230 The Poetry of Physics and The Physics of Poetry
filled quickly. If I can fill the states with both neutrons and protons, I can
put a neutron and a proton into each energy state and therefore do not fill
the higher energy states as fast. The lower the energy of all the nucleons,
the more binding energy there is and hence the more stable the nucleus.
This explains the near equality of neutrons and protons in the stable
nuclei. The ratio of neutrons to total nucleons increases from 50%
for the light nuclei to about 60% for the heaviest nuclei. This increase is
due to the repulsive electric force between protons. The reason for the
increase of this ratio is that it costs more energy to add a proton to a
heavier nucleus than a neutron because of the repulsive electric force
between the proton and the rest of the nucleus.
There are both stable and unstable nuclei. A stable nucleus is one
which left undisturbed will remain in the same state. A stable nucleus by
definition is in its ground state. Like the atom, the nucleus has various
excited states. When a nucleus is in one of its excited states, it will emit
electromagnetic radiation making transitions to lower levels until it
reaches its ground state. This is familiar to us from our study of atomic
physics but differs from the atomic case in that the nuclear radiation is of
a much higher energy and hence involves γ-rays rather than x-rays or
visible light.
All nuclei in excited states are unstable and hence radioactive. There
are nuclei, however, which are radioactive even in their ground state.
These nuclei emit other forms of radiation such as alpha particles
(helium nuclei), beta rays (electrons), positrons, protons or neutrons. The
radioactive nucleus is transformed into another nucleus as a result of this
transition. If the nucleus into which the radioactive nucleus is
transformed is the ground state of a stable nucleus, then there will be no
more emission of radiation. But if the nucleus is transformed into an
excited state it will continue to emit radiation until the ground state of a
stable nucleus is reached. The lifetime of radioactive nuclei, which is the
time from the creation of the nucleus to its spontaneous decay, varies
from nucleus to nucleus. Berylium-8 only lives 3 × 10-16 seconds on the
average whereas the average lifetime of Lead-204 is 1.4 × 10^17 years,
a time greater than the apparent lifetime of the universe. If the lifetime of
a nucleus is τ, it does not mean that all the nuclei decay exactly after time
τ has passed. The decay of each individual nucleus is a random process
but the average the lifetime it τ.
Alpha radiation or the spontaneous emission of a helium nucleus
is the usual mode of radioactivity of the heavier nuclei such as lead,