Question

Radioactive ¹³¹I has a half-life of 8.0 days. A sample containing ¹³¹I has activity 20 µCi at t = 0. (a) What is its activity at t = 4 days? (b) What is its decay constant at t = 4.0 days?

Answer 1

Given:
Half-life of radioactive ¹³¹I, T_1/2 = 8 days
Activity of the sample at t = 0, A₀ = 20 µCi
Time, t = 4 days

(a) Disintegration constant, `lambda = 0.693/T_"1/2" = 0.0866`

Activity (A) at t = 4 days is given by

`A = A_0e^-"λt"`

⇒ `A = 20 xx 10^-6 xx e^(-0.0866 xx 4)`

= `1.41 xx 10^-6 "Ci" = 14  "µCi"`

(b) Decay constant is a constant for a radioactive sample and depends only on its half-life.

`lambda = 0.693/[[8 xx 24 xx 3600]]`

= `1.0026 xx 10^-6  "s"^-1`