (b) There is a lower limit to the wavelength, however, because there is an upper limit of 13.6 eV
to the energy difference between any two energy levels.
10.
All of these questions can be answered by referring to Figure 31-17 and Table 31-3. (a) Not allowed; there is
no d subshell in the n = 2 shell. (b) Not allowed for two reasons. First, there is no p subshell in the n = 1 shell.
Second, a p subshell cannot hold seven electrons. (c) Allowed. (d) Not allowed; the n = 4 shell does not have a
g subshell.
12.
No. Atoms in their ground states can emit no radiation. Even if an electron dropped from a highly excited state
to the ground state in one of these atoms, the result would not be an X-ray. The reason is that the binding
energy of these atoms is simply much lower than the energy of a typical X-ray photon.
Chapter 32: Nuclear Physics and Nuclear Radiation
Answers to Even-Numbered Conceptual Questions
2.
The difference is that in an α decay only a single particle is emitted—the α particle—and it carries the energy
released by the decay. In the case of β decay, two particles are emitted—the β particle (electron) and the
corresponding antineutrino. These two particles can share the energy of decay in different amounts, which
accounts for the range of observed energies for the β particles. (Of course, the antineutrinos are very difficult
to detect.)
4.
Alpha particles, which can barely penetrate a sheet of paper, are very unlikely to expose film in a cardboard
box. Beta particles, on the other hand, are able to penetrate a few millimeters of aluminum. Therefore, beta
particles are more likely to expose the film than alpha particles.
6.
A change in isotope is simply a change in the number of neutrons in a nucleus. The electrons in the atom,
however, respond only to the protons with their positive charge. Because electrons are responsible for
chemical reactions, it follows that chemical properties are generally unaffected by a change in isotope.
8.
Above the N = Z line, a nucleus contains more neutrons than protons. This helps to make the nucleus stable, by
spreading out the positive charge of the protons. If a nucleus were below the N = Z line, it would have more
protons than neutrons, and electrostatic repulsion would blow the nucleus apart.
10.
No. Fossil dinosaur skeletons represent organic material—which is necessary for carbon-14 dating—but they
are thousands of times too old for the technique to be practical.
12.
Yes. If the different isotopes have different decay rates—which is generally the case—they can still have the
same activity if they are present in different amounts.