Page 58 - Radiochemistry and nuclear chemistry

Nuclear Mass and Stability 47

nuclear reaction formulas and energies refer to single atoms (or molecules), while chemical
reactions and equations refer to number of moles; we have:

1 eV/molecule = 1.6022 • 10-19 x 6.0221 • 1023 = 96.48 kJ mole- 1 =
3.8268 • 10 -2o • 6.0221 • 1023 = 23.045 kcal mole -1

Thus, the formation of deuterium from a neutron and a hydrogen atom would lead to the
liberation of 214.6 • 106 kJ (51.3 • 106 kcal) for each mole of deuterium atoms formed.
By comparison, then, the nuclear reaction leading to the formation of deuterium is
approximately half a million times more energetic than the chemical reaction leading to
formation of CO 2.
It is not common practice to use mole quantities in considering nuclear reactions as the
number of individual reactions under laboratory conditions is well below 6.02 • 1023.
Therefore, in nuclear science one uses the energy and mass changes involved in the reaction
of individual particles and nuclei.

3.4. Binding energy

The energy liberated m the formation of CO 2 from the elements, the heat of formation,
is a measure of the stability of the CO 2 molecule. The larger the heat of formation the more
stable the molecule since the more energy is required to decompose the molecule into its
component atoms. Similarly, the energy liberated in the formation of a nucleus from its
component nucleons is a measure of the stability of that nucleus. This energy is known as
the binding energy (En) and has the same significance in nuclear science as the heat of
formation has in chemical thermodynamics. We have seen that the binding energy of
deuterium is 2.22 MeV. The ~He nucleus is composed of 2 neutrons and 2 protons. The
measured mass of the 4He atom is 4.002 603 u. The mass defect is:

AM'He = MHe -- 2 M H - 2 M n = 4.002603-2 • 1.007825-2 • 1.008665 = -0.030377 u

The binding energy between the nucleons in a nucleus follows the simple relation

E B (MeV) = -931.5 AM A (u) (3.5)

which is just another form of eqn. (3.3). Thus the binding energy for 4He is 28.3 MeV. It
is quite unlikely that 2 neutrons and 2 protons would ever collide simultaneously to form
a 4He nucleus; nevertheless, this calculation is useful because it indicates that to break 4He
into its basic component nucleons would require at least 28.3 MeV.
A better indication of the relative stability of nuclei is obtained when the binding energy
is divided by the total number of nucleons to give the binding energy per nucleon, EB/A.
For 4He the value of EB/A is 28.3/4 or 7.1 MeV, whereas for H it is 1.11 for the bond
2
between the two nucleons. Clearly, the 4He nucleus is considerably more stable than the
2H nucleus. For most nuclei the values of EB/A vary in the rather narrow range 5 - 8
MeV. To a first approximation, therefore, EB/A is relatively constant which means that the