Half-life of a radioactive substance is 18 minutes. The time interval between its 20 % decay and 80 % decay in minutes is

Step-by-step solution

After n half-life, the numbers of atom left undecayed is given by, aligned & N=N₀ ( 1 2 )^n & n= t T_ 1 2 or N=N₀ ( 1 2 )^ t T_ 1 / 2 aligned For 20 % decay of radioactive substance, N=N₀- 20 100 N₀=0.8 N₀ For 80 % decay of radioactive substance, From Eqs. (i) and (ii), we get 4= ( 1 2 )^ t₁-t₂ 18 Taking log on the both sides, we get aligned 4 & = ( 1 2 )^ t₁-t₂ 18 2^2= 2^ ( t₂-t₁ 18 ) 2 & = t₂-t₁ 18 t₂-t₁=36 ~min aligned