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 be

Options

A. 20 years and 5 years , respectively
B. 20 years and 10 years , respectively
C. 10 years each
D. 5 years each

Answer

A

Explanation

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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