The rate of disintegration of a radioactivity element changes from initial value of 10,000 dpm to 2,500 dpm in 50 days . The decay constant is

Options

A. `(2500)/(10000)d^(-1)`
B. `1.386 xx 10^(-2) d^(-1)`
C. `(0.693)/(2.303)xx50s^(-1)`
D. `2.772 xx 10^(-2) d^(-1)`

Answer

D

Explanation

`N_(0)=10000` dpm, `N=2500` dpm
t=50 days
`lambda=(2.303)/(t)"log"(N_(0))/(N)=(2.303)/(50)"log"(10000)/(2500)`
`=(2.303)/(50)"log"4=(2.303xx0.6020)/(50)`
`=0.027728 "days"^(-1)`
`=2.772xx10^(-2) "days"^(-1)`