A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 min, the rate becomes 1250 disintegration per minute. Then, its decay constant (per minute) is

Options

A. 0.8 `log_(e)` 2
B. 0.4 `log_(e)` 2
C. 0.2 `log_(e)` 2
D. 0.1 `log_(e)` 2

Answer

B

Explanation

Given R = 1250, `R_(0)` = 5000 and t = 5 min
Hence `R = R_(0)e^(-lambda t)`
1250 = 5000 `e^(-lambda xx 5)`
`lambda = 0.4 log_(e)2`