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 isA. (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

Two radioactive samples of different elements (half-lives `t_1` and `t

1.	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 isA. (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» 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.

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