The decay constant `(lambda)` of radium is `0.0356` per year `(1.13 xx 10^(-9)` per sec). How much time is taken to reduce
a. to `(1//10)^(th)` of the original value?
b. by `(1//10)^(th)` of the original value?

Explanation

Data supplied,
a. `N = (N_0)/(N) , " " lambda = 0.0356` per year
`t = 1/(lambda) xx 2.303 log ((N_0)/(N)) = (1 xx 2.303 xx log 10)/(0.0356) = 64.69 ` years
b. `N = (9N_0)/(10) " " :. (N_0)/N = 10/9`
`t = 1/lambda xx 2.303 log ((N_0)/(N)) = (2.303 xx log (10/9))/(0.0356)`
`= (2.303)/(0.0356) xx (log 10 - log 9) = (2.303)/(0.0356) xx 0.0458 = 2.96` years .