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

Mass defect and nuclear binding energy — practice question

One nuclear reaction that may occur is $^{235}_{92}\text{U} + ^{1}_{0}\text{n} \rightarrow ^{95}_{42}\text{Mo} + ^{139}_{57}\text{La} + 2\,^{1}_{0}\text{n} + 7\,^{0}_{-1}\text{e}$. The nuclei data for this reaction are shown in Fig. 12.1.
(a)[2]

Show that the energy equivalent to a mass of $1.00\,\text{u}$ is $934\,\text{MeV}$.

(b(i))[2]

Use data from Fig. 12.1 to calculate the binding energy per nucleon of a nucleus of uranium-235 $\left(^{235}_{92}\text{U}\right)$. Finish Fig. 12.1.

(b(ii))[1]

The nucleon number of an isotope of the element rutherfordium is $267$. State whether the binding energy per nucleon of this isotope will be greater than, equal to or less than the binding energy per nucleon of uranium-235.

(c)[2]

Calculate the total energy, in $\text{MeV}$, released in this nuclear reaction.

(d)[3]

The nuclei in $1.2 \times 10^{-7}\,\text{mol}$ of uranium-235 all undergo this reaction in a time of $25\,\text{ms}$. Calculate the average power release during the time of $25\,\text{ms}$.

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This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: The relation is $E = mc^2$.

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