Energy from nuclei
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Excerpt of Otto Robert Frisch F.R.S., What little I remember
Did I say that all nuclei had weights that were multiples of that
of a hydrogen nucleus? That is not quite true; most of them are
about 1 % lighter than that, and therein lies the secret of nuclear
(often called 'atomic') energy. When protons come together to form
heavier nuclei their joint mass becomes less by an amount
m
, and
a lot of energy
E
is set free, following Einstein's formulae
E=mc²
.
The factor
c²
(speed of light multiplied by itself) is very large, so
a minute amount of mass corresponds to a lot of energy; for
instance the mass of a paper-clip is equivalent to the entire energy
a small town uses during a day.
Energy is measured in a variety of units: kWh (kilowatt-hours)
on your electricity meter, Btu (British thermal units) for the gas
man, and so on. Those are man-size units, much too large for a
single nucleus. For them the common unit is the MeV (a million
electron-volt, but usually we say 'an emmeevee'). It is the energy
of motion which an electron (or a proton) acquires when it is
accelerated by a voltage of a million volts. An alpha particle has
typically 5 to 10 MeV; to keep a watch going needs several million
times as much energy every second.
Einstein's formula was put to the test in the 1930s by measuring
the energy of the particles (e.g. protons) set free in 'atom splitting'.
The collision of two nuclei caused the nucleons to be rearranged
so as to form two new nuclei; when those were both of a kind found
in nature it was possible to compare the masses of the nuclei before
and after the collision and check the mass difference against the
energy set free. That was done with mass spectrographs which were
soon made so precise that Einstein's formula could be checked to
within a fraction of an MeV; it was always found correct when the
nuclei formed by the reaction were stable and hence available for
mass spectroscopy. When unstable nuclei were formed one had to
take into account the energy of the particles they subsequently sent
out in transforming themselves into stable nuclei again. Soon there
was a network of literally thousands of measurements, cross-
checking each other, and the masses of several hundred isotopes
were accurately known.
What do those masses teil us? Well, for one thing, they tell us
why the sun keeps shining. If you could dive into the huge white-hot
ball of not-quite-pure hydrogen which we call the sun you would
find rapidly rising pressure and temperature until near the centre
the temperature is around ten million degrees Centigrade. At such
heat of the hydrogen nuclei move so fast (about 500 km/sec) that they
occasionally collide despite their mutual electric repulsion. There
are traces of other elements, which complicate what happens; Hans
Bethe, whom I later met in Los Alamos, was the first to work out
a possible mechanism for this process in detail. To cut the story
short, the main outcome is simply that helium nuclei are formed,
one from four hydrogen nuclei (two of which are chariged from
protons into neutrons), and each hydrogen nucleus gives up 7 MeV
in that process. In this 'nuclear fire' about a million times more
energy is produced than in ordinary (chemical) fire, for instance
when hydrogen burns by combining with oxygen. Even so the
amount of hydrogen the sun has to burn to keep shining is
stupendous: about ten billion tons every second! But the sun is big:
in the four billion years since the Earth became solid the sun has
used up only a fraction of its hydrogen.
If you go on to build up heavier nuclei you still liberate energy,
but much less, and stars that run out of hydrogen become unstable.
That raises fascinating questions regarding the nature of novae,
supernovae, pulsars and so on. But here I'm getting on thin ice
(or into hot water?), so let us return to solid ground.
Here we have some simple clues. Light nuclei contain as many
neutrons as protons. The reason is a variant of Pauli's housing rule:
two protons, spinning oppositely, can inhabit one quantum state,
together with two neutrons behaving the same way. The first
complete family of that kind is indeed the helium nucleus, rare on
Earth but exceedingly common in the sun and the stars. But then
why do heavier nuclei contain relatively more neutrons? Why is the
ratio of neutrons to protons about 1.2 : 1 for copper, 1.4 : 1 for iodine
and 1.6 : 1 for uranium? Because protons are bad club members: they
are electrically charged and hence repel each other, and it makes
a heavy nucleus more stable if some of them are turned into
neutrons even though, as a result, they may have to move into
higher quantum states. Nuclei with too few or too many protons
adjust the ratio after a while by sending out an electron or a
positron, as I mentioned earlier.
