Two different radioactive isotopes, P and Q , have half-lives of 10 hours and 30 hours respectively. Initially, both isotopes contain the exact same number of active nuclei. The ratio of the activity of P to the activity of Q after 30 hours will be:

Step-by-step solution

The number of active nuclei remaining after time t is given by N = N₀ ( 1 2 )^ t T_ 1/2 . For isotope P , the number of half-lives in 30 hours is 30 10 = 3 . Remaining nuclei of P : N_P = N₀ 2^3 = N₀ 8 . For isotope Q , the number of half-lives in 30 hours is 30 30 = 1 . Remaining nuclei of Q : N_Q = N₀ 2^1 = N₀ 2 . The activity of a radioactive substance is given by A = N = 2 T_ 1/2 N . Activity of P at t = 30 hours: A_P = 2 10 N₀ 8 = N₀ 2 80 Activity of Q at t = 30 hours: A_Q = 2 30 N₀ 2 = N₀ 2 60 The ratio of th