Question

Radioactive material 'A' has decay constant '8λ' and material 'B' has decay constant 'λ'. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be 1/e?(a) $\frac{1}{7\lambda}$(b) $\frac{1}{8\lambda}$(c) $\frac{1}{9\lambda}$(d) $\frac{1}{\lambda}$

Answer 1

Answer:

Explanation:

=> Steps are given here to calculate the time :

=> Radioactive decay formula:  

N = N ₀e^-λt

=>Thus, Radioactive decay N_A and N_B for both the materials A and B:

N_A = N ₀e^-λ_At ...(1)

N_B = N ₀e^-λ_Bt ...(2)

=> By dividing eq (1) by (2) and equate it to 1/e, we get

N_A/N_B = 1/e = e^-(λ_A - λ_B)t

=> After substituting Decay constant for both the material, we get the value of t:

t = 1 / 8λ - λ

t = 1 / 7λ

Therefore,  after 1 / 7λ time, the ratio of number of nuclei of material 'B' to that 'A' will be 1/e.