Radioactive disintegration is a first order reaction and it's rate depends only upon the nature of nucleus and does not depend upon external factors like temperature and pressure . The rate of radioactive disintegration (Activity) is represented as `- (dN)/(dt) = lambda N` , Where `lambda` = decay constant , N number of nuclei at time t , `N_(0)` = initial no. of nuclei.
The above equation after integration can be represented as `lambda = (2.303)/(t) "log" ((N_(0))/(N))`
Half-life period of `U^(232)` is `2.5 xx 10^(5)` years . In how much time will the amount of `U^(237)` remaining be only 25% of the original amount ?

Options

A. `2. 5 xx 10^(5)` years
B. `1.25 xx 10^(5)` years
C. `5 xx 10^(5)` years
D. `10^(6)` years

Answer

C

Explanation

`t_(1//2) = 2.5 xx 10^(5)` years , `N_(0) overset(t_(1//2)) (to) (N_0)/(2) overset(t_(1//2))(to) (N_(0))/(4) , t = 2 xx t_(1//2) = 5 xx 10^(5)`