But in the heaviest nuclei, even when the ratio of neutrons to
protons is at its optimum, the protons are still under pressure from
their mutual repulsion. Then why don't they just get pushed out?
In fact what is holding nuclei together? The protons repel each
other, and the neutrons - being electrically neutral - cannot be
held by electric forces. Gravity? Many million times too weak.
Today we know that any two nucleons attract each other very
strongly, but only when they are very close together. We have no
special name for that attraction; we call it simply 'the nuclear
force'. It is more like a kind of stickiness, and we even think we
know something about the nature of the glue. It acts only between
nucleons in the same nucleus, except for a brief moment when two
nuclei collide.
But the heavy nuclei have a trick to unload some of their
quarrelsome protons. Two protons can combine with two neutrons
and emigrate as a family; the 28 MeV which are gained (as in the
process that keeps the sun shining!) serve to pay for the exit visa,
as it were. In classical mechanics such a process would be
impossible; like mountaineers trying to climb out of a crater on an
insufficient supply of food, they would find that their energy gives
out before they reach the rim and overcome the pull of the other
nucleons.
Classical physics is adamant about that, but the laws of quantum
mechanics are more flexible. They allow our subatomic moun-
taineer to 'tunnel' through the crater wall, as some physicists like
to put it. Or you may imagine that two protons and two neutrons
use Heisenberg's uncertainty principle to borrow some energy, to
be repaid after they have left the nucleus and become a helium
nucleus, a newborn alpha particle, rapidly driven away by the
electric repulsion of the remaining nucleus, sliding down the outer
crater wall as it were. But such a loan is granted only after
uncounted billions of applications; in other words the chance of
an alpha particle to escape in any given split second is minute and
depends of course on the kind of nucleus. That chance was
calculated from Schrödinger's wave equation, by Edward Condon
(U.S.A.) with Ronald Gurney (U.K.), and also by the Russian,
George Gamov, in 1926.
Until 1938 nobody dreamt that there was yet another way for
a heavy nucleus to react to the mutual repulsion of its many
protons, namely by dividing itself into two roughly equal halves.
It was mere chance that I became involved in the discovery of that
'nuclear fission', which for the first time showed a way to make
huge numbers of nuclei give up their hidden energy; the way to
the atom bomb and to atomic power.
The occupation of Austria in March 1938 changed my aunt, the
physicist Lise Meitner technically from an Austrian into a
German. She had acquired fame by many years' work in Germany,
but now had to fear dismissal as a descendant of a Jewish family.
Moreover, there was a rumour that scientists might not be allowed
to leave Germany; so she was persuaded - or perhaps stampeded
- into leaving at very short notice, assisted by friends in Holland,
and in the autumn she accepted an invitationto work in Stockholm,
at the Nobel Institute led by Manne Siegbahn. I had always kept
the habit of celebrating Christmas with her in Berlin; this time she
was invited to spend Christmas with Swedish friends in the small
town of Kungälv (near Gothenburg), and she asked me to join her
there. That was the most momentous visit of my whole life.
Let me first explain that Lise Meitner had been workingin Berlin
with the chemist Otto Hahn for about thirty years, and during the
last three years they had been bombarding uranium with neutrons
and studying the radioactive substances that were formed. Fermi,
who had first done that, thought he had made 'transuranic'
elements - that is, elements beyond uranium (the heaviest element
then known to the chemists), and Hahn the chemist was delighted
to have a lot of new elements to study. But Lise Meitner saw how
difficult it was to account for the large number of different
substances formed, and things got even more complicated when
some were found (in Paris) that were apparently lighter than
uranium. Just before Lise Meitner left Germany, Hahn had
confirmed that this was so, and that three of those substances
behaved chemically like radium. It was hard to see how radium
- four places below uranium could be formed by the impact of
a neutron, and Lise Meitner wrote to Hahn, imploring him not to
publish that incomprehensible result until he was completely sure
of it. Accordingly Hahn, together with his collaborator, the chemist
Fritz Strassmann, decided to carry out thorough tests in order to
make quite sure that those substances were indeed of the same
chemical nature as radium.
