Problem Set 3
Due: See website for due dates
Quantization of Light and Energy
Reading: Taylor, Zafiratos, Dubson, Chapter 4; Tipler and Llewellyn, Chapter 3
Question A
Explain physically how the introduction of Planck’s constant resolved the Ultraviolet
Catastrophe (UVC)?
Question B
Explain why the existence of a cutoff frequency in the photoelectric effect more strongly
favors a particle theory rather than a wave theory of light.
Question C
In our treatment of the photoelectric effect, we neglected conservation of momentum.
Why is this approach justified? Suppose you take conservation of momentum into
account – what qualitative change would it make to the energy of the electron that is
emitted?
Question D
(i) In both the photoelectric effect and in the Compton Effect we have a photon colliding
with an electron causing the electron to fly off. What then, is the difference between the
two processes? (ii) Can Compton scattering occur with protons as well as electrons. For
example, suppose a beam of X-rays is directed at a target of liquid hydrogen. Compared
to Compton scattering with electrons, what similarities and differences would you
expect?
Problem 1
When light of wavelength 450 nm is shone on potassium, photoelectrons with stopping
potential of 0.52 V are emitted. If the wavelength of the incident light is changed to 300
nm, the stopping potential is 1.90 eV. Using only these numbers together with the values
of the speed of light and the electron charge, (a) find the work function of potassium and
(b) compute a value for Planck’s constant.
Answer: 2.24 eV; 6.63  1034 J.s
Problem 2
The work function for tungsten is 4.6 eV. (a) If light is incident on tungsten, find the
critical frequency, below which no electrons will be ejected, and the corresponding
wavelength. Find the maximum kinetic energy of ejected electrons if tungsten is
irradiated with light with (b) 200 nm and (c) 300 nm. Explain your answer to part (c).
Answer: 1.1  1015 Hz, 270 nm, 1.6 eV, −0.5 eV.
Problem 3
Millikan’s data for the photoelectric effect in lithium are shown in the table. (a) Graph
these data and determine the work function for lithium. (b) Find a value of Planck’s
constant from the graph in (a). (c) The work function for lead is 4.14 eV. Which of the
wavelengths in the table would cause emission of photoelectrons from lead?
Answer: 2.40 eV; 6.89  1034 J.s; 306 nm
Incident (nm) 253.5
Vstop (V)
2.57
312.5
1.67
365.0
1.09
404.7
0.73
433.9
0.55
Problem 4
Using the Phet simulation of the Photoelectric Effect to describe in detail the (a) inability
of the wave interpretation of light to correctly describe the data whereas the (b) correct
description by the particle (or photon) interpretation of light. That is, describe for both
models the following three plots
 Current vs. Battery Voltage
 Current vs. Light Intensity
 Electron energy vs. Light Frequency
Website: http://phet.colorado.edu/en/simulation/photoelectric
Problem 5
Use Compton’s equation to compute the value of  for the figure. To
what percent shift in the wavelength does this correspond when the
incident wavelength is 0.0711 nm?
Answer: 4.14  10 nm; 5.8%
Problem 6
Compton used photons of wavelength of 0.0711 nm. (a) What is the energy of these
photons? (b) What is the wavelength and (c) energy of the photons scattered at  =
1800? (d) What is the recoil energy of the electrons?
Answer: 1.747  104 eV; 0.0760 nm; 1.128  103 eV
Problem 7
Consider a head-on, elastic collision between a massless photon (momentum p0 and
energy E0 and a stationary free electron. (a) Assuming that the photon bounces directly
back with momentum p and energy E, use conservation energy and momentum to find
p. (b) Verify that your answer aggress with that given by Compton’s formula with  = .
Problem 8 (Challenge)
Derive the Compton Shift equation (  2  1  C (1  cos ) ).