A-Level Physics May/June 2025 Q7(b)(ii): Nucleus X undergoes β⁻ decay to form nucleus Z. Complete the equation representing this…

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  In β⁻ decay, a neutron transforms into a proton, an electron (the β⁻ particle), and an electron antineutrino.

  The general form of the decay is: ${^A_Z}X \rightarrow {^A_{Z+1}}Z + {^0_{-1}}e + {^0_0}\bar{\nu}_e$

  From the previous part of the question, nucleus X has a proton number of 6 and a mass number of 14. We apply the conservation laws:

  1. Conservation of Mass Number (A): The mass number does not change in β⁻ decay. The mass number of Z is 14.

  2. Conservation of Proton Number (Z): The proton number increases by 1. The proton number of Z is $6 + 1 = 7$.

  3. Particles Emitted: A β⁻ particle (electron) and an electron antineutrino are emitted.

  Therefore, the complete equation is:

  $^{14}_{6}\text{X} \rightarrow ^{14}_{7}\text{Z} + ^{0}_{-1}\text{e} + ^{0}_{0}\bar{\nu}_e$

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  How the marks are awarded

  • B1 — The mass number of nucleus Z is correctly written as 14 in the final equation.
  • B1 — The proton number of nucleus Z is correctly calculated and written as 7, based on the proton number of X being 6.
  • B1 — Both the beta particle ($^{0}_{-1}\text{e}$) and the electron antineutrino ($^{0}_{0}\bar{\nu}_e$) are correctly identified with their respective mass and proton numbers.

  Common mistakes

  • Omitting the electron antineutrino ($\bar{\nu}_e$) from the products, which is required to conserve lepton number.
  • Incorrectly calculating the proton number of Z as 5 (by subtracting 1) instead of 7, which would be characteristic of positron emission or electron capture.
  • Incorrectly changing the mass number of Z, for example to 13. The mass number is conserved in beta decay.
  • Writing a neutrino ($\nu_e$) instead of an antineutrino ($\bar{\nu}_e$); in β⁻ decay, an anti-lepton is produced alongside the lepton (electron).

  Examiner tip: Always check that both the total mass number (top number) and the total proton number (bottom number) are conserved on both sides of any nuclear decay equation.

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