A-level Physics (Advancing Physics)/Binding Energy/Worked Solutions

1. Deuterium (an isotope of Hydrogen with an extra neutron) has a nuclear mass of 2.01355321270 u. What is its binding energy?

Total mass of neutron and proton is 1.00727647 + 1.00866492 = 2.01594139 u

Mass defect = 2.01594139 - 2.01355321270 = 0.002388178 u = 3.965662187 x 10⁻³⁰ kg

$E=\Delta mc^{2}=3.57\times 10^{-13}{\mbox{ J }}=2.23{\mbox{ MeV}}$

2. Uranium-235 has a nuclear mass of 235.0439299 u. It contains 92 protons. What is its binding energy?

235 - 92 = 143 neutrons

Total mass of baryons is (92 x 1.00727647) + (143 x 1.00866492) = 236.9085188 u

Mass defect = 236.9085188 - 235.0439299 = 1.8645889 u = 3.096222181 x 10⁻²⁷ kg

$E=\Delta mc^{2}=2.79\times 10^{-10}{\mbox{ J }}=1.74{\mbox{ GeV}}$

3. How would you expect H-2 and U-235 to be used in nuclear reactors? Why?

H-2 is used in experimental fusion reactors, since it has a smaller nucleus than Iron-56.

U-235 is used in fission reactors, since it has a much larger nucleus than Iron-56.