IB Physics HL E.3 Radioactive decay questions

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Question 1

Multiple choiceHard1 mark

A hypothetical nuclear reaction combines nuclei with nucleon numbers 12 and 24 to form a nucleus with nucleon number 36. The combined initial rest mass is $M_i=35.70\,\mathrm{u}$ Use $1\,\mathrm{u}\,c^2=931.5\,\mathrm{MeV}$

Here, $\Delta m$ is the mass equivalent of the increase in total binding energy. What is $\Delta m/M_i$

Show answer and explanation

Answer: B. The graph gives binding energy per nucleon, so multiply each value by its nucleon number to obtain total binding energy. The initial total is $12(7.7)+24(8.0)=284.4\,\mathrm{MeV}$ and the final total is $36(8.5)=306.0\,\mathrm{MeV}$ Thus the increase is $21.6\,\mathrm{MeV}$ and

\frac{\Delta m}{M_i}=\frac{21.6}{(931.5)(35.70)}=6.50\times10^{-4}.

A: subtracts the per-nucleon values without weighting them by nucleon number, giving a negative result.
C: uses the initial total binding energy rather than its increase.
D: converts the energy increase to a mass in u but does not divide by the initial mass.
Remember: total binding energy is nucleon number multiplied by binding energy per nucleon.

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