The half life of a radioactive substance is ( 20 ) minutes. The time taken between ( 50 % ) decay and ( 87.5 % ) decay of the substance will be

Step-by-step solution

Given, half-life of radioactive substance, ( T_ 1 2 =20 ) minutes Using [ array l N=N₀ e^ - t N N₀ =e^ - t - t= ( N N₀ ) t=- 1 ( N N₀ ) array ] We know ( 1 = T_ 1 / 2 2 ) [ t= - 2 T_ 1 / 2 ( N N₀ ) ] If ( t₁ ) is time for ( 50 % ) decay and ( t₂ ) is time for ( 87.5 % ) decay, we have [ array l t₂-t₁=- T_ 1 / 2 2 ( N₂ N₀ )+ T_ 1 / 2 2 ( N₁ N₀ ) = T_ 1 / 2 2 (- N₂+ N₀+ N₁- N₀ )= T_ 1 / 2 2 ( N₁- N₂ ) = T_ 1 / 2 2 ( N₁ N₂ ) array ] Substituting the values, we get ( t₂-t₁= 20 ~min 0.693 ( 50 12.5 )= 20 0.693 4=40 ) mi