A certain sample of a radioactive marerial decays at the rate of 500 per second at a cartain time .the count rate falls to 200 per second after 50 minutes .(a) What is decay constant of the sample? (b) what is its half-life?

Answer

A, B, C, D

Explanation

Given `A = 200, `
` A_0 = 500 , t = 50 min`
`A = A_0 e^(-lambdatau)`
or `200 = 500 xx e^(-50 xx 60 xx lambda)`
`rArr 2/5 = e^(-3000lambda)`
`rArr In 2/5 = - 3000 lambda`
`rArr lambda = 3.05 xx 10^(-4) S`
(b) `t_(1/2) = 0.693/lambda = 2272.13 sec`
= 38 min.