Question-32 Two radioactive materials A and B having decay constant 7\lambda and \lambda respectively, initially have same number of nuclei. The time taken to have the ratio of number of nuclei of material B to that of A as e is
(A) \frac{1}{\lambda}
(B) \frac{1}{6\lambda}
(C) \frac{1}{7\lambda}
(D) \frac{1}{8\lambda}
Answer : (B)
Explanation:
Given: λ_A = 7λ, λ_B = λ, (N_B)_0 = (N_A)_0 = N_0
For, N_B = \frac{N_A}{e} ;
N_0 e^{-\lambda t} = \frac{N_0 e^{-7\lambda t}}{e}∴ -\lambda t = -7\lambda t - 1
∴ 6\lambda t = -1
∴ t = \frac{-1}{6\lambda}
Negative sign here, indicates process of disintegration,
∴ t = \frac{1}{6\lambda}