Question

The radioactive decay rate of a radioactive element is found to be `10^(3) ` disintegration per second at a cartain time . If the half life of the element is one second , the dacay rate after one second ….. And after three second is ……

Answer 1

It is known that radioactive decay rate is directly proportional to the number of nuclei left. `N_(0)` corresponds to `10^(3)` (disintegrations/sec).
As half life T=1sec. , therefore
(i) no. of half lives in 1 sec., `n=1`
As `N=N_(0)(1/2)^(n) :. N=1000(1/2)^(1)=500 :.` No. of disintegrations/sec. after one sec. `=500`
(ii) no,. of half lives in `3 sec. n=3/1=3`
As `N=N_(0)(1/2)^(n) :. N=1000(1/2)^(3)=1000/8=125`
`:.` No. of disintegration/sec. after three sec.`=125`