650 14 Classical Mechanics and the Old Quantum TheoryExercise 14.16
a.Substitute the values of the constants into the expression of Eq. (14.4-21) to verify the value
ofR∞.
b.Calculate the wavelength and frequency of the light emitted whennchanges from 4 to 2.
What color does this correspond to?
c.When radiation passes through air instead of a vacuum, wavelengths are increased by a factor
equal to the refractive index of air, equal to 1.00027 for visible wavelengths. Find the value
of Rydberg’s constant for radiation passing through air.The first set of transitions shown in Figure 14.15, in which the lower-energy state
(n 2 state) is then1 state, corresponds to the series of spectral lines in the ultraviolet
that is known as the Lyman series. The second set of transitions, in whichn 2 2, is
the Balmer series. The first four lines of the Balmer series are in the visible region and
the others are in the ultraviolet. The next series, in whichn 2 3, is the Paschen series.
It lies in the infrared. It is not shown in the figure.n 55 n^56n 51215210250Energy/eVn 52n 53n 54Figure 14.15 The Transitions bet-
ween Energies of the Hydrogen
Atom According to the Bohr Theory.
The Bohr theory gives the correct energy expression for the hydrogen atom. Like
the other theories of the old quantum theory, it is based on unproved assumptions, not
all of which have turned out to be correct. Bohr was unable to extend the theory to
apply to the helium atom or any other atom, and it became obvious that the theory was
inadequate. However, it and the other theories of the old quantum theory provided the
incentive for others to find a more satisfactory theory.PROBLEMS
Section 14.4: The Old Quantum Theory
14.18a.Find the temperature of a black body with a
maximum in its spectral radiant emittance curve at a
wavelength of 480 nm.
b.Assume that the surface temperature of the sun
is 5800 K and that it radiates like a black body.
Find the wavelength of maximum spectral radiant
emittance. What color of visible light does this
correspond to?
c.Construct a graph of the spectral radiant emittance of
a black body with a temperature of 5800 K from a
wavelength of 200 nm to a wavelength of 2000 nm.
This includes the visible region, which is roughly
from 400 nm to 750 nm.
14.19Interstellar space is filled with isotropic radiation that
corresponds to black-body radiation with a temperature
of 2.736 K. Find the wavelength of maximum spectral
radiant emittance of black-body radiation at this
temperature and construct a graph of the spectral radiant
emittance as a function of wavelength for this
temperature.14.20The work function of sodium metal is 2.28 eV, where
1eV 1. 6022 × 10 −^19 J.
a.Find the threshold frequency and wavelength for
sodium.
b.Find the frequency and wavelength of light capable of
ejecting electrons from sodium metal with a speed of
4. 00 × 104 ms−^1.14.21The work function of platinum is equal to 6.30 eV.
a.Find the threshold frequency and wavelength for
sodium.
b.If ultraviolet light of wavelength 253.7 nm irradiates a
platinum surface, find the maximum kinetic energy
of electrons that can be ejected from the surface.14.22Find the value of the centripetal force on an electron in
then1 orbit of the Bohr theory.
14.23a.Calculate the speed of an electron in then4 Bohr
orbit and in then400 Bohr orbit of a hydrogen
atom.
b.Express these speeds as fractions of the speed of light.