18.3.3 Nuclear Fission

Nuclear fission occurs when a large atomic nucleus splits into two smaller nuclei of approximately the same size. Of particular interest to us is the fission of uranium-235, since this is the reaction that powers our nuclear plants (and also the atomic bomb dropped on Hiroshima).

When U-235 nuclei are “stimulated” by neutrons, one of the many fission reactions it can undergo is the following:

$\displaystyle \displaystyle {}_{0}^{1}n+{}_{{92}}^{{235}}U\to {}_{{56}}^{{141}}Ba+{}_{{36}}^{{92}}Kr+3{}_{0}^{1}n$

Let’s calculate the energy released in this reaction.

BE per nucleon of $\displaystyle \displaystyle {}_{{92}}^{{235}}U=7.591\text{ MeV}$

BE per nucleon of $\displaystyle {}_{{56}}^{{141}}Ba=8.326\text{ MeV}$

BE per nucleon of $\displaystyle {}_{{36}}^{{92}}Kr=8.513\text{ MeV}$

Total BE before fission

$\displaystyle \sum B{{E}_{i}}=235\times 7.591=1783.9\text{ MeV}$

Total BE after fission

$\displaystyle \begin{aligned}\sum B{{E}_{f}}&=141\times 8.326+92\times 8.513\\&=1957.2\text{ MeV}\end{aligned}$

Increase in BE,

$\displaystyle \begin{aligned}\Delta BE&=\sum B{{E}_{f}}-\sum B{{E}_{i}}\\&=1957.2-1783.9\\&=173\text{ MeV}\end{aligned}$

The increase in BE of 173 MeV implies that 173 MeV of energy is released during the fission. This energy is carried by the KE of the fission products.

Conveniently, the fission products include 3 neutrons. If these 3 neutrons strike 3 other U-235, they can trigger 3 more fissions. This results in a chain reaction that can be self-sustaining in the nuclear reactor. The power output of nuclear reactors is adjusted using control rods containing elements (boron, cadmium, etc.) which absorb neutrons strongly. If uncontrolled, the exponential nature of the chain reaction results in a nuclear explosion, which is of course disastrous. Having said that, in the only two nuclear disasters in the past (namely the Chernobyl and the Fukushima), the meltdown was not caused by the nuclear fission of the fissile fuel, but the radioactivity of the fission products (such as Ba-141 and Kr-92 in this example), which is the subject of section 18.4.