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1 markCapacitors

CAPE Physics Unit 2 · 2013 · Paper 2 · Question 6(b)(ii)

A capacitor C initially charged to V0 discharges through R according to V = V0 exp(-t/τ).

If the capacitive discharge is used to model radioactive decay, where voltage is the analogue of number of particles, what would be the relationship between time constant, τ, and decay constant, λ?

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Other parts of this question

  1. 6(a)Write the equation describing this decay.[1 mark]
  2. 6(b)(i)Write the equation expressing τ in terms of R and C.[1 mark]
  3. 6(b)(iii)Given that t_1/2 is the half-life of a radioactive sample, use the decay equation from Part (a) to show that t_1/2 = 0.69 / λ.[3 marks]
  4. 6(c)(i)Describe the change in the voltages across R and C, both of which initially had no voltage across them.[2 marks]
  5. 6(c)(ii)After a sufficiently long time, voltages across R and C become stable and S1 is switched to terminal b to model decay. Using R = 1 MΩ, calculate the value of C…[4 marks]
  6. 6(d)(i)State what is meant by the term 'activity' of a radioactive nucleus and write its expression in mathematical form.[1 mark]
  7. 6(d)(ii)A sample of Francium-221 contains 10^12 atoms. Calculate its activity.[2 marks]

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