Substances P and Q undergo first-order radioactive decay in a container. The initial concentration of P is 16 times that of Q. The half-life of P is 10 min . If both start decaying at the same time and after exactly 60 min , their concentrations become equal, the half-life of Q is ________ min.

Step-by-step solution

For a first-order decay, the concentration at time t is given by: [A]_t = [A]₀ ( 1 2 )^ t t_ 1/2 For substance P: [P]_t = [P]₀ ( 1 2 )^ 60 10 = [P]₀ ( 1 2 )^6 = [P]₀ 64 Given that [P]₀ = 16[Q]₀ , we can substitute this into the equation for P: [P]_t = 16[Q]₀ 64 = [Q]₀ 4 For substance Q: [Q]_t = [Q]₀ ( 1 2 )^ 60 t_ 1/2, Q Since the concentrations are equal at 60 min , [P]_t = [Q]_t : [Q]₀ 4 = [Q]₀ ( 1 2 )^ 60 t_ 1/2, Q ( 1 2 )^2 = ( 1 2 )^ 60 t_ 1/2, Q Equating the exponents: 60 t_ 1/2, Q = 2 t_ 1/2, Q = 30 min Answ