Nuclear Fission
Nuclear fission is the process in which a heavy atomic nucleus splits into two or more lighter nuclei, accompanied by the release of a large amount of energy.
This process usually occurs when the nucleus absorbs a neutron, becomes unstable, and divides into smaller fragments.
Examples
$$ {}^{235}_{92}\text{U} + {}^{1}_{0}\text{n} \rightarrow {}^{141}_{56}\text{Ba} + {}^{92}_{36}\text{Kr} + 3{}^{1}_{0}\text{n} $$
$$ {}^{239}_{94}\text{Pu} + {}^{1}_{0}\text{n} \rightarrow {}^{140}_{55}\text{Cs} + {}^{99}_{37}\text{Rb} + 2{}^{1}_{0}\text{n} $$
$$ {}^{233}_{92}\text{U} + {}^{1}_{0}\text{n} \rightarrow {}^{144}_{56}\text{Ba} + {}^{89}_{36}\text{Kr} + 3{}^{1}_{0}\text{n} $$
$$ {}^{232}_{90}\text{Th} + {}^{1}_{0}\text{n} \rightarrow {}^{140}_{54}\text{Xe} + {}^{93}_{36}\text{Kr} + 3{}^{1}_{0}\text{n} $$
Nuclear Fusion
Nuclear fusion is the process by which two light atomic nuclei combine to form a heavier nucleus with the release of a tremendous amount of energy.
Fusion occurs at extremely high temperatures and pressures, such as those found in stars, including the sun.
Examples
$$ {}^{2}_{1}\text{H} + {}^{3}_{1}\text{H} \rightarrow {}^{4}_{2}\text{He} + {}^{1}_{0}\text{n} $$
$$ {}^{2}_{1}\text{H} + {}^{2}_{1}\text{H} \rightarrow {}^{3}_{2}\text{He} + {}^{1}_{0}\text{n} $$
$$ {}^{3}_{1}\text{H} + {}^{3}_{1}\text{H} \rightarrow {}^{4}_{2}\text{He} + 2{}^{1}_{0}\text{n} $$
$$ {}^{2}_{1}\text{H} + {}^{3}_{2}\text{He} \rightarrow {}^{4}_{2}\text{He} + {}^{1}_{1}\text{H} $$
Binding Energy
Binding energy is the energy required to separate all the nucleons (protons and neutrons) in a nucleus into individual particles.
It represents the energy that holds the nucleus together. The greater the binding energy per nucleon, the more stable the nucleus.
Comparison
The table below highlights the major differences between nuclear fission and nuclear fusion based on their processes, energy yield, fuel used, and other characteristics.
| Feature |
Nuclear Fission |
Nuclear Fusion |
| Definition |
Splitting of a heavy nucleus into two or more lighter nuclei with the release of energy. |
Combining of two light nuclei to form a heavier nucleus with the release of energy. |
| Example of Reaction |
$$ {}^{235}_{92}\text{U} + {}^{1}_{0}\text{n} \rightarrow {}^{141}_{56}\text{Ba} + {}^{92}_{36}\text{Kr} + 3{}^{1}_{0}\text{n} + \text{energy} $$ |
$$ {}^{2}_{1}\text{H} + {}^{3}_{1}\text{H} \rightarrow {}^{4}_{2}\text{He} + {}^{1}_{0}\text{n} + \text{energy} $$ |
| Energy Released |
About 200 MeV per fission reaction. |
About 17 MeV per fusion reaction, but much higher per unit mass of fuel. |
| Fuel Used |
Heavy nuclei such as Uranium-235 and Plutonium-239. |
Light nuclei such as Deuterium and Tritium (isotopes of hydrogen). |
| Products Formed |
Two or more lighter nuclei, neutrons, and gamma rays. |
A heavier nucleus (usually helium), neutrons, and energy. |
| Chain Reaction |
Can occur because released neutrons trigger further fission reactions. |
No chain reaction; requires continuous high temperature and pressure. |
| Conditions Required |
Can occur at ordinary temperatures using slow neutrons. |
Requires extremely high temperature (about 10⁷ K) and pressure as in stars. |
| By-products |
Produces radioactive waste which can be hazardous. |
Produces little or no radioactive waste. |
| Application |
Used in nuclear reactors and atomic bombs. |
Used in hydrogen bombs and under research for fusion power plants. |
Worked Examples
Example 1: The mass of a helium nucleus is 4.0015 amu. Calculate its binding energy given that the mass of a proton is 1.0078 amu and a neutron is 1.0087 amu. (1 amu = 1.6 × 10⁻²⁷ kg, c = 3 × 10⁸ m/s)
Solution
$$ \text{Total mass of nucleons } $$
$$ = 2(1.0078) + 2(1.0087) $$
$$ = 4.0330 amu $$
$$ \text{Mass defect }= 4.0330 − 4.0015 $$
$$= 0.0315 amu $$
$$Energy = Δm × c² $$
$$ = 0.0315 × 1.6×10^{-27} × (3×10⁸)² $$
$$= 4.54×10^{-12} J$$
Example 2: The mass of a deuterium nucleus is 2.0136 amu. Calculate its binding energy.
Solution
$$\text{Mass of nucleons} $$
$$ = 1.0078 + 1.0087 = 2.0165 amu $$
$$ \text{Mass defect} = 2.0165 − 2.0136 $$
$$ = 0.0029 amu $$
$$ \text{Energy }= 0.0029 × 1.6×10^{-27} × (3×10⁸)² $$
$$ = 4.18×10^{-13}J $$
Example 3: The mass of a lithium nucleus is 7.0144 amu. Calculate its binding energy.
Solution
$$ \text{Mass of nucleons} $$
$$= 3(1.0078) + 4(1.0087) $$
$$ = 7.0589 amu $$
$$ \text{Mass defect} = 7.0589 − 7.0144 $$
$$ = 0.0445 amu $$
$$ \text{Energy} = 0.0445 × 1.6×10^{-27} × (3×10⁸)² $$
$$= 6.41×10^{-12} J $$
Example 4: The atomic mass of oxygen is 15.99 amu. If the individual mass of a proton and neutron is 1.0078 and 1.0087 amu respectively, calculate the binding energy of an oxygen nucleus in joules. (1 amu = 1.6×10⁻²⁷ kg, c = 3×10⁸ m/s)
Solution
$$ \text{Number of protons }= 8 $$
$$ \text{Number of neutrons }= 16 − 8 = 8 $$
$$ \text{Total mass of nucleons } $$
$$ = (8 × 1.0078) + (8 × 1.0087) $$
$$ = 16.1320 amu $$
$$ \text{Mass defect } $$
$$= 16.1320 − 15.99 = 0.1420 amu $$
$$ \text{Energy } $$
$$= 0.1420 × 1.6×10^{-27} × (3×10⁸)² $$
$$ = 2.05×10^{-11} J $$