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

`(N)/(N_(0))=e^(-lambdat)`
`therefore (2500)/(10000)=e^(-lambda xx 4)`
`therefore 1/4=e^(-4)`
`therefore e^(4lambda)=4`
`therefore 4lambda=log_(e)4`
`therefore 4lambda=log_(e)2^(2)`
`therefore 4lambda=2log_(e)2`
`therefore lambda=2/4 log_(e)2`
`therefore lambda=0.5 log_(e)2`