#### Question

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

#### Solution

Given:-

Initial rate of decay, A_{0} = 500,

Rate of decay after 50 minutes, A = 200

Time, t = 50 min

= 50 × 60

= 3000 s

(a)

Activity, A = A_{0}e^{−λ}^{t}

Here, `lambda` = Disintegration constant

`therefore 200 = 500 xx e^(-50 xx 60 xx lambda)`

`⇒ 2/5 = e^(-3000lambda)`

`⇒ "In" 2/5 = -3000lambda`

`⇒ lambda = 3.05 xx 10^-4 "s"^-1`

(b)

Half - life, `T_"1/2" = 0.693/lambda`

`= 2272.13 "s"`

= 38 min

Is there an error in this question or solution?

Solution A Certain Sample of a Radioactive Material Decays at the Rate of 500 per Second at a Certain Time. the Count Rate Falls to 200 per Second After 50 Minutes. Concept: Radioactivity - Introduction of Radioactivity.