Reactions Between Nuclei
The alchemists tried to transform one element into another artificially.
They used heat, they used chemicals; they even used witchcraft. They
failed. Their simplest method—to heat the substance in order to
transform it—was really correct. The trouble was that their temperatures
were too low by a factor of more than 10,000. What is needed, is a
temperature of the order of tens of millions of degrees.
At such high temperatures two nuclei may occasionally approach each
other in spite of the electrical repulsion between them. Sometimes they
may even get close enough to each other to undergo a nuclear reaction.
This, of course, happens with least difficulty if the nuclear charge is
small. Hydrogen nuclei, which carry charge 1, participate in such
reactions most easily.
In the interior of stars temperatures range from about 10 to 100 million
degrees, and nuclear reactions do occur. The reaction responsible for
the production of energy in the stars is:
4H¹ → He⁴ + energy
Four protons combine to make an alpha particle with a release of energy.
Actually this reaction does not take place all at once but several steps
are required. That energy should be released, one expects from the fact
that the alpha particle is very stable. Any process in which light
nuclei combine to form a heavier nucleus with a release of energy is
known as “fusion.”
The particular fusion process that goes on in the stars releases its
energy in many forms: as positrons, neutrinos, electromagnetic
radiation, and motion of the reacting particles. The positrons also
carry off the excess charge of the reaction.
The neutrinos fly through the star without interacting, carrying their
energy away into outer space, probably never again to make contact with
the material universe. The remainder of the fusion energy is deposited
within the star’s interior, which is thus kept hot enough so that the
fusion reaction can keep going. The name “thermonuclear” is
appropriately applied to this type of reaction.
A lot of effort and imagination is being devoted to the problem of
making a controlled thermonuclear reaction. The motivation for this
project comes from the fact that good thermonuclear fuels, such as
deuterium (H²), are abundant and cheap. There is enough deuterium in the
oceans of the world to supply man’s energy needs for many millions of
years. One difficulty, of course, is to find a container for the
reaction.
Even under stellar conditions the rate of fusion reactions is not very
great. It takes approximately a billion years for only one per cent of
the nuclei to react. Consequently even higher temperatures than those
found in stars are required to produce large amounts of energy in a
short time. But no known materials can withstand temperatures of more
than a few thousand degrees centigrade. One idea is to keep the
“burning” fuel away from material walls by means of magnetic fields.
Is there a way to make nuclei react without the extreme temperatures
needed in the thermonuclear reactions? What one is really trying to do
is bring two nuclear particles into intimate enough contact so that the
nuclear forces can act between them. There is no reason why one should
not use a _cold_ target material, which is bombarded from the outside by
energetic nuclear projectiles, for example protons or alpha particles.
The projectiles, if they are energetic enough, can overcome the
electrical repulsion of the target nuclei, and they actually can
penetrate. The resulting “compound” nuclei would either be unstable and
disintegrate instantaneously, or else be almost stable (i.e.,
radioactive) and disintegrate after some period of time. In either case
nuclei of new elements would probably be formed in the reaction. This
procedure sounds simple, but it has its difficulties.
[Illustration: Interior of the sun. The thermonuclear reactions take
place mainly in the very hot, very dense central region (shaded).
This region is about 20,000 miles in radius and has a density
approximately 80 times the density of water.]
The main difficulty is that the nucleus is a very tiny target. Its area
is about 100 million times smaller than the area of the atom as a whole.
If a piece of matter is bombarded by an energetic particle, chance alone
will determine whether the particle is directed toward a nucleus. To be
sure, if the particle misses the nucleus of one atom, it still has the
opportunity of hitting the nuclei of other atoms which may lie in its
path. It does not have many such opportunities, however, because, being
charged, it constantly interacts with the atomic electrons, which
gradually absorb energy causing the particle to slow down.
As the particle slows down, its chance of hitting a nucleus decreases,
even if it is heading directly toward one, because of the repulsion
between its charge and that of the nucleus. Unless the particle has
sufficient speed, it cannot overcome this repulsion.
