Two identical samples (same material and same amout) P and Q of a radioactive substance having mean life T are observed to have activities `A_P` and `A_Q` respectively at the time of observation. If P is older than Q, then the difference in their age isA. (a) `T 1n ((A_P)/(A_Q))`B. (b) `T 1n ((A_Q)/(A_P))`C. (c) `T((A_P)/(A_Q))`D. (d) `T((A_Q)/(A_P))`

Two identical samples (same material and same amout) P and Q of a radi

1.	Two identical samples (same material and same amout) P and Q of a radioactive substance having mean life T are observed to have activities `A_P` and `A_Q` respectively at the time of observation. If P is older than Q, then the difference in their age isA. (a) `T 1n ((A_P)/(A_Q))`B. (b) `T 1n ((A_Q)/(A_P))`C. (c) `T((A_P)/(A_Q))`D. (d) `T((A_Q)/(A_P))`
Answer» Correct Answer - B `A_P=A_0e^(-lambdat_1)` `A_Q=A_0e^(-lambdat_2)` `lambda_(t_1)=1n(A_0//A_P)` `:.` `t_1=1/lambda1n(A_0//A_P)=T1n(A_0//A_P)` Similarly, `t_2=T1n(A_0//A_Q)` `:.` `t_1-t_2=T1n((A_Q)/(A_P))`

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