A-Level Physics October/November 2024 Q9(a)(iii): Determine the activity of 2.1 × 10⁻¹²kg of fluorine-18.

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  Step 1: Calculate the number of nuclei (N)

  The mass of a single fluorine-18 nucleus is its mass number (18) multiplied by the atomic mass unit ($u$).

  Mass of one nucleus, $m = 18u = 18 \times 1.66 \times 10^{-27}$ kg

  The total number of nuclei, $N$, in a sample of mass $M = 2.1 \times 10^{-12}$ kg is given by:

  $N = \frac{\text{Total mass}}{\text{Mass of one nucleus}} = \frac{M}{18u}$

  $N = \frac{2.1 \times 10^{-12}}{18 \times 1.66 \times 10^{-27}}$

  $N = 7.028... \times 10^{13}$

  Step 2: Calculate the activity (A)

  The activity $A$ is given by the formula $A = \lambda N$, where $\lambda$ is the decay constant. From the previous part of the question, $\lambda = 1.05 \times 10^{-4} \text{ s}^{-1}$.

  $A = (1.05 \times 10^{-4}) \times (7.028... \times 10^{13})$

  $A = 7.379... \times 10^9$ Bq

  $A \approx 7.4 \times 10^9$ Bq (to 2 s.f.)

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  How the marks are awarded

  • C1 — Stating the correct formula to find the number of nuclei (N), which involves dividing the total mass of the sample by the mass of a single fluorine-18 nucleus (18u).
  • C1 — Correctly substituting the given mass (2.1 × 10⁻¹² kg) and the mass of a single nucleus (18 × 1.66 × 10⁻²⁷ kg) to calculate the number of nuclei, N.
  • A1 — Using the activity formula A = λN with the calculated value of N and the decay constant to find a final answer of 7.4 x 10⁹ Bq.

  Common mistakes

  • Using the mass number (18) alone instead of the mass in kg (18 × u), leading to an incorrect calculation for N e.g., N = (2.1 × 10⁻¹²) / 18.
  • Mixing units when using Avogadro's constant, for example, using the mass in kg with the molar mass in g/mol without conversion.
  • Using the atomic number (9) instead of the mass number (18) for the mass of the nucleus.
  • Making a calculation error when dealing with powers of ten, or a rounding error that leads to an incorrect final answer.

  Examiner tip: For multi-step calculations, clearly lay out each stage with the relevant formula before substituting values to minimise errors and secure method marks.

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