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 ……

Explanation

As is known, a radioactive element's decay rate is directly proportional to the number of nuclei actually present.
`:. N_0` correponds to `10^3` disintegration/sec
Half life=1sec
(i) Number of half lives in 1sec `n=t/T=1/1=1`
form `N=N_0(1/2)^n=1000(1/2)^1=500`
`:.` Number of disintegrations/sec one second
`=500`
(ii) In 3sec, `n=t/T=3/1=3`
form `N=N_0(1/2)^n=1000(1/2)^3=125`
`:.` Number of disintegrations/sec after 3 second =125.