The activity of a radioactive sample is measured as A₁ at time t₁ = 2 days and as A₂ at time t₂ = 8 days . If the ratio A₁ A₂ is 8 , the half-life of the sample is

Step-by-step solution

The activity of a radioactive sample at time t is given by A = A₀ e^ - t . The activities at times t₁ and t₂ are: A₁ = A₀ e^ - t₁ A₂ = A₀ e^ - t₂ Taking the ratio of the two activities: A₁ A₂ = e^ - t₁ e^ - t₂ = e^ (t₂ - t₁) Given t₁ = 2 days , t₂ = 8 days , and A₁ A₂ = 8 : 8 = e^ (8 - 2) 8 = e^ 6 Since 8 = 2^3 and e^ = 2^ 1 T_ 1/2 : 2^3 = 2^ 6 T_ 1/2 Equating the exponents: 6 T_ 1/2 = 3 T_ 1/2 = 2 days Answer: 2 days