Fusion Reactions in Stars (DP IB Physics: HL): Revision Note

Fusion Reactions in Stars

• Nuclear fusion is defined as:

The joining of two small nuclei to produce a larger nucleus

• Low-mass nuclei, such as hydrogen and helium, can undergo fusion and release energy

• For example, when two hydrogen nuclei (protons) fuse, a deuterium nucleus is produced

  • A positron and an electron neutrino are also produced as one of the protons converts into a neutron through beta-plus decay

${}_1{}^1\mathrm{H}+\hspace{0.17em}{}_1{}^1\mathrm{H}\to {}_1{}^2\mathrm{H}+\hspace{0.17em}{\mathrm{e}}^{+}+\hspace{0.17em}{\mathrm{\nu }}_{\mathrm{e}}$

• In the centres of stars, four hydrogen nuclei $\left({}_1{}^1\mathrm{H}\right)$ fuse to produce a helium nucleus $\left({}_2{}^4\mathrm{He}\right)$

  • A huge amount of energy is released in the reaction

  • This provides a radiation pressure that prevents the star from collapsing under its gravity

• On Earth, research is focused on achieving the deuterium-tritium (D-T) reaction

• This involves fusing a deuterium nucleus and a tritium nucleus together to produce a helium nucleus and a neutron

${}_1{}^2\mathrm{H}+\hspace{0.17em}{}_1{}^3\mathrm{H}\to {}_2{}^4\mathrm{He}+\hspace{0.17em}{}_0{}^1\mathrm{n}$

• The total mass of the helium nucleus is less than the total mass of the individual nucleons

• As a result, this reaction releases a large amount of energy per unit mass of fuel, which can be harnessed for power generation in a fusion reactor

Deuterium-tritium fusion

The role of the strong nuclear force in fusion

• For two nuclei to fuse, both nuclei must have high kinetic energy

• This is because

  • nuclei must overcome the repulsive Coulomb forces between protons

  • the strong nuclear force, which binds nucleons together, has a very short range

• Therefore, nuclei must get very close together for the strong nuclear force to take effect

• This means that, to achieve fusion, the nuclei must be

  • in an extremely hot and dense environment, e.g. the core of a star

  • accelerated to extremely high velocities, e.g. in a particle accelerator