Two radioactive samples P and Q initially contain the same number of undecayed nuclei. The half-life of sample P is 3 hours. After 12 hours, the ratio of the number of undecayed nuclei of P to that of Q is 1 : 8 . The half-life of sample Q is

Step-by-step solution

Let the initial number of nuclei for both samples be N₀ . The number of undecayed nuclei of P after t = 12 hours is: N_P = N₀ ( 1 2 )^ t T_P = N₀ ( 1 2 )^ 12 3 = N₀ ( 1 2 )^4 = N₀ 16 We are given that N_P N_Q = 1 8 . Therefore, N_Q = 8 N_P = 8 ( N₀ 16 ) = N₀ 2 The number of undecayed nuclei of Q after 12 hours is also given by: N_Q = N₀ ( 1 2 )^ 12 T_Q Equating the two expressions for N_Q : N₀ 2 = N₀ ( 1 2 )^ 12 T_Q ( 1 2 )^1 = ( 1 2 )^ 12 T_Q 12 T_Q = 1 T_Q = 12 hours. Answer: 12 hours