Question

Two radioactive materials A and B have decay constants 25λ and 16λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be ‘e’ after a time $\frac{1}{(aλ)}$. The value of a is _____.

Answer 1

NA=N0e−25λt
NB=N0e−16λt
$\frac{N_B}{N_A}$=e9λt
$t=\frac{1}{9λ}$
Given that, ratio of the number of nuclei of B to that of A will be e after a time $\frac{1}{9λ}$
On comparing, a = 9
So, the answer is 9.