A-Level Physics May/June 2024 Q9(b)(i): For the polonium-212 nucleus, determine: (i) the mass defect Δm, in kg

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  The mass defect, $\Delta m$, is the difference between the total mass of the individual constituent nucleons and the mass of the nucleus.

  For Polonium-212 ($^{212}_{84}$Po): Number of protons, $Z = 84$ Number of neutrons, $N = A - Z = 212 - 84 = 128$

  1. Calculate the total mass of the constituent nucleons: Mass of protons = $84 \times 1.007276 \text{ u} = 84.611184 \text{ u}$ Mass of neutrons = $128 \times 1.008665 \text{ u} = 129.10912 \text{ u}$ Total mass of constituents = $84.611184 + 129.10912 = 213.720304 \text{ u}$

  2. Calculate the mass defect in atomic mass units (u): $\Delta m = (\text{Total mass of constituents}) - (\text{Mass of nucleus})$ $\Delta m = 213.720304 \text{ u} - 211.942749 \text{ u}$ $\Delta m = 1.777555 \text{ u} \approx 1.778 \text{ u}$

  3. Convert the mass defect to kilograms (kg): $\Delta m = 1.777555 \times (1.66 \times 10^{-27} \text{ kg})$ $\Delta m = 2.9507413 \times 10^{-27} \text{ kg}$

  4. Final answer to 3 significant figures: $\Delta m = 2.95 \times 10^{-27} \text{ kg}$

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  How the marks are awarded

  • C1 — For correctly setting up the calculation for mass defect by finding the total mass of the 84 protons and 128 neutrons and subtracting the given mass of the polonium-212 nucleus. This is shown by the expression {[(84 × 1.007276) + (128 × 1.008665)] – 211.942749}.
  • C1 — For correctly converting the calculated mass defect from atomic mass units (u) to kilograms (kg) by multiplying by the conversion factor 1.66 × 10⁻²⁷.
  • A1 — For the final, correct answer of 2.95 × 10⁻²⁷ kg, stated to an appropriate number of significant figures (3 s.f.).

  Common mistakes

  • Incorrectly determining the number of neutrons, for example by using the nucleon number (212) or proton number (84) instead of calculating 212 - 84 = 128.
  • Reversing the subtraction, i.e., calculating (mass of nucleus) - (mass of constituents), which results in a physically incorrect negative mass defect.
  • Forgetting the final step of converting the mass defect from atomic mass units (u) to kilograms (kg) as required by the question.
  • Using the mass of a hydrogen atom instead of a proton, or mixing up the proton and neutron masses during the calculation.

  Examiner tip: Always write out the full definition for mass defect (mass of parts minus mass of whole) and clearly calculate the number of each nucleon before substituting values to prevent calculation or conceptual errors.

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