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?

Answer 1

Given:-
Initial rate of decay, A₀ = 500,
Rate of decay after 50 minutes, A = 200
Time, t = 50 min
            = 50 × 60
            = 3000 s

(a)
Activity, A = A₀e^−λt
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