Fission and the Chain Reaction
Neutrons are ideal projectiles for nuclear bombardment because they
carry no charge, can approach nuclei easily, and interact with them
strongly. These neutral particles, discovered by James Chadwick in 1932,
were used soon afterward by Enrico Fermi and his collaborators to
bombard most of the elements of the periodic table. Very often in these
experiments a nucleus would capture a neutron and become unstable with
too much weight for its charge. Stability would then be restored by a
beta decay, leaving the nucleus with one more unit of charge than it had
to begin with. In 1934 Fermi tried this experiment with uranium, charge
92, the most highly charged element known at that time. He hoped to make
a transuranic element with charge 93.
Throughout the experiments the uranium was observed with radioactive
counters and found to become far more radioactive than uranium
ordinarily is in its natural state. There was no way to account for all
this radioactivity except to assume that new elements had been formed in
the process of neutron bombardment. A chemical analysis revealed no
elements with charges between 86 and 91. From this evidence Fermi
concluded that no elements of charge less than 92 had been made and
therefore the radioactivity must be due to charges greater than 92. He
concluded that transuranic elements had been made in the laboratory.
Neither Fermi nor anyone else, however, was happy with this conclusion.
There was far too great a variety of radioactivity for comfort. It had
to be assumed that not only was the element with charge 93 being made,
but also elements with charges 94, 95, and many more. This was very hard
to understand. Ida Noddack,[8] a chemist, published a paper proposing an
alternative explanation of the experiment: that a nucleus of uranium,
when it captures a neutron, might break up into two fragments that could
have any of various weights and charges. In other words, she suggested
that Fermi had produced nuclear fission.
Fermi, however, believed that the fission process was an impossibility.
He had a convincing proof, based on the measured values of the weights
of nuclei and the formula of Einstein, E = mc². From this formula Fermi
calculated the energy liberated when uranium breaks into two pieces;
then he took into account the energy of electric repulsion between the
pieces and found that the energy barrier was so large that the fission
process could not take place. This proof was absolutely correct. The
only trouble was that the measured values of the weights of nuclei
happened to be inaccurate at that time!
But for this accident, fission would have been discovered in 1934
instead of 1938. If it had been, Nazi Germany might easily have been the
first country to make the atomic bomb. At that time some German
scientists were active in the field of military applications. The
American physicists had not yet turned much attention to the subject.
An important feature of Fermi’s experiment is the large amount and
variety of radioactivity that he found. The reason for this variety, as
we now know, is that the fission process does not take place in a unique
manner. The two primary fission fragments are very rarely of equal
weight and charge. On the average the lighter fragment weighs about 90,
and the heavier one about 140. Sometimes the lighter fragment will weigh
as little as 75, and the heavier one as much as 160. As the weight
varies, of course, so also does the charge. The charge of the lighter
fragment averages 38, which is strontium, and the heavier one 54, which
is xenon. All in all there are more than a hundred different species of
nuclei represented among the primary fission fragments.
Practically all of these nuclei are radioactive and undergo three or
four disintegrations before reaching stability. Overall therefore,
several hundred distinct radioactive species are created by the fission
process in uranium. Elements with charges 43 and 61 (which are not found
in nature) have been identified as fission products in fairly
appreciable quantities. Most of the fission products are short-lived
electron and gamma emitters that can contribute only to the local and
immediate radioactive hazard. Two of the long-lived products are
abundant and important. These are cesium¹³⁷ and strontium⁹⁰.
Cesium¹³⁷ has a half-life of 30 years and emits a gamma ray with an
energy of 0.6 million electron-volts. Strontium⁹⁰ has a half-life of 28
years and emits an electron with an average energy of 0.22 million
electron-volts. The daughter nucleus in this process is yttrium⁹⁰, which
emits another electron with an average energy of one million
electron-volts. The half-life of yttrium⁹⁰ is 64 hours. In effect,
therefore, strontium⁹⁰ emits two electrons, each with an average energy
of 0.6 million electron-volts. For the long-term radioactive hazard,
particularly the world-wide fallout associated with atomic explosions,
the two isotopes cesium¹³⁷ and strontium⁹⁰ are the most significant.
Strontium⁹⁰ is the more dangerous to living organisms because it is
deposited in the bones and retained in the body for long periods.
Besides radioactivity there is another feature of the fission process
which is so conspicuous that it may seem hard to understand how Fermi
failed to notice it—namely the large amount of energy released. The
fission of a single nucleus of uranium releases an energy of 200 million
electron-volts as contrasted with ordinary radioactive decay energies of
5 to 10 million electron-volts. (The energy released from the burning of
one atom of coal is only 4 electron-volts.)
Of the 200 million electron-volts released in fission, about 10 million
go into gamma rays and neutrons created in the fission process itself.
