Physics 212 – Problem Set 8 – Spring 2010
1. Show that the relationship we obtained from imposing the condition that our atoms are in a steady state
of thermal equilibrium at temperature
T
and the applied radiation field is also in thermal equilibrium at
temperature
T
:
B
ij
¯
hω
3
π
2
c
3
1
e
¯
hω/kT

1
A
ji
+
B
ji
¯
hω
3
π
2
c
3
1
e
¯
hω/kT

1
=
g
j
g
i
e

¯
hω/kT
requires that
g
i
B
ij
=
g
j
B
ji
and
A
ji
=
¯
hω
3
π
2
c
3
B
ji
if the Einstein coefficients are independent of temperature.
2. Show that the number of photon states per unit volume per unit frequency range for radiation confined to a
box is
ω
2
π
2
c
3
.
3. Obtain the lifetime of the
n
= 2,
l
= 1 level of hydrogen against spontaneous decay by dipole radiation.
4. Show (I already sketched this in class; you need to justify the steps) that the ratio of the typical size of a
magnetic dipole matrix element to the typical size of an electric dipole matrix element is
Zα
, for a hydrogenic
atom with
Z
protons. Find the ratio of a typical quadrupole matrix element to a typical electric dipole matrix
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 Spring '09
 mechanics, Atom, Radiation, Fundamental physics concepts, Excited state, dipole matrix element

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