When I came out of my hotel room after my first night in
Kungälv I found Lise Meitner studying a letter from Hahn and
obviously worried by it. I wanted to teil her of a new experiment
I was planning, but she wouldn't listen; I had to read that letter.
lts content was indeed so startling that I was at first inclined to
be sceptical. Hahn and Strassmann had found that those three
substances were not radium, chemically speaking; indeed they had
found it impossible to separate them from the barium which,
routinely, they had added in order to facilitate the chemical
separations. They had come to the conclusion, reluctantly and with
hesitation, that they were isotopes of barium.
Was it just a mistake? No, said Lise Meitner; Hahn was too good
a chemist for that. But how could barium be formed from uranium?
No larger fragments than protons or helium nuclei (alpha particles)
had ever been chipped away from nuclei, and to chip off a large
number not nearly enough energy was available. Nor was it
possible that the uranium nucleus could have been cleaved right
across. A nucleus was not like a brittle solid that can be cleaved
or broken; George Gamov had suggested early on, and Bohr had
given good arguments that a nucleus was much more like a liquid
drop. Perhaps a drop could divide itself into two smaller drops in
a more gradual manner, by first becoming elongated, then con-
stricted, and finally being torn rather than broken in two? We knew
that there were strong forces that would resist such a process, just
as the surface tension of an ordinary liquid drop tends to resist its
division into two smaller ones. But the nuclei differed from
ordinary drops in one important way: they were electrically
charged, and that was known to counteract the surface tension.
At that point we both sat down on a tree trunk (all that discussion
had taken place while we walked through the wood in the snow,
I with my skis on, Lise Meitner making good her claim that she
could walk just as fast without), and started to calculate on scraps
of paper. The charge of a uranium nucleus, we found, was indeed
large enough to overcome the effect of the surface tension almost
completely; so the uranium nucleus might indeed resemble a very
wobbly, unstable drop, ready to divide itself at the slightest
provocation, such as the impact of a single neutron.
But there was another problem. After separation, the two drops
would be driven apart by their mutual electric repulsion and would
acquire high speed and hence a very large energy, about 200 MeV
in all; where could that energy come from? Fortunately Lise
Meitner remembered the empirical formula for computing the
masses of nuclei and worked out that the two nuclei formed by the
division of a uranium nucleus together would be lighter than the
original uranium nucleus by about one-fifth the mass of a proton.
Now whenever mass disappears energy is created, according to
Einstein's formula
E = mc²
, and one-fifth of a proton mass was
just equivalentto 200 MeV. So here was the source for that energy;
it all fitted!
A couple of days later I travelled back to Copenhagen in
considerable excitement. I was keen to submit our speculations -
it wasn't really more at the time to Bohr, who was just about to
leave for the U.S.A. He had only a few minutes for me; but I had
hardly begun to tell him when he smote his forehead with his hand
and exclaimed: 'Oh what idiots we all have been! Oh but this is
wonderful! This is just as it must be! Have you and Lise Meitner
written a paper about it?' Not yet, I said, but we would at once;
and Bohr promised not to talk about it before the paper was out.
Then he went off to catch his boat.
The paper was composed by several long-distance telephone
calls, Lise Meitner having returned to Stockholm in the meantime.
I asked an American biologist who was working with Hevesy what
they call the process by which single cells divide in two; 'fission',
he said, so I used the term 'nuclear fission' in that paper. Placzek
was sceptical; couldn't I do some experiments to show the existence
of those fast-moving fragments of the uranium nucleus? Oddly
enough that thought hadn't occurred to me, but now I quickly set
to work, and the experiment (which was really very easy) was done
in two days, and a short note about it was sent off to
Nature
together
with the other note I had composed over the telephone with Lise
Meitner. This time with no Blackett to speed things up about
five weeks passed before
Nature
printed those notes.
