A radioactive element X converts into another stable element Y. Half life of X is 2 hrs . Initially only X is present. After time t , the ratio of atoms of X and Y is found to be 1: 4, then t in hours is

Step-by-step solution

Let N ₀ be the number of atoms of X at time t =0 Then at t =4 hrs (two half lives) N _ x = N ₀ 4 and N _ y = 3 ~N ₀ 4 N _ x / N _ y =1 / 3 and at t =6 hrs (three half lives) N _ x = N ₀ 8 and N _ y = 7 ~N ₀ 8 or N _ x N _ y = 1 7 The given ratio 1 4 lies between 1 3 and 1 7 Therefore, t lies between 4 hrs and 6 hrs .