This energy contributes to the immediate and local radiation danger.
Another 24 million electron-volts go into radioactivity of the fission
products, and of this, about half go into neutrinos, which are neither
dangerous nor useful; the other half is carried by electrons and gives
rise to the delayed radioactive hazard. But the bulk of the energy, over
160 million electron-volts, goes into kinetic energy of the two primary
fission fragments. Of this amount, 100 million, on the average, go to
the lighter fragment.
One hundred million electron-volt fission fragments should certainly
have been noticed by Fermi’s radioactive counters—if they had been able
to reach the counters. The fragments were not able to reach the
counters, however. The reason is that Fermi was a careful worker. He
knew that his sample of uranium would emit some radioactive particles
even before neutron bombardment. This natural radioactivity he did not
want to get mixed up with the radioactivity that would be produced in
the experiment. So he put an absorbing foil between the uranium sample
and the radioactive counters. The fission fragments could not get
through the foil.
It is amusing that shortly afterward another noted physicist repeated
Fermi’s experiment, but this time without the foil. He reported that he
was unable to get any significant results because his counter, for
reasons unknown, started to spark.
Thus fission remained a secret. But in England Leo Szilard obtained
patent papers on the nuclear chain reaction. He pointed out that in some
nuclear reactions free neutrons might be released. These neutrons might
then succeed in producing further reactions which would produce more
neutrons. Provided that at least one neutron made in each reaction were
able to induce a reaction in another nucleus, a chain reaction would
take place.
The main problem, of course, was to avoid excessive neutron losses.
There are two ways in which the losses mainly occur. One is by wasteful,
nonreproductive capture in the nuclei; the other, by neutron leakage
from the material surface. This second loss, Szilard showed, could be
minimized by using a sufficiently large amount of chain-reacting
material.
The point is that a neutron born in a nuclear reaction must travel on
the average a certain distance before it can produce another reaction.
If the size of the chain-reacting material is much less than this
distance, practically all of the neutrons produced will be able to
escape through the material surface, and no chain reaction will be
possible. If the size of the material is large compared to this
distance, the leakage loss becomes negligible, and the possibility of a
chain reaction depends entirely on the magnitude of the first kind of
loss, the wasteful captures in nuclei. If this loss is not too great,
and a chain reaction is possible, there will be a _critical_ size of the
material at which on the average exactly one neutron per reaction will
be able to induce another reaction. A just critical chain reaction of
this kind is what is needed for an atomic reactor.
If the size of the material is greater than the critical size, on the
average more than one neutron per reaction will cause another reaction
and the chain reaction will run away. If, for example, two neutrons can
cause another reaction, there will be two neutrons after the first
generation, four after the second, eight after the third, and so forth.
This is the principle of the atomic bomb.
After about 80 generations, an appreciable fraction of all the nuclei in
the material will have undergone a nuclear transformation and so much
energy will have been released that the material will not stay together
even for the short time needed to produce the next generation. The whole
material begins to fly apart, the system becomes sub-critical, and the
chain reaction stops. The entire process lasts only a fraction of a
microsecond.
Thus even before fission was discovered, Szilard laid the basis for
constructing the atomic bomb and the nuclear chain reactor. As materials
in which a chain reaction might conceivably be made to occur he named
thorium, uranium and beryllium. On beryllium he was wrong because the
mass of this atom was incorrectly known. On thorium, his guess was good.
On uranium, he hit the bull’s eye.
Finally in December 1938 the secret broke. Hahn and Strassmann in
Germany made a chemical analysis of a uranium target that had been
exposed to neutrons. They were far more thorough than previous
investigators had been, and they found barium, charge 56, which had not
been present in the target material before the experiment. The only
possible explanation was the fission process. Within a few weeks the
violent kicks caused by the fission products in counters were found, and
in the following days this experiment was repeated around the world.
There was no doubt that neutrons could induce fission in uranium nuclei.
A few more weeks, and it was ascertained that the fission process
released neutrons which might lead to more fissions.
The chain reaction, however, was still far from a reality. Niels Bohr
and John Wheeler proved that a neutron could not cause fission in U²³⁸
unless its energy were greater than about one million electron-volts.
When the neutrons are first made in the fission process, many of them do
have energies greater than one million electron-volts. But before they
can cause a fission, they usually make a few nonfission collisions with
uranium nuclei, giving part of their energy to the nuclei and escaping
with the remainder. The nuclei are then left with too little energy to
undergo fission and the neutrons with too little energy to cause
fissions in their next encounters. Thus too few neutrons reproduce
themselves and no chain is possible.
