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

Mass defect and nuclear binding energy — practice question

A possible nuclear reaction 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 a mass of $1.00\,\text{u}$ has an energy equivalent of $934\,\text{MeV}$.

(b(i))[2]

Use the information in Fig. 12.1 to calculate the binding energy per nucleon for a uranium-235 nucleus ($^{235}_{92}\text{U}$). Fill in Fig. 12.1.

(b(ii))[1]

An isotope of the element rutherfordium has nucleon number 267. State whether its binding energy per nucleon will be greater than, equal to or less than the binding energy per nucleon of uranium-235.

(c)[2]

Calculate the total energy, in MeV, released in this nuclear reaction.

(d)[3]

All of the nuclei in $1.2 \times 10^{-7}\,\text{mol}$ of uranium-235 undergo this reaction over a period of $25\,\text{ms}$. Calculate the average power released during $25\,\text{ms}$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Therefore, $E=(3.0\times10^8)^2(1.66\times10^{-27})$

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