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. 0.8 ln 2
B. 0.4 ln 2
C. 0.2 ln 2
D. 0.1 ln 2

Answer

B

Explanation

According to activity law,
`R=R_(0)e^(-lambdat)=(R_(0))/(R )=e^(lambdat)`
Taking the logarithm on both sides, we get
`lambdat=ln((R_(0))/(R )) rArr lambda=(1)/(t)ln((R_(0))/(R ))`
Here, `R_(0)="5000 decay min"^(-1), R="1250 decay min"^(-1)`
`t = " 5 min"`
`therefore lambda=(1)/(5)ln((5000)/(1250))=(1)/(5)ln(4)=(1)/(5)ln(2^(2))=(2)/(5)ln2 =0.4ln2`