Bohr and Wheeler suggested, however, that the rare isotope of uranium,
U²³⁵, can undergo fission when any neutron, even a slow neutron, hits
it. Thus a chain reaction is possible in U²³⁵. This was confirmed
experimentally shortly afterwards by John Dunning and Alfred Drier and
their co-workers at Columbia University.
Why the isotopes 235 and 238 behave so differently, is not difficult to
understand. The 235 is more explosive and more prone to undergo fission
than 238 because it is smaller and therefore its protons repel each
other more strongly. More important still, when a neutron is captured by
235, it acquires a greater kinetic energy by virtue of the short-range
nuclear attraction than a neutron acquires when it is captured by 238.
This happens for the simple reason that nuclei tend to be more stable
when they have an even number of neutrons (or protons) than when they
have an odd number. U²³⁵, having an odd number of neutrons, is more
eager to receive an additional neutron than 238, which already has an
even number of neutrons. Consequently, the capture of a slow neutron by
235 almost always eventuates in the fission process; while in 238, the
excess energy, introduced by the neutron, is merely ejected from the
nucleus in the form of a gamma ray, and U²³⁸ becomes U²³⁹.
A chain reaction is possible in U²³⁵ , but it is necessary to separate
this rare isotope from the abundant U²³⁸. The separation process is
anything but simple since isotopes of the same element are chemically
indistinguishable. Even the weight difference in this case, is little
more than one per cent. Bohr rejected the idea of a large-scale
separation with the remark: “You would have to turn the whole country
into a factory.” Of course it is now a matter of history that the job
was actually done under the Manhattan project during World War II.
During the war Bohr (alias Nicholas Baker) again visited the United
States and was shown the separation plants. He said: “You see I was
right. You _did_ turn the country into a factory.”
Natural uranium contains U²³⁵ in the ratio of 1 part to 139 of U²³⁸. It
was hoped at first that this concentration would be sufficient to make a
chain reaction, and that the expensive enrichment processes could be
avoided. This seemed possible because at energies of a fraction of an
electron-volt the neutrons are much more easily caught by U²³⁵ than by
U²³⁸, which compensates for the low concentration. Actually neutrons are
slowed down until their energy is as low as the energy of all other
particles participating in the general agitation caused by the
temperature. This energy is low enough for the purpose.
However, the neutrons are made in the fission process with an energy of
about a million electron-volts. Before they slow down sufficiently, they
must pass through a stage in which their energy is about 7
electron-volts. In the neighborhood of this energy, it happens that the
U²³⁸ has an extremely high probability for capturing a neutron and
changing into U²³⁹. Near some other energies, similar though smaller
absorption hurdles must be passed. Therefore natural uranium by itself
cannot be used to make a chain reaction. In 1940, Fermi and Szilard,
working now in the United States, found a way around this difficulty.
Their trick was to mix the natural uranium with a material whose nuclei
are so lightweight that they suffer a big recoil when struck by a
neutron and thus absorb a large fraction of the neutron energy. The
neutron is thus _moderated_ down to a low energy, rapidly and in big
energy jumps, so that either it does not spend much time at the
unfavorable energies where it can be caught by U²³⁸ or else it misses
these energies altogether. By imbedding the uranium in lumps in the
moderating material instead of making a homogeneous mixture of the two,
the absorption can be circumvented even better.
For the purpose of making a _controlled_ chain reaction, one may use the
method of enrichment, or the method of moderation, or both. But to
produce a _violent_ chain reaction, an atomic bomb, only the enrichment
method will work. The reason is that all the energy of the bomb must be
generated in a time that is as short as the time it takes the bomb to
fly apart, which is a fraction of a microsecond. If natural uranium were
used, the reaction would be slow and sluggish and would be extinguished
before a substantial fraction of the nuclei could have reacted.
It is interesting to consider that chain-reacting substances could have
been obtained easily six billion years ago, before the U²³⁸ had time to
decay and become a rare isotope. (The U²³⁵ was then about as abundant as
U²³⁸.) A chemical separation would still have been necessary and so we
do not need to imagine that chain-reacting mixtures accumulated
spontaneously on the young earth.
On the other hand, six billion years from now U²³⁵ will have become so
rare that it will be impossible to get a reactor going by moderation. At
the same time the isotope separation will have become most expensive
since the isotope to be separated will be present in an abundance of
less than 100 parts in a million. For those who like to worry about the
distant future we should hasten to add that other methods of obtaining
atomic energy will remain possible. And in any case there is good reason
to believe that some stellar explosions produce fresh supplies of U²³⁵
which space merchants could undoubtedly make available.
As to our present terrestrial supplies: uranium, like other heavy
elements, is quite rare. But the earth is divided into layers of which
the topmost 10 miles, forming something of a slag or scum, contain quite
a few rare compounds. In particular almost all of the uranium in our
planet is conveniently collected right under our feet, for us to use as
we see fit.