The activity of a radioactive element decreases in 10 years to 1 / 5 of initial activity A 0 . After further next 10 years, its activity will be

Step-by-step solution

∵ The activity of a radioactive sample, A   =   A 0 ( 1 2 ) t t 1 2 Where, A 0 = initial activity. In the first case, A 0 5   =   A 0 ( 1 2 ) 10 t 1 2 1 5   =   ( 1 2 ) 10 t 1 2 ...(i) In the second case, A   =   A 0 ( 1 2 ) 20 t 1 2 ...(ii) From Equations. (i) and (ii), we get 1 / 5 A   =   ( 1 2 ) 20 t 1 2 A 0 ( 1 2 ) 20 t 1 2 ⇒ 1 5 A = 1 A 0 1 2 10 t 1 2 ⇒ 1 5 A = 1 A o 5 [from Equation (i)] ∴ A = A 0 5 × 5 = A 0 25