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

Mass defect and nuclear binding energy — practice question

A uranium-238 nucleus ($^{238}_{92}\text{U}$) that is at rest decays by alpha emission to form a thorium-234 nucleus ($^{234}_{90}\text{Th}$). The alpha particle emitted has kinetic energy $4.200\,\text{MeV}$. A gamma-ray photon is emitted in the decay as well. Take the recoil kinetic energy of the thorium nucleus to be negligible. Table 8.1 lists the nuclide masses involved in the decay reaction, but the mass of the uranium-238 nuclide is not given. The energy released in the decay of uranium-238 is $4.274\,\text{MeV}$.
(a)[2]

State the meaning of a photon.

(b(i))[3]

Calculate the mass, in $\text{u}$, 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 released in the decay of the uranium-238 nucleus.

(b(iii))[1]

In practice, the recoil kinetic energy of the thorium nucleus is not negligible. Without doing any more calculation, explain how your answer in (b)(ii) compares with the true wavelength of the gamma radiation emitted when uranium-238 decays.

(c)[2]

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

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