Biomedical Engineering Reference
In-Depth Information
is referred to as the
distribution function
of the kinetic energy. When the experiments are
carried out, we find a characteristic spread of kinetic energies as shown in Figure 12.4. The
distribution is independent of the type of atom, the solid curve refers to a temperature of
500 K and the dashed curve refers to a temperature of 1500 K. The peak moves to higher
energy as the temperature increases, but the area under the curve remains constant.
8
·
10
19
6
·
10
19
4
·
10
19
2
·
10
19
0
1
·
10
-20
2
·
10
-20
3
·
10
-20
4
·
10
-20
0
Energy/J
Figure 12.4
Distribution of atomic kinetic energies
The quantity
g
(ε) gives the number of atoms whose energies lie between ε and ε
+
dε.
The number of atoms whose energies lie between ε
A
and ε
B
is therefore
ε
B
g
(ε) dε
ε
A
and the total number of atoms is given by
∞
N
=
g
(ε) dε
0
I can give a very simple explanation of Figure 12.4, on the assumption that the sample of
particles is constrained to a cubic three-dimensional infinite well. My explanation depends
on the continuum approximation and so will only work for ordinary temperatures, for at
low temperatures the spacing between quantum states will be comparable to
k
B
T
and so the
continuum approximation will not apply. Also, it will not work for anything but an atom
