PHY3063 Spring 2007 Problem Set 5
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PHY 3063 Problem Set #5
Due Thursday February 22 (in class)
(Total Points = 60, Late homework = 50%)
Reading: Finish reading Tipler & Llewellyn Chapter 3 and start reading Chapter 4.
Problem 1 (5 points): A metal has a work function of 3.0 electron volts. What is the maximum
kinetic energy (in eV) of a photoelectron emitted by the surface of the metal if light with a
wavelength of 500 nm falls on the surface?
Problem 2 (15 points):
θ
= 90
o
Photon: E
1
, p
1
Photon: E
0
, p
0
Before
Electron at Rest
Electron: E
2
, p
2
After
Ψ
A photon with energy E0 strikes an electron at rest in a Compton scattering and exits at an angle
θ = 90o relative to its incoming direction, where mec2 = 0.511 MeV.
Part A (5 points): If E0 = 2mec2, what is the energy of the outgoing photon (in MeV)?
Part B (5 points): If E0 = 2mec2, what is the recoil kinetic energy of the electron (in MeV)?
Part C (5 points): If E0 = 2mec2, what is the recoil angle Ψ of the electron (in degrees)?
Problem 3 (10 points): Use Bohr’s postulate that the orbital angular
momentum is quantized according to hnL
=
, where n = 1, 2, 3, … and
consider an atom with one electron with mass me, and with a nucleus
with Z protons and mass M as shown in the figure.
Part A (5 points): Show the allowed radii are given by
0
2
r
m
Z
n
re
n
µ
=,
where
Mm
Mm
e
e
+
=
µ
,
o
DAr e529.0
0≈=
α
, 137
1
2
≈= c
Ke
h
α
, and cme
e
h
D=.
Part B (5 points): Show the allowed energy levels are given by
0
2
2
E
mn
Z
E
e
n
µ
=,
where
eVcmE e6.13)(
2
122
0−≈−=
α
.
r
Electron
charge = -e
mass = m
e
Nucleus
charge = +Ze
mass = M
CM
×
