Energy from nuclei


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 (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).