Question

The activity of a sample of radioactive material is A₁ at time t₁ and A₂ at time t₂ (t₂ > t₁). Its mean life is T.

(a) A₁ t₁ = A₂ t₂

(b) A₁ - A₂/t₂ - t₁ = constant

(c) A₂ = A₁ e^{(t₁ - t₂/T)}

(d) A₂ = A₁ e^(t₁/Tt₂)

Answer 1

Correct Answer is: (c) A₂ = A₁ e^{(t₁ - t₂/T)}

Let A₀ = initial activity.

Then, A₁ = A₀ e ^-λt₁ and A₂ = A₀ e ^-λt₂. Also, λ = 1/T

∴ A₂/A₁ = e ^-λt₂ / e ^-λt₁  e(-λt₂ + λt₁) 

or A₂ = A₁ e ^{λ(t₁ - t₂)} = A₁ e^{(t₁ - t₂)/T.}