RADIATION PROTECTION - ILEA

6 | Bonding Energies 15
ture is a measure of the kinetic energy of the atoms and molecules as a result
of that motion.
The colliding particles do not all have the same energy; rather, a distribution
of energies exists in any collection of molecules or atoms. The
energies increase with increased temperature. The distribution N(E) of N
molecules with energy E in an ideal gas containing a large number of molecules
at absolute temperature T is given by an equation known as the
Maxwell-Boltzmann distribution (derived by Clerk Maxwell and Ludwig
Boltzmann in 1860)
NE ( )
dE
=
N π
2
( kT )
−E e kT
E dE
1 2
3
2
1 2
(1.8)
where k is the Boltzmann constant (0.86 × 10 −4 eV/K). We need not be
concerned with the exact shape of the distribution, except to note that it
increases at first with increased energy (given by the √E term in the numerator),
reaches a maximum, and then decreases as the negative exponential
takes over. The energy at the maximum is the most probable kinetic energy
per molecule in an ideal gas at temperature T and is equal to kT. The most
probable energy is often used to characterize a distribution of energies at a
given temperature, such as the energies of neutrons in a nuclear reactor.
The average translational energy, equal to 1.5 kT, is also used to characterize
the spectrum.
Example 1.3 What is the most probable energy of the molecules in
the body at body temperature?
Since body temperature, T, is 310 K, kT = 0.86 × 10 –4 eV/K ×
310 K = 0.027 eV.
This is a measure of the kinetic energy of the molecules in the body.
This energy is much greater than the energies of photons of electromagnetic
energy transmitted in radio and television communications. Physicists
often cite this disparity in arguing that the effect of these radiations in
producing molecular changes is insignificant in comparison with the energies
imparted by the motion of the body’s own molecules.
6 Bonding Energies
A fraction of the molecules in a Maxwell-Boltzmann distribution attain
energies much higher than the most probable energy, although fewer and
fewer molecules do so as the level of attained energy rises. Thus, a fraction