Physics 9702 · AS & A Level · Mass defect and nuclear binding energy

Mass defect and nuclear binding energy — practice question

A uranium-238 nucleus at rest $\left(^{238}_{92}\text{U}\right)$ decays by alpha emission to form a thorium-234 nucleus $\left(^{234}_{90}\text{Th}\right)$. The emitted alpha particle has kinetic energy $4.200\,\text{MeV}$. A gamma-ray photon is emitted as well during the decay. Take the rebound kinetic energy of the thorium nucleus to be negligible. The total energy released when the uranium-238 nucleus decays is $4.274\,\text{MeV}$.
(a)[2]

State what is meant by a photon.

(b(i))[3]

Calculate the mass, in u, of the uranium-238 nuclide. Give your answer to five decimal places.

(b(ii))[3]

Determine a value for the wavelength of the gamma radiation produced in the decay of the uranium-238 nucleus.

(b(iii))[1]

The rebound kinetic energy of the thorium nucleus is, in practice, not negligible. Without doing any further calculation, explain how your answer in (b)(ii) compares with the true wavelength of the gamma radiation emitted in the decay of the uranium-238 nucleus.

(c)[2]

Gamma radiation produced in the decay of a sample of uranium-238 has one wavelength. Nuclei of cobalt-60 $\left(^{60}_{27}\text{Co}\right)$ decay by beta emission, and gamma radiation is also emitted in the process. Suggest why the gamma radiation emitted in the decay of a sample of cobalt-60 does not have a single wavelength.

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