Question

Two radioactive samples of different elements (half-lives `t_1` and `t_2` respectively) have same number of nuclei at `t=0`. The time after which their activities are same is
A. (a) `(t_1t_2)/(0.693(t_2-t_1))1n(t_2)/(t_1)`
B. (b) `(t_1t_2)/(0.693)1n(t_2)/(t_1)`
C. (c) `(t_1t_2)/(0.693(t_1+t_2))1n(t_2)/(t_1)`
D. (d) None of these

Answer 1

Correct Answer - A
`R_1=R_2`
`R_(01)e^(-lambda_1t)=R_(02)e^(-lambdat)`
`:.` `lambda_1N_0e^(-lambda_1t)=lambda_2N_0e^(-lambda_2t)` …(i)
`lambda_1N_0e^(-lambda_1t)=lambda_2N_0e^(-lambda_2t)` …(i)
`lambda_1=(1n2)/(t_1)=0.693/t_1`
`lambda_2=(0.693)/(t_2)`
Substituting these values in Eq. (i), we can get the t.