Biomedical Engineering Reference
In-Depth Information
6000
5000
4000
3000
2000
1000
0
2
·
10
-6
4
·
10
-6
6
·
10
-6
8
·
10
-6
1
·
10
-5
0
Wavelength/m
Figure 12.5
Black body radiation
=
=
wavelength λ is
hc
0
/λ. We also know that d
U
ε
g
(ε)dε. The experiment actually
gives a distribution function
g
(ε) such that the number of photons with energies between ε
and ε
εd
N
+
dε is
g
(ε)dε. Equation (12.12) can be developed to give
8π
V
h
3
c
0
1
exp
ε
k
B
T
g
(ε)
=
ε
2
(12.13)
−
1
If we interpret this expression as
g
(ε)
=
(density of states)
×
(average occupancy of a state)
we see that the density of states for photons is proportional to ε
2
whilst the average
occupancy of a state is proportional to
1
exp
ε
k
B
T
−
1
rather than the Boltzmann factor. This factor is referred to as the
Bose factor
after S.N.
Bose.
I can explain the density of states quite easily; photons have zero mass and so the energy
formula (Equation (12.1)) for a particle in a three-dimensional infinite well
