Find the decay constant (per minute) of a radioactive sample if at any instant its disintegration rate is 5000 disintegrations per minute and after 5 minutes, the rate is 1250 disintegrations per minute.

Options

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

Answer

A

Explanation

According to question,
Rate of di sin tegration = Activity
`= (d N _(0))/( d t) =- N _(0) lamda = 5000......(1)`
Rate of di sin tegration = Activity
`= ( d N )/(dt) = - N lamda = 1250 .....(2)`
After time (t) = 5 min
`N = N _(0) e ^(- lamda t )`
equation `( 1) div (2)`
`(5000)/(1250) = (N _(0))/(N) = (N _(0))/( N _(0) e ^(- lamda t))`
` e ^( - lamda t ) = (1)/(4)`
`lamda t = 2 ln 2`
`lamda = ( 2 ln 2)/(t) = ( 2 ln 2)/(5) = 4 ln 2 min^(-1)`