A-Level Physics May/June 2025 Q7(b)(i): A nucleus X has 14 nucleons and p protons. The ratio of charge to mass for nucleus X is…

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  The charge of nucleus X is the number of protons, $p$, multiplied by the elementary charge, $e$. Charge $= p \times e$

  The mass of nucleus X is the number of nucleons, 14, multiplied by the unified atomic mass unit, $u$. Mass $= 14 \times u$

  The ratio of charge to mass is given: $\frac{\text{Charge}}{\text{Mass}} = \frac{p \times e}{14 \times u} = 4.1 \times 10^7 \text{ Ckg}^{-1}$

  Rearranging the equation to solve for $p$: $p = \frac{4.1 \times 10^7 \times 14 \times u}{e}$

  Substituting the values for $u$ ($1.66 \times 10^{-27}$ kg) and $e$ ($1.60 \times 10^{-19}$ C): $p = \frac{4.1 \times 10^7 \times 14 \times (1.66 \times 10^{-27})}{1.60 \times 10^{-19}}$

  $p = \frac{9.5404 \times 10^{-19}}{1.60 \times 10^{-19}}$ $p = 5.96275$

  Since the proton number must be an integer, we round to the nearest whole number. $p = 6$

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  How the marks are awarded

  • C1 — Correctly setting up the initial equation for the charge-to-mass ratio, by expressing charge as $(p \times e)$ and mass as $(14 \times u)$ and equating it to $4.1 \times 10^7$.
  • C1 — Correctly rearranging the formula to make $p$ the subject and showing the full substitution of values for the elementary charge ($e$) and the unified atomic mass unit ($u$).
  • A1 — Calculating the final answer and stating it as the integer 6, correctly interpreting that the proton number must be a whole number.

  Common mistakes

  • Using the mass of a proton or neutron (in kg) instead of the unified atomic mass unit (u), which represents the average mass of a nucleon in a nucleus.
  • Confusing the number of nucleons (14) with the number of neutrons, or using 'p' for the mass calculation.
  • Leaving the final answer as a decimal (e.g., 5.96) instead of rounding to the nearest integer, failing to recognise that the proton number must be a whole number.
  • Calculation errors due to incorrect entry of powers of ten into a calculator.

  Examiner tip: Always express physical ratios by first writing down the algebraic formula for each component (e.g., charge = $p \times e$, mass = $A \times u$) before substituting any numerical values.

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