Two samples A and B contain equal amount of radioactive substances. If ( 1 8 )^ th of sample A and ( 1 128 )^ th of sample B, remain after 9 hours, then the ratio of half life period of B to that of A is

Step-by-step solution

Let the initial amount of both samples be N₀ . The amount of radioactive substance remaining after time t is given by N = N₀ ( 1 2 )^ t T_ 1/2 . For sample A, after t = 9 hours: N₀ 8 = N₀ ( 1 2 )^ 9 T_A ( 1 2 )^3 = ( 1 2 )^ 9 T_A 9 T_A = 3 T_A = 3 hours. For sample B, after t = 9 hours: N₀ 128 = N₀ ( 1 2 )^ 9 T_B ( 1 2 )^7 = ( 1 2 )^ 9 T_B 9 T_B = 7 T_B = 9 7 hours. The ratio of the half-life period of B to that of A is: T_B T_A = 9 7 3 = 3 7 Answer: 3:7