Radioactive material A has decay constant 8 λ and material B has decay constant λ . Initially they have the same number of nuclei. After what time, the ratio of number of nuclei of material A to that B will be 1 e ?

Step-by-step solution

Number of undecayed nuclei present at time t is N = N 0 e - λ t , here N 0 is the number of radioactive nuclei in sample at time t = 0 . So for A ,   N A = N 0 e - 8 λ t for B ,   N B = N 0 e - λ t given N A N B = 1 e Then N A N B = N 0 e - 8 λ t N 0 e - λ t 1 e = e - 7 λ t - 1 = - 7 λ t t = 1 7 λ