energy release from nuclear reactions
As mentioned when we looked at energy
generation, it is now known that most of the energy
radiated by stars must be released by nuclear reactions. In this section
we will consider why it is that energy can be released by nuclear reactions.
Atomic nuclei are composed of protons and neutrons (or nucleons).
The total mass of a nucleus is less than the mass of its constituent
nucleons. This means that if a compound nucleus is formed from nucleons
there is a loss of mass which, by Einstein's mass-energy relation,
E=mc2, is released as energy. This energy is known
as the binding energy. The binding energy, Q(Z,N), of
a nucleus composed of Z protons and N neutrons is:
Q(Z,N) = [Zmp+Nmn-
where mp is the proton mass, mn the
neutron mass and m(Z,N) the mass of the compound nucleus. The more
stable the nucleus, the greater the energy that must be supplied to
unbind it, or equivalently, the greater the energy that is released when it
is formed. A more useful measure of stability is the binding energy
per nucleon, Q(Z,N)/(Z+N). This
is the energy needed to remove an average nucleon from the nucleus and is
proportional to the fractional loss of mass when the compound nucleus is
formed. Figure 14 shows a plot of the average
binding energy per nucleon versus the atomic mass number,
A = Z+N.
It can be seen that the curve increases rapidly with low A, hits a
broad maximum for atomic mass numbers of 50 to 60 (corresponding to
nuclei in the neighbourhood of iron in the periodic table, which are the most
strongly bound nuclei) and then gradually declines
for nuclei with higher values of A.
Binding energy per nucleon plotted as a function of the atomic mass number.
Figure 14 shows how nuclear fusion and
fission reactions can release energy. If two nuclei lying to the left
of the maximum in figure 14 fuse to form
a compound which also lies to the left of the maximum, the compound
nucleus will have a larger binding energy per nucleon than the original
nuclei. As the total number of nucleons has not been changed, such
nuclear fusion reactions must release energy.
Once the compound
nucleus lies in the iron region of figure 14,
however, further energy release from fusion reactions becomes
impossible. Thus if a star initially consisted of pure hydrogen, it could
generate a maximum of about 9 MeV per nucleon by fusion to 56Fe,
but about 7 MeV of this would have already been released when
4He is formed during the first step. (Note that
1 eV = 1.6x10-19 J.)
If a heavy nucleus lying to the right of the maximum in
figure 14 splits into two or more fragments
which also lie to the right of the maximum, the newly formed nuclei
will have a larger binding energy per nucleon than the original nucleus.
Such nuclear fission reactions must therefore also release energy.
However, the binding energy per nucleon of very heavy nuclei, although less
than that of iron, is still quite large. This means that the maximum
possible energy release per kg from fission reactions is much less than
that from fusion reactions. Coupled with the fact that very heavy nuclei
do not appear to be very abundant in nature, we may conclude that nuclear
fusion reactions are by far the most important source of energy generation
©Vik Dhillon, 27th September 2010