Page 59 - Radiochemistry and nuclear chemistry

48 Radiochemistry and Nuclear Chemistry

total nuclear binding energy is roughly proportional to the total number of nucleons in the
nucleus.
Figure 3.3 shows that the EBIA values increase with increasing mass number up to a
maximum around mass number 60 and then decrease. Therefore the nuclei with mass
numbers in the region of 60, i.e. nickel, iron, etc., are the most stable. Also in this Figure
we see that certain numbers of neutrons and protons form especially stable configurations
- this effect is observed as small humps on the curve.
If two nuclides can be caused to react so as to form a new nucleus whose EB/A value is
larger than that of the reacting species, obviously a certain amount of binding energy would
be released. The process which is called fusion is "exothermic" only for the nuclides of
mass number below 60. As an example, we can choose the reaction

20 20 40
10Ne + 10Ne --, 20Ca

From Figure 3.3 we estimate that EBIA for neon is about 8.0 MeV and for calcium about
8.6 MeV. Therefore, in the 2 neon nuclei 2 x 20 x 8.0 = 320 MeV are involved in the
binding energy, while 40 x 8.6 = 344 MeV binding energy are involved in the calcium
nucleus. When 2 neon nuclei react to form the calcium nucleus the difference in the total
binding energy of reactants and products is releasext; the estimate gives 344 - 320 = 24
MeV; a calculation using measured masses gives 20.75 MeV.
Figure 3.3 also shows that a similar release of binding energy can be obtained if the
dements with mass numbers greater than 60 are split into lighter nuclides with higher EB/A
values. Such a process, whereby a nucleus is split into two smaller nuclides, is known as
fission. An example of such a fission process is the reaction

236Tr92,., ~ l~4~ + 38 Sr93 + 3n

The bindin~ energy per nucleon for the uranium nucleus is 7.6 MeV, while those for the
140 Xe and 93 Sr are 8.4 and 8.7 MeV respectively. The amount of energy releasexl in this
fission reaction is approximately 140 • 8.4 + 93 x 8.7 - 236 x 7.6 = 191.5 MeV for
each uranium fission.

3.5. Nuclear radius

Rutherford showed by his scattering experiments that the nucleus occupies a very small
portion of the total volume of the atom. Roughly, the radii of nuclei vary from 1/10 000
to 1/100 000 of the radii of atoms. While atomic sizes are of the order of 100 pm (10-10
m), the common unit of nuclear size is the femtometer (1 fm = 10 -15 m), sometimes
referred to as 1 Fermi.
Experiments designed to study the size of nuclei indicate that the volumes of nuclei (Vn)
are directly proportional to the total number of nucleons present, i.e.

V n oc A (3.6)

Since for a sphere V oc r 3, where r is the radius of the sphere, for a spherical nucleus r 3
~ A, or r ~ A 1/3. Using r o as the proportionality constant