devarshi-dt-logo

Question:

Two radioactive materials A and B have decay constants 10λ and λ, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1/e after a time:

19λ

110λ

1110λ

1111λ

Solution:

N1 = N0e^(-10λt)
N2 = N0e^(-λt)
1/e = N1/N2 = e^(-10λt)/e^(-λt) = e^(-9λt)
→ -9λt = 1
t = 1/9λ