In the meantime the paper by Hahn and Strassmann arrived in
the U.S. A., and several teams did within hours the same experiment
which I had done on Placzek's challenge. A few days later Bohr
heard about my own experiments, not from me (I wanted to get
more results before wasting money on a transatlantic telegram!) but
from his son Hans to whom I had casually talked about my work.
Bohr responded with a barrage of telegrams, asking for details and
proposing further experiments, and he worked hard to convince
journalists that the decisive experiment had been done by Frisch
in Copenhagen before the Americans. That was probably the
source of the story reprinted several times that I was Bohr's
son-in-law (although he never had a daughter, and I was then
unmarried). I can see how it happened: a journalist asks: 'How do
you know of this, Dr Bohr?' Bohr: 'My son wrote to me',
Journalist mutters: 'His son, but name is Frisch; must be
son-in-law'.
During this turmoil in the U.S.A. we were quietly continuing
our work in Copenhagen. Lise Meitner feit that probably most of
the radioactive substances which had been thought to lie beyond
uranium those 'transuranic' substances which Hahn thought they
had discovered were also fission products; a month or two later
she came to Copenhagen and we proved that point by using a
technique of 'radioactive recoil' which she had been the first to
use, about thirty years previously. Yet transuranic elements were
also formed; that was proved in California by Ed McMillan, with
techniques much more sensitive than those available to Hahn and
Meitner.
In all this excitement we had missed the most important point:
the chain reaction. It was Christian Møller, a Danish colleague, who
first suggested to me that the fission fragments (the two freshly
formed nuclei) might contain enough surplus energy each to eject
a neutron or two; each of these might cause another fission and
generate more neutrons. By such a 'chain reaction' the neutrons
would multiply in uranium like rabbits in a meadow!
My immediate
answer was that in that case no uranium ore deposits could exist:
they would have blown up long ago by the explosive multiplication
of neutrons in them. But I quickly saw that my argument was too
naive; ores contained lots of other elements which might swallow
up the neutrons; and the seams were perhaps thin, and then most
of the neutrons would escape. So, from Møller's remark the
exciting vision arose that by assembling enough pure uranium (with
appropriate care!) one might start a controlled chain reaction and
liberate nuclear energy on a scale that really mattered. Many others
independently had the same thought, as I soon found out. Of course
the spectre of a bomb an uncontrolled chain reaction was there
as well; but for a while anyhow, it looked as though it need not
frighten us. That complacency was based on an argument by Bohr,
which was subtle but appeared quite sound.
In a paper on the theory of fission that he wrote in the U.S.A.
with John Wheeler, Bohr concluded that most of the neutrons
emitted by the fission fragments would be too slow to cause fission
of the chief isotope, uranium-238. Yet slow neutrons did cause
fission; this he attributed to the rare isotope uranium-235. If he
was right the only chance of getting a chain reaction with natural
uranium was to arrange for the neutrons to be slovved down,
whereby their effect on uranium-235 is increased. But in that
manner one could not get a violent explosion; slow neutrons take
their time, and even if the conditions for rapid neutron multiplica-
tion were created this would at best (or at worst!) cause the
assembly to heat up and disperse itself, with only a minute fraction
of its nuclear energy liberated.
All this was quite correct, and the development of nuclear
reactors followed on the whole the lines which Bohr foresaw. What
he did not foresee was the fanatical ingenuity of the allied physicists
and engineers, driven by the fear that Hitler might develop the
decisive weapon before they did. I was in England when the war
broke out, and in Los Alamos when I saw Bohr again. By that time
it was clear that there were even two ways for getting an effective
nuclear explosion: either through the separation of the highly fissile
isotope uranium-235 or by using the new element plutonium
formed in a nuclear reactor. But I am again getting ahead of my
story.
© Cambridge University Press, 1979 (my emphasis HJS).
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