(a) Show that if the decay rate is R 0 at time t 0 and R 1 at some later time t 1 , the decay constant is given by t 1 1 ln(R 0 R 1 ) and the half life is given by t 1 2 0 693t 1 ln(R 0 R 1 ) (b) Use these results to find the decay constant and the half life if the decay rate is 1200 Bq at t 0 and 800 Bq at t 1 60 s

Question: (a) Show that if the decay rate is R 0 at time t = 0 and R 1 at some later time t 1 ,

(a) Show that if the decay rate is R₀ at time t = 0 and R₁ at some later time t₁, the decay constant is given by λ = t₁^-1 ln(R₀/R₁) and the half-life is given by t_1/2 = 0.693t₁/ln(R₀/R₁).

(b) Use these results to find the decay constant and the half-life if the decay rate is 1200 Bq at t = 0 and 800 Bq at t₁ = 60 s.

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