#### Question

Radioactive ^{131}I has a half-life of 8.0 days. A sample containing ^{131}I 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?

#### Solution

Given:

Half-life of radioactive ^{131}I, T_{1}_{/2} = 8 days

Activity of the sample at t = 0, A_{0} = 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`

Is there an error in this question or solution?

Solution 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? Concept: Radioactivity - Introduction of Radioactivity.