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

Options

A. `0.2 ln2`
B. `0.2 ln2`
C. `0.1 ln2`
D. `0.8 ln2`

Answer

A

Explanation

As rate of disintegration is proportional to the number of atoms actually present, therefore,
`N_(0)=5000, N=1250, t=" 5 min"`
As `N=N_(0)e^(-lambdat)`
`therefore" "ln=(N)/(N_(0))=-lambdat, ln((1250)/(5000))=-lambdat,ln((1)/(4))=-lambdaxx5`
`-2ln2 = -lambdaxx5, lambda=0.4 ln 2`