A radioactive sample `S_(1)` having an activity `5 mu Ci` has twice the number of inucle as another sample `S_(2)` which has as activity of `10 mu Ci` . The half lives of `S_(1) `and `S_(2) `can beA. `20 years and 5 years , respectively `B. `20 years and 10 years , respectively `C. `10 years eatch `D. `5 years eatch `

A radioactive sample `S_(1)` having an activity `5 mu Ci` has twice th

1.	A radioactive sample `S_(1)` having an activity `5 mu Ci` has twice the number of inucle as another sample `S_(2)` which has as activity of `10 mu Ci` . The half lives of `S_(1) `and `S_(2) `can beA. `20 years and 5 years , respectively `B. `20 years and 10 years , respectively `C. `10 years eatch `D. `5 years eatch `
Answer» Correct Answer - A Sample S- 1 Activity `5 nu Ci` No of nucle `N_(1) = 2N` `- ((dN)/(dt)0 _(1) = lambda_(1) N_(1)` rArr - 5 = lambda_(1) xx 2N ` ….(i) From (i) and (ii) `(5)/(10) = (lambda_(1) xx 2 N)/(lambda_(2) + N)` rArr (lambda_(1))/(lambda_(2)) = (1)/(4)` `rArr (T_(1//2)_(2))/((T_(1//2) _(1)) = (1)/(4) [(:. lambda prop (1)/(T_(1//2))]` Sample S - 2 `10 mu Ci` `N_(2) = N` `- ((dN)/(dt)) _(2) = lambda_(2) N_(2)` ` - 10 = lambda_(2) prop N` ....(ii) `

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