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4 marksCapacitors

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

Figure 6 shows a circuit modeling decay of Francium-221 (half-life 288 s). Switch S1 is initially at terminal a.

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 needed to model the radioactive decay of Francium-221.

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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)(ii)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…[1 mark]
  4. 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]
  5. 6(c)(i)Describe the change in the voltages across R and C, both of which initially had no voltage across them.[2 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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