Breakup of the Nucleus
The positive electric charges within an atomic nucleus repel one
another. In the most heavily charged nuclei this repulsion becomes so
great that the nucleus can break into two parts, simultaneously
releasing a considerable amount of energy. In the case of _spontaneous
nuclear fission_ the two parts are more or less equal in size. In the
process of _alpha decay_ one of the parts (the alpha particle) is much
smaller than the other.
An alpha particle consists of two neutrons and two protons and is
identical with the nucleus of the helium atom. (The symbol for this
nucleus is He⁴.) Since two neutrons and two protons can simultaneously
occupy the lowest energy state, the alpha particle is an especially
stable nuclear unit. As a result, from time to time in heavy nuclei, two
neutrons and two protons will coalesce into an alpha particle, which may
then attempt to escape.
In attempting to escape from the nucleus, however, an alpha particle
encounters considerable resistance because of the short-range nuclear
attraction of the other neutrons and protons. This resistance which an
alpha particle experiences in trying to leave the nucleus is usually
referred to as an “energy barrier.” If the alpha particle could acquire
a little additional energy, it would be able to overcome the barrier and
get away from the nuclear attraction. Once outside the nucleus, just
beyond the reach of the nuclear attraction, the alpha particle would be
accelerated violently outward by the large electrical repulsion between
its two protons and the other protons in the residual nucleus.
[Illustration: How an alpha particle escapes from the nucleus. From
A to B it goes “uphill,” losing speed. At B its speed is zero and it
almost always turns around. With a small probability it may sneak
through the energy barrier B to C. Beyond C, it is repelled and
emerges with increasing speed.]
The alpha particle needs some extra energy to escape. According to the
laws of older physics there is no possibility for it to obtain this
extra energy and therefore escape is impossible. But the more newly
discovered laws governing the motion of neutrons and protons (the laws
of quantum mechanics) are not so stringent; they permit the alpha
particle to use “borrowed” energy to overcome the energy barrier. Of
course the alpha particle must always repay the loan—which it can easily
do out of the large fund of electric energy that is released when it
gets out of the repulsive range of the residual nucleus. There is no
interest on the loan.
Such energy loans are not automatically granted in nature. There are two
factors which make the loan improbable: if the amount is big or if the
term is long. These restrictions effectively limit the particles which
may apply for an energy loan. Objects of great size and weight are
unable to qualify, but the small particles of the atomic world often do.
The more energy carried off by the alpha particle after the alpha decay,
the less energy must be borrowed in order to overcome the barrier, and
the more rapidly the decay may be expected to occur. So sensitive is the
decay to the energy of the alpha particle, that an alpha particle
carrying twice the energy is emitted a hundred trillion times fester.
Half-lives for alpha decay vary from a fraction of a second to billions
of years. But even the shortest half-life for alpha decay is remarkably
long compared to the time required for the alpha particle to cross the
nucleus. This means that the alpha particle makes a tremendous number of
attempts to escape from the nucleus before it actually succeeds.
According to the older classical theory the alpha process should never
occur, and in fact it occurs with a very small probability.
A single alpha decay is not usually a sufficient process to bring about
stability of the daughter nucleus. A whole chain of radioactive decays
is usually required before stability is achieved. Most nuclei which emit
alpha particles belong to one of these radioactive decay chains.
The heavy nuclei for which alpha decay occurs all contain a large excess
of neutrons. Since the alpha particle carries off exactly two neutrons
and two protons, the ratio of the number of neutrons to the number of
protons is increased in the daughter nucleus. This has an unstabilizing
influence. (Actually, in lighter nuclei stability requires that the
ratio of neutrons to protons be closer to unity.) The daughter nucleus
is thus apt to be beta-active, converting a neutron into a proton (plus
an electron and a neutrino) in order to decrease its ratio of neutrons
to protons. In this way a chain of radioactive decays may occur, more or
less alternating between alpha and beta emissions, with gamma rays being
occasionally emitted also.
There are four radioactive chains. One of them starts with the abundant
isotope of uranium, U²³⁸. This isotope undergoes a few alpha decays and
a couple of beta decays to become radium, which has a charge of 88 and a
weight of 226. All the radium in the world is produced in this manner as
a daughter product in the fifth decay of the chain. After a number of
further decays, stable lead (weight 206) is produced and the chain
terminates.
The other chains are similar to the U²³⁸ chain, though not quite as
long. One chain starts with the rare isotope of uranium, U²³⁵; another
starts with the isotope of thorium that weighs 232. Both of these
terminate in stable isotopes of lead. In all cases the first decay of
the chain has a very long half-life. The half-life of U²³⁸ is 4.5
billion years; of U²³⁵, 710 million years; and of thorium, 14 billion
years.
The fourth radioactive chain has been made in the laboratory but is not
found in nature because its first isotope, neptunium with weight 237,
has too short a half-life. It decays in two million years and all the
other members of the chain live for even shorter periods. Thus the
neptunium chain decayed long ago, whereas the three other chains have
survived from the time when the elements were made.
