A-level Physics (Advancing Physics)/Fusion/Worked Solutions

c = 3 x 10⁸ ms⁻¹

1. In the Sun, two tritium nuclei ($_{1}^{3}H$) are fused to produce helium-4 ($_{2}^{4}He$). What else is produced, apart from energy?

$2_{1}^{3}H\to \;_{2}^{4}He\;+\;2_{0}^{2}n$

2. In larger stars, carbon-12 ($_{6}^{12}C$) is fused with protium ($_{1}^{1}H$). What single nucleus does this produce?

$_{6}^{12}C\;+\;_{1}^{1}H\to \;_{7}^{13}N$

3. In this reaction, 1.95MeV of energy is released. What difference in binding energy, in J, does this correspond to?

1.95MeV = 1.95 x 10⁶ x 1.6 x 10⁻¹⁹ J = 3.12 x 10⁻¹³ J

4. If all this energy was emitted as a photon, what would its frequency be?

$E=hf$

$f={\frac {E}{h}}={\frac {3.12\times 10^{6}}{6.63\times 10^{-34}}}=4.71\times 10^{20}{\mbox{ Hz}}$

This is a within the wavelength spectrum of a gamma-ray, so we can assume all energy is released as a gamma-ray photon.

5. In order to contain a fusion reaction, electromagnetism may be used. What other force could be used? Why is this not being used for fusion reactors on Earth?

Gravity, as in stars. However, the amount of mass required to do this is far larger than the Earth, so we cannot do this.