Elements of Modern Physics
62
2. A spherical object of radius 10 cm and whose surface approximates that
of a black body is maintained at a temperature of 1000 K. What is the
energy radiated by the body per second? Estimate the energy radiated in
the visible range.
3. Show that the number of photons per unit volume of a black body cavity,
per unit frequency, is
2
3
/
8
( )
(
1 )
hv kt
N
c e
πν
ν =
−
.
4. A small 10 W source of ultraviolet light of wavelength 1000 Å is held at a
distance of 0.1 m from a metal surface. If the radius of an atom is
approximately 0.5 Å, how many photons strike an atom per minute? If the
efficiency, i.e., the fraction of the photons that succeed in knocking out the
photons, is 1%, how many electrons are ejected from a unit area per second?
5. In a photoionization experiment, let ε be the binding energy and let the
photon with frequency v be incident. Assuming that the recoil energy of
the atom is small, show that the electron comes out with a momentum
approximately equal to [2m(hv – ε)]
1/2
. Obtain an expression for the recoil
energy of the atom when the electron comes out at an angle of φ with
respect to momentum of the photon.
6. Show that the recoil electron in Compton scattering always comes out in
the forward hemisphere, i.e., recoil angle is less than or equal to 90°.
When is the angle between the scattered photon and the recoil electron, a
maximum? What is the corresponding recoil energy of the electron? Assume
hv 0 < mc
2
for the second part.
7. An x-ray of wavelength λ = 0.1 Å is scattered by an electron. What are
the maximum and minimum wavelengths of the scattered photon? At what
angle will the scattered photon have a wavelength of 0.11 Å?
8. An electron has a de Broglie wavelength equal to that of a photon. Compare
its kinetic energy with the energy of the photons? What is the limiting
value of this ratio for low energy photons? If the photon has an energy of
100 keV, what is the kinetic energy of the electron?
9. What is the de Broglie wavelength of neutrons at room temperature? Can
they be used to study crystal structure?
10. A beam of 0.25 eV neutrons incident on a nickel surface is found to produce
a maximum at an angle of 70° with the initial beam direction, but no other
maxima are produced for angles greater than 70°. Determine the order of
the maximum and the interplanar distance for the crystal.
62
2. A spherical object of radius 10 cm and whose surface approximates that
of a black body is maintained at a temperature of 1000 K. What is the
energy radiated by the body per second? Estimate the energy radiated in
the visible range.
3. Show that the number of photons per unit volume of a black body cavity,
per unit frequency, is
2
3
/
8
( )
(
1 )
hv kt
N
c e
πν
ν =
−
.
4. A small 10 W source of ultraviolet light of wavelength 1000 Å is held at a
distance of 0.1 m from a metal surface. If the radius of an atom is
approximately 0.5 Å, how many photons strike an atom per minute? If the
efficiency, i.e., the fraction of the photons that succeed in knocking out the
photons, is 1%, how many electrons are ejected from a unit area per second?
5. In a photoionization experiment, let ε be the binding energy and let the
photon with frequency v be incident. Assuming that the recoil energy of
the atom is small, show that the electron comes out with a momentum
approximately equal to [2m(hv – ε)]
1/2
. Obtain an expression for the recoil
energy of the atom when the electron comes out at an angle of φ with
respect to momentum of the photon.
6. Show that the recoil electron in Compton scattering always comes out in
the forward hemisphere, i.e., recoil angle is less than or equal to 90°.
When is the angle between the scattered photon and the recoil electron, a
maximum? What is the corresponding recoil energy of the electron? Assume
hv 0 < mc
2
for the second part.
7. An x-ray of wavelength λ = 0.1 Å is scattered by an electron. What are
the maximum and minimum wavelengths of the scattered photon? At what
angle will the scattered photon have a wavelength of 0.11 Å?
8. An electron has a de Broglie wavelength equal to that of a photon. Compare
its kinetic energy with the energy of the photons? What is the limiting
value of this ratio for low energy photons? If the photon has an energy of
100 keV, what is the kinetic energy of the electron?
9. What is the de Broglie wavelength of neutrons at room temperature? Can
they be used to study crystal structure?
10. A beam of 0.25 eV neutrons incident on a nickel surface is found to produce
a maximum at an angle of 70° with the initial beam direction, but no other
maxima are produced for angles greater than 70°. Determine the order of
the maximum and the interplanar distance for the crystal.