It is interesting to notice that the lesser abundance of U²³⁵, as
compared with U²³⁸, is connected with its shorter half-life. Assuming
that comparable amounts of both isotopes were present at the beginning
of the universe (and there is good reason to believe that this was the
case), one would expect to find significantly less U²³⁵ than U²³⁸ after
a period of a few hundred million years. After 710 million years (the
half-life for U²³⁵) only one half of the original number of U²³⁵ nuclei
would still exist. But 90 per cent of the original U²³⁸ nuclei
(half-life 4.5 billion years) would remain. From the presently observed
ratio of U²³⁵ to U²³⁸ nuclei (1 to 139), it may be calculated, using the
law of radioactive decay, that 6 billion years ago natural uranium
consisted of equal parts of U²³⁵ and U²³⁸. The age of the universe is
hotly debated. With each passing year the universe seems to be a billion
years older. Right now six billion years does not seem widely off the
mark.
Natural radioactivity occurs mainly among the heavy elements, but there
are a few light elements that are naturally radioactive. Of these,
potassium⁴⁰ is an especially interesting one because it can decay either
by electron emission or by electron capture. The processes are:
potassium⁴⁰ → calcium⁴⁰ + electron + neutrino,
(1.1 billion years)
and
potassium⁴⁰ + electron → argon⁴⁰ + neutrino.
(11 billion years)
Calcium⁴⁰ and argon⁴⁰ are both stable nuclei. The second reaction is
followed immediately by a gamma ray emission from the argon⁴⁰. The one
per cent of argon found in the earth’s atmosphere comes almost entirely
from the second reaction. These radioactivities are also interesting
because appreciable amounts of potassium⁴⁰ are always present in human
tissue.
All nuclei at the heavy end of the periodic system are radioactive alpha
emitters. Uranium, for example, has no stable isotopes; they all undergo
alpha decay. But there is another mode of spontaneous decay of uranium,
which is much less frequent than alpha decay but is of much greater
practical importance. This is the fission process.
The fission process is just like alpha decay in that the nucleus breaks
up into two fragments. The main difference between these processes is in
the relative weights of the fragments. In the alpha decay of U²³⁸, for
instance, one fragment has a weight of four and the other 234. In the
fission process the fragments tend to be more nearly equal in weight.
For example, one may weigh 90 and the other 148.[6] Other weight
combinations are also possible.
The explanation of spontaneous fission is in essence the same as that of
alpha decay. Spontaneous fission, however, is a less probable process
because the two fragments are more strongly bound to each other by the
nuclear forces than they are in alpha decay. More energy must be
borrowed, and it must be borrowed for a longer term in order to
penetrate the energy barrier.
The relative likelihoods of spontaneous fission and alpha decay can be
appreciated from the following fact. In one hour in a gram of U²³⁸ there
occur about 45 million alpha decays but only about 25 spontaneous
fissions.
Once the energy barrier has been overcome, the energy released in alpha
decay or spontaneous fission is proportional to the charges on the two
fragments. For alpha decay, the product of the charges is 2 × 90 = 180;
for spontaneous fission, this product will typically be about 40 × 52 =
2,080. Hence one might expect the fission energy release to be 10 to 15
times greater than the alpha energy release. As a matter of fact the
fission energy release is even greater than this estimate indicates,
being about 30 to 50 times greater than the alpha energy release. That
so large an amount of energy is released, is a very important feature of
the fission process from the point of view of practical utilization of
atomic energy.
Being at the end of the periodic system, uranium requires a large ratio
of neutrons to protons for its greatest stability. The fission
fragments, however, lie in the middle of the system of elements,
requiring a much smaller ratio of neutrons to protons for stability.
This has two consequences.
One is that the fragments themselves may be expected to be unstable.
They will undergo beta decay (electron emission) several times
consecutively before a stable combination of neutrons and protons is
reached. This radioactivity of the fission products constitutes a
potential hazard in any practical application of fission atomic energy.
In later chapters of this book we shall consider particularly the
possible hazard from the fallout of radioactive fission products created
in atomic explosions, and also the hazard associated with the operation
and maintenance of atomic reactors.
The second consequence of the neutron excess is that neutrons may boil
off from the fragments immediately after the fission process has
occurred. This can happen because a lot of disorderly internal motion is
generated by the fission process within the fragments, and these
fragments do not have a particularly strong hold on their neutrons. The
practical value of the released neutrons is something we shall discuss
at length in a later chapter. For the present we mention only that these
neutrons provide the mechanism whereby a chain reaction is made
possible.
Spontaneous fission and alpha decay are responsible for the fact that
elements with charge greater than 92 are not found in nature. There is
little doubt that these elements were made in the beginning. But they
have long since decayed.
An interesting case of spontaneous nuclear fission is californium²⁵⁴
(charge 98), with a half-life of 55 days. This isotope is formed in
large quantities in certain stellar explosions called super-novae. Once
in a millennium one of a collection of a billion stars flares into
incredible brilliance. For a few weeks this single star shines with the
combined energy and luster of a billion ordinary stars—then it fades
away gradually. Such a “new” star (nova), with the greatest power of
radiation, is called a “super-nova.”
We believe that many nuclear reactions take place in a super-nova. It
has been observed that a few weeks after the initial outburst of light,
the intensity of light is reduced almost exactly by a factor of two
every 55 days for a year or so. This is precisely what would be expected
if the energy generated in the star during this time were due to the
spontaneous fission of californium²⁵⁴. Here we see a model of what
happens to naturally radioactive elements. Of these we have retained on
earth only the ones with the longest half-lives, like uranium, thorium,
and potassium.