A radioactive element has rate of disintegration `10,000` disintegrations per minute at a particular instant. After four minutes it becomes `2500` disintegrations per minute. The decay constant per minute is

Options

A. `0.2 log_(e) 2`
B. `0.5 log_(e) 2`
C. `0.6 log_(e) 2`
D. `0.8 log_(e) 2`

Answer

B

Explanation

Given `N_(0) = 10,000` disintegeration/min
`N = 2500` disintegeration/min
`t = 4` min
From the radioactive decay law, we have
`(N)/(N_(0)) = e^(-lambdat)`
`:. (2500)/(10000) = e^(-lambdatxx 4)`
`rArr 1/4 = e^(-4lambda) rArr e^(4lambda) = 4`
`rArr 4 lambda = log_(e) 4 rArr 4 lambda = log_(e) 2^(2)`
`rArr 4 lambda = 2 log_(e) 2`
`lambda = 2/4 log_(e) 2`
`:. lambda = 0.5 log_(e) 2`