A radioactive element A converts into another stable element B , half-life of A is 1.5 hrs . After time t the ratio of atoms of A and B is found to be 1: 8 , then t in hours is

Step-by-step solution

Number of atoms of A and B are as shown For A ₀ T N₀ 2 T N₀ 4 T N₀ 8 T N₀ 16 . . for B T N₀ 2 T 3 4 N₀ T 7 8 N₀ T 15 16 N₀ Ratio of atoms of A and B After one half-life, time period = N₀ 2 N₀ 2 =1 After 2 half-life, time period = N₀ 4 3 N₀ 4 = 1 3 After 3 half-life, time period = N₀ 8 7 N₀ 8 = 1 7 After 4 half-life, time period = N₀ 16 15 N₀ 16 = 1 15 As 1 7 < 1 8 < 1 15 ; ratio of A: B becomes 1 8 sometime between 3 half-lifes to 4 half -lifes. . So, ratio becomes 1: 8 after 3 1.5 hrs but earlier than 4 1.5 hours.