The activity of a radioactive sample is measured as N ₀ counts per minute at t =0 and N ₀ / e counts per minute at t =5 ~min . The time (in minute) at which the activity reduces to half its value is

Step-by-step solution

Fraction remains after n half lives N N ₀ = ( 1 2 )^ n = ( 1 2 )^ t / T Given N = N ₀ e N ₀ eN ₀ = ( 1 2 )^ 5 / T or 1 e = ( 1 2 )^ 5 / T Taking on both sides, we get aligned 1- e & = 5 ~T 1 2 -1 & = 5 ~T (- 2) T & =5 _ e 2 aligned Now, let t ^ be the time after which activity reduces to half aligned ( 1 2 ) & = ( 1 2 )^ t ^ / 5 _ e 2 t ^ & =5 _ e 2 aligned