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

Explanation:

In the question, it is given:

Radioactive 131I has the half-life, T1/2 = 8 days

At t = 0, the sample’s activity, A0 = 20 µCi

Time is shown as t = 4 days

(a) Constant of disintegration,

λ = 0.693T1/2 = 0.0866

At t