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 Mi=35.70 uM_i=35.70\,\mathrm{u} Use 1 u c2=931.5 MeV1\,\mathrm{u}\,c^2=931.5\,\mathrm{MeV}

040801201602002400246810nucleon number, Abinding energy per nucleon / MeV(1, 0.0)(12, 7.7)(24, 8.0)(36, 8.5)(56, 8.8)(100, 8.4)(240, 7.6)

Here, Δm\Delta m is the mass equivalent of the increase in total binding energy. What is Δm/Mi\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 MeV12(7.7)+24(8.0)=284.4\,\mathrm{MeV} and the final total is 36(8.5)=306.0 MeV36(8.5)=306.0\,\mathrm{MeV} Thus the increase is 21.6 MeV21.6\,\mathrm{MeV} and

ΔmMi=21.6(931.5)(35.70)=6.50×10−4.\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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