In a radioactive material the activity at time t₁ , is A₁ and at a later time t₂ , it is A₂ . If the decay constant of the material is , then

Step-by-step solution

From radioactive decay law, - d N d t N or - d N d t = N Thus, A=- d N d t or A= N A= N₀ e^ - t Where, A₀= N₀ is the activity of the radioactive material at time, t=0 At time, t₁ A₁=A₀ e^ - t₁ At time, t₂ A₂=A₀ e^ - t₂ On dividing Eq. (ii) by Eq. (iii), we have aligned A₁ A₂ & = e^ - t₁ e^ - t₂ =e^ - (t₁-t₂ ) A₁ & =A₂ e^ - (t₁-t₂ ) aligned