Charged particles may be given the required speeds by accelerating them
through large electric fields. If a unit charge is accelerated through a
potential difference of one volt, it acquires an energy of one
_electron-volt_. The energies required for nuclear bombardment are of
the order of several million electron-volts, which can be provided by
atom-smashing machines such as the cyclotron.
Even at such high energies very few of the nuclear projectiles actually
find their way to a target nucleus. Most of them are slowed down by the
electrons, wasting their energy in heating up the target material.
Perhaps one particle out of a million will be lucky enough to induce a
nuclear reaction.
If the purpose of the nuclear accelerating machines were to produce
cheap energy, they would not be of much value. A nuclear reaction may
typically release five to 20 million electron-volts of energy. But to
obtain this reaction, a million particles had to be accelerated to
energies of several million electron-volts. The recoverable and useable
energy will be only a minute fraction of the total invested.
On the other hand, as a tool for scientific discovery, the atom-smashers
have been of great importance. That one event in a million has given us
much of our knowledge of nuclear physics.
The achievement of nuclear reactions by particle bombardment did not
actually wait on the invention of man-made accelerating machines.
Energetic alpha particles are available from the radioactive decay of
heavy elements. In 1919 Ernest Rutherford used such radioactive elements
as a source of alpha particles. The alpha particles were made to bombard
ordinary nitrogen, causing the reaction:
He⁴ + N¹⁴ → O¹⁷ + proton
(2 protons) (7 protons) (8 protons)
(2 neutrons) (7 neutrons) (9 neutrons)
That is, an alpha particle plus a nitrogen¹⁴ nucleus react to produce a
nucleus of (stable) oxygen¹⁷ plus a proton. Oxygen¹⁷ is a nucleus with 8
protons and 9 neutrons. The ordinary abundant form of oxygen has 8
protons and 8 neutrons. Natural oxygen contains a small amount of
oxygen¹⁷.
Later, in 1934, Irene Curie Joliot (the daughter of the discoverer of
radium, Madame Curie) and her husband, Frederic Joliot, used naturally
available alpha particles to make artificial radioactive nuclei for the
first time. The reaction was:
He⁴ + aluminum²⁷ → phosphorus³⁰ + neutron
(2 protons) (13 protons) (15 protons)
(2 neutrons) (14 neutrons) (15 neutrons)
Phosphorus³⁰ is an unstable nucleus and emits a beta ray (a positron) to
become silicon³⁰ (which is stable). The half-life for this decay is
about 2.5 minutes. The Joliots’ reaction was the first instance in which
man had produced radioactivity and known it. Actually cyclotrons had
been producing radioactivity in good abundance for the preceding two
years—but physicists had been unaware of this fact.
It is amusing that nature has also provided us with an atom-smashing
machine and indeed one that produces far greater energies than any
apparatus yet devised by man. This machine operates on the principle of
fluctuating, turbulent magnetic fields in interstellar space. Cosmic
particles—mainly protons, but also some alpha particles and even heavier
nuclei—are accelerated by these changing magnetic fields and hurled
occasionally into the earth’s atmosphere. The energies of these cosmic
particles are enormous, ranging from billions of electron-volts to
values a million times higher.
When a cosmic particle gets inside the earth’s atmosphere, it does not
go far before colliding with a nucleus of nitrogen or oxygen. Out of
this nuclear event emerge all the fundamental particles mentioned so
far, and some others known as mesons. Mesons are particles which may be
charged or neutral, and which have a weight a few hundred times that of
the electron. Some of these particles are believed to be connected with
the forces that hold the nucleus together.
The nuclear debris from the collision will itself be very energetic and
will further disrupt other nitrogen and oxygen nuclei. There soon
develops a cascade of electrons, positrons, mesons, neutrons, protons,
and electromagnetic radiation moving toward the surface of the earth.
About once a second every square inch of the earth’s atmosphere receives
such an energetic particle from outer space. The cascade that results
carries penetrating radiations to the surface of the earth. All living
organisms are constantly subjected to this radiation background. It is
an important fact that the intensity of this radiation is reduced in its
passage through the air, and inhabitants of Denver or Lima receive more
cosmic radiation than the inhabitants of Los Angeles or New York.
