In a radioactive material the activity at time t₁ is R₁ and at a later time t₂ , it is R₂ . If the decay constant of the material is , then

Step-by-step solution

The decay rate R of a radioactive material is the number of decays per second. From radioactive decay law. - d N d t N or - d N d t = N Thus, R=- d N d t Or R= N or R= N₀ e^ - t ..(i) where R₀= N₀ is the activity of the radioactive material at time t=0 . At time t₁, R₁=R₀ e^ - t₁ At time t₂, R₂=R₀ e^ - t₂ Dividing Eq. (ii) by (iii), we have or array l R₁ R₂ = e^ - t₁ e^ - t₂ =e^ - (t₁-t₂ ) R₁=R₂ e^ - (t₁-t₂ ) array