4.5: Nuclear Fission


After the discovery of the neutron by James Chadwick in 1932, and after learning, shortly afterwards, how to prepare strong neutron sources, physicists rushed to carry out experiments in which they "bombarded" with neutrons any nuclei that were available. Literally, all elements from the periodic table were investigated in such way. Typically, the bombardment led to the so-called $$(n, y)$$ reaction:

${ }_{Z}^{A} \mathrm{X}+{ }_{0}^{1} n \rightarrow{ }_{Z}^{A+1} \mathrm{Y}+{ }_{0}^{0} \gamma$

In most cases, the daughter nucleus $$\mathrm{X}$$ was radioactive - so, a large number of new previously unknown radioisotopes were discovered.

In December 1938 such an experiment was performed on uranium by two German radiochemists, Otto Hahn and Fritz Strassmann. In the irradiated material they found Barium, an element with $$Z=56$$. Since for Uranium $$Z$$ $$=92$$, Barium could be created by a typical $$(n, \gamma)$$ reaction. The riddle was solved shortly afterwards by Lise Meitner, a long-time Hahn collaborator, who was Jewish and therefore some time earlier she had had to leave then Nazi Germany and to seek safety in Sweden. Meitner deduced that a reaction product that much lighter than the parent nucleus could only mean that a completely new process had occurred - namely, that the uranium nucleus had been split by the incident neutron. Soon afterwards, Meitner's explanation was confirmed by a large number of experiments performed independently by several labs. A new term has been coined for the newly discovered process namely, "nuclear fission".

Natural uranium consists of $$99.3 \%$$ of the U-238 isotope, and only 0.7\% of the U-235 isotope. But the fission process in the Hahn and Strasmann occurred in U-235 nuclei only. It turned out that the production of Barium was only one of the many other possible decay schemes. The two daughter nuclei produced by the fission are called "fragments": their Z numbers must always add up to 92 , but there are altogether about 150 possible such combinations. Two more properties of the fission reaction are of great importance:

• The total energy released by the fission process is unusually high about $$200 \mathrm{MeV}$$ per one event, 100 times more than in the most energetic known $$a$$ and $$\beta$$ decays; and
• Each fission reaction, in addition to the two fragment, releases a few (2.4 per average) free "daughter neutrons".

Especially, the discovery of the latter property created a great excitement among physicist, because it meant that a "chain reaction" might occur. Namely, one one neutron incident on a block of U-235 might fission one nucleus and release 2-3 daughter neutrons; which in turn might fission 2-3 more U-235 nuclei, producing some 5-6 "second-generation daughter neutrons", these might trigger up to six more fission reaction, and so on - an avalanche might develop and last up to the moment when there would be no more U-235 nuclei left in the block. Such process might release an enormous amount of energy: in one pound of pure U-235, if all nuclei underwent fission, would release nearly $$4 \times 10^{14} \mathrm{~J}$$ of energy. It's about the same amount of energy that would be released by burning $$10^{7}$$ kilograms, or three million gallons of gasoline.

As follows from the above, pure Uranium-235 isotope would be a very dangerous material: a single neutron - and there are always such particles around us, created by cosmic radiation-might trigger a powerful explosion. In fact, the very first atomic bomb ever used in warfare was nothing else than a big block of nearly-pure U-235 isotope. Good news, however, is that natural uranium contains only $$0.7 \%$$ of the dangerous isotope and extracting the latter from the former is an incredible difficult process, requiring a huge industrial-scale facility to be carried out. And a small amount of U-235 say, a pound or so - is not dangerous at all. The thing is that the "daughter neutrons", necessary to maintain the chain reaction, are more likely to escape to the outside than to induce another fission event. In order to "keep enough daughter neutrons inside", one has to diminish the "escape route" - in other words, to make attain a small-enough ratio of the surface area to the block volume. ForU-235 a chain reaction may develop in a sphere of radius nearly 9 $$\mathrm{cm}$$, and a mass of about $$52 \mathrm{~kg}$$. It's the infamous "critical mass" of Uranium 235

Interestingly, the other Uranium isotope in the natural composition may also undergo a fission reaction $${ }^{2}$$ - however, the essential difference between the U-235 and U-238 fission is that the latter reaction does not yield any daughter neutrons. Hence, a chain reaction can't occur in U-238. So,there are two categories of nuclei that exhibit the fission reaction. The ones that release daughter neutrons and are thus capable to maintain chain reaction are called fissile (a term derived by merging "fissionable" and "fertile"). Of naturally occurring heavy nuclei only U-235 is fissile, and only U-238 fissionable. Yet, there are "human-made" fissile nuclei, Plutonium-239 (obtained by irradiating U-238 with neutrons) and U-233 (by irradiating Thorium-232). There are more man-made fissile materials, but only Pu-239 and U-233 are of practical importance from the viewpoint of electric power generation.

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1. In U-238 fission can be triggered only by neutrons of relatively high energy, $$>1 \mathrm{MeV}$$ -in contrast, quite surprisingly, for U-235 it's the low-energy neutrons which are the most efficient in triggering the fission reaction.

4.5: Nuclear Fission is shared under a CC BY 1.3 license and was authored, remixed, and/or curated by Tom Giebultowicz.