Why Fusion and Fission Release Energy | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

Products move towards the curve maximum

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Fusion of light nuclei and fission of heavy nuclei both move products towards the maximum. The products have greater binding energy per nucleon.

In both processes, the products have a greater binding energy per nucleon. Therefore their total binding energy is greater, their total rest mass is smaller, and the mass decrease is released as energy (9702/42/O/N/24 Q10(b)(ii)).

products higher on the curve → greater total binding energy → smaller final mass → energy released

Your turn9702/42/O/N/24 Q10(b)(ii)

Explain, using the binding-energy-per-nucleon curve, why the fusion of light nuclei releases energy. [3]

Show worked answer

The product lies closer to the maximum and has a greater binding energy per nucleon. Its total binding energy is therefore greater, so its total rest mass is smaller. The mass decrease is released as energy.

Worked example

Energy released by uranium fission

Uranium-235 has 7.59 MeV per nucleon. The products are xenon-142 at 8.37 MeV per nucleon and strontium-90 at 8.72 MeV per nucleon (9702/42/F/M/24 Q8(b)(ii)).

Find the total binding energy after fission.
$E_{\mathrm{Xe}}=142(8.37)$
$E_{\mathrm{Sr}}=90(8.72)$
$E_{\mathrm{after}}=1973.34\ \mathrm{MeV}$
Find the total binding energy before fission.
$E_{\mathrm{before}}=235(7.59)$
$E_{\mathrm{before}}=1783.65\ \mathrm{MeV}$
The increase in total binding energy is released.
$\Delta E=E_{\mathrm{after}}-E_{\mathrm{before}}$
$\Delta E=189.69\ \mathrm{MeV}$

Answer

1.9\times10^2\ \mathrm{MeV}

Common mistake

Do not subtract two binding-energy-per-nucleon values and stop. The nuclei contain different numbers of nucleons. First multiply each value by its nucleon number to obtain total binding energy.