Elements of Modern Physics
320
decreases slowly reaching a value of about 7.5 MeV for the heaviest natural
element, uranium. The general dependence of the binding energy per nucleon
on the mass number is shown in Fig. 9.1, for the stable nuclei. Two important
results follow from the general behaviour of E b /A: Energy can be released (i) in
the fission of a heavy nucleus into lighter nuclei, and (ii) in the fusion of lighter
nuclei into a heavier nucleus. For example, a nucleus with A = 220 (E b /A ≈ 7.5
MeV), breaking into two nuclei with A = 110 each (E b /A ≈ 8.5 MeV) will liberate
an energy of about 220 × (8.5 – 7.5) = 220 MeV. Similarly two
2
1 H
nuclei (E b /A ≈ 1.1 MeV) can combine into a
4
2 H nucleus (E b /A ≈ 7.1 MeV) to
liberate an energy of about 4 × (7.1 – 1.1) = 24 MeV. These energies are very
large compared to the few electron volts released in chemical reactions which
are governed by electromagnetic forces.
0
40
80
120
160
200
240
A
10
8
6
4
2
0
E
A
b
0
H e
Ni
Mo
144 Nd
208 Pb
2
H
Fig. 9.1 The general behaviour of the binding energy per nucleon as a function of A.
Though the fission and fusion processes leading to nuclei with A ≈ 55 are
feasible, it is observed that most of the nuclei are stable. The reason for this is
that before a heavy nucleus breaks up, the components must go through an
intermediate state with higher energy than the ground state (this can be induced
by providing extra energy available in the capture of a neutron). Similarly, lighter
nuclei encounter a higher energy intermediate state with large Coulomb
repulsion, before they can combine (the fusion can take place at high temperature,
e.g. in stars).