Some neutrons made by collisions of the primary cosmic particles in the
atmosphere may collide with nuclei of nitrogen. When this happens, the
following reaction occurs:
nitrogen¹⁴ + neutron → carbon¹⁴ + proton
(7 protons) (6 protons)
(7 neutrons) (8 neutrons)
Carbon¹⁴ is a radioactive electron emitter with a half-life of 5,600
years. This half-life is long enough so that much of the carbon¹⁴ in the
world today was probably made ten to twenty thousand years ago. Willard
Libby studied this process in a careful and quantitative way, traced the
history of the radioactive carbon from the atmosphere into living
beings, and, by measuring the carbon¹⁴ content in historical remains,
opened up a whole new branch of archeology.
Living organisms breathe in carbon (in the form of carbon dioxide) from
the air. Most of this carbon is ordinary stable carbon¹²; a tiny
fraction is radioactive carbon¹⁴. The organism is unable to distinguish
between the two isotopes, and takes in carbon¹⁴ in the same ratio to
carbon¹² as exists in the atmosphere. This ratio persists throughout the
organism’s lifetime, but when the organism dies and no more carbon is
assimilated, the ratio begins to decrease as the carbon¹⁴ nuclei
gradually disintegrate. By observing the ratio of carbon¹⁴ to carbon¹²
in fossil remains and other archeological objects, the date at which
death occurred can be calculated. In this way the age of ancient
Egyptian mummies has been found, and it has been shown that some sequoia
wood is more than 1,500 years old. By measuring the carbon¹⁴ in trees
that were killed by the last advance of glaciation, and looking into
other remains of life from the last ice age, it has been possible to
show that this last ice age occurred only 10,000 years ago—instead of
20,000 years, as had been previously believed. Carbon¹⁴-dating has
therefore thoroughly revised our ideas about the rapidity with which the
empires known to history have emerged from the most primitive
conditions. A crucial part of the argument is that isotopes of the same
element are chemically indistinguishable.
An alternative reaction which may occur when neutrons strike nitrogen,
is
N¹⁴ + neutron → carbon¹² + H³
(7 protons) (6 protons) (1 proton)
(7 neutrons) (6 neutrons) (2 neutrons)
H³, triton, is also radioactive, undergoing a beta decay to become He³
(2 protons and 1 neutron) with a half-life of 12.25 years. Tritons too
can be used for dating old objects—for example, old wine. The water in
the wine cannot be replenished with cosmic-ray tritons after the wine
has been bottled. Thus fifty per cent of the tritons disappear every
12.25 years.
We have here two examples of nuclear reactions induced by neutron
bombardment. Recalling the disadvantages of charged particles as nuclear
projectiles for alchemists, it must surely seem that neutrons would be
ideal for this purpose. Being chargeless, they are neither electrically
repelled by the nuclei nor constantly slowed down by energy-losing
collisions with the electrons. The fate of almost every neutron moving
in a large piece of matter is eventual collision with a nucleus.[7]
Neutrons are ideal nuclear projectiles, except for one thing: they are
hard to get.
Protons and alpha particles are found abundantly in nature as the nuclei
of hydrogen and helium atoms. Neutrons, however, are not found in
nature, and in the past have been made in nuclear reactions that were
themselves initiated by charged particles. For example,
He⁴ + beryllium⁹ → C¹² + neutron
(2 protons) (4 protons) (6 protons)
(2 neutrons) (5 neutrons) (6 neutrons)
But now we encounter again the difficulty associated with charged
particles. Only one alpha particle in a million undergoes a nuclear
reaction to produce a neutron. The neutron, of course, makes a nuclear
reaction every time. Over-all, then, we obtain two nuclear reactions per
million nuclear projectiles, instead of one per million. With such
methods we are not so much better off than the old alchemists. A cheap
and plentiful source of neutrons would, however, put the alchemist in
business. In this way one could make rare elements and radioactive
isotopes, and what is more important, he would be able to utilize
concentrated nuclear energy.