A and B are two substances undergoing radioactive decay in a container. The half life of A is 15 min and that of B is 5 min . If the initial concentration of B is 4 times that of A and they both start decaying at the same time, how much time will it take for the concentration of both of them to be same? ________min.

Step-by-step solution

For a first order reaction: ⇒ [ A ] t = [ A ] 0 e - kt For A : Let [ A ] t be y and [ A ] 0 be x For a first order reaction: ∴ k = ln 2 t 1 / 2 = ln 2 15   min ⇒ y = xe - kt = xe - ln 2 15 t ....(1) Similarly For B: [ B ] t = [ B ] 0 e - kt Let [ B ] t = y ; [ B ] 0 = 4 x ; k = ln 2 t 1 / 2 = ln 2 5   min ⇒ y = 4 xe - ln 2 5 t ....(2) Equating equation(1) and (2) we get: ⇒ xe - ln 2 15 t = 4 xe - ln 2 5 t ⇒ t × ln   2 5 - ln   2 15 = ln   4 ⇒ t