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Multiple choice
Einstein's detailed-balance argument relates the spontaneous-emission coefficient
A
b
a
A_{ba}
A
ba
to the stimulated coefficient
B
b
a
B_{ba}
B
ba
via
A
b
a
/
B
b
a
=
ℏ
ω
0
3
π
2
c
3
A_{ba}/B_{ba} = \frac{\hbar \omega_0^3}{\pi^2 c^3}
A
ba
/
B
ba
=
π
2
c
3
ℏ
ω
0
3
. What observable consequence follows from the
ω
0
3
\omega_0^3
ω
0
3
dependence?
Spontaneous emission grows steeply with frequency, so excited states decay faster for higher-energy (e.g. ultraviolet) transitions than for low-energy ones
Higher-frequency transitions decay more slowly than low-frequency ones
Spontaneous emission is independent of the transition frequency
Stimulated emission vanishes at high frequency while absorption dominates
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