# Nuclear fission

Nuclear fission is the process by which a large nucleus is split into two smaller nuclei.[1]

The fission of a nucleus of sufficient mass releases an enormous amount of energy, which can be harnessed in a nuclear reactor to generate electrical power. Nuclear fission can also be used in a destructive fashion, such as in a nuclear weapon. Fission also releases neutrons which can then impact and cause other nuclei to split, causing a chain reaction. The two most common fissile elements used in nuclear power applications and weapons applications are uranium 235 and plutonium 239.

A critical mass of the right radioactive material is required to begin this chain reaction. This is because if the mass undergoing fission is not sufficiently large, it's high surface area to mass ratio allows a large percentage of the neutrons required to sustain the chain reaction to escape. Once a critical mass of the proper radioactive material of good enough purity is achieved, the chain reaction begins.

## Typical reaction

particle mass
${}^{235}_{92}U$ 235.04393 amu
${}^{139}_{56}Ba$ 138.90884 amu
${}^{94}_{36}Kr$ 93.93436 amu
${}_0^1n$ 1.00866 amu

When Uranium-235 235U is bombarded with neutrons, a nucleus may absorb a neutron ${}_0^1n$ and become very unstable. It splits into fragments, generally two new smaller nuclei and a few neutrons. A typical reaction[2] would be:

${}^{235}_{92}U + {}_0^1n \qquad \rarr \qquad {}^{139}_{56}Ba + {}^{94}_{36}Kr + 3 {}_0^1n$

The reaction releases a great amount of binding energy, as the binding energy of the 235U is much higher than the binding energy of ${}^{139}_{56}Ba$ and ${}^{94}_{36}Kr$ combined. This can be seen when we compare the masses of the elements involved on both sides of the equation: though the number of protons and neutrons on both sides is the same, the masses are different!

Indeed, the particles of the left hand side have a weight of 236.0526amu, those of the right hand side only 235.8692amu. The difference of 0.18341amu were turned into energy, according to Einstein's E=mc²:

$0.18341amu \cdot c^2 = 0.18341 \cdot 1.6605 \cdot 10^{-27} kg \cdot 299,792,458 \frac{m^2}{s^2} =$
$2.7372 \cdot 10^{-11}J \approx 170MeV$.