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

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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 m c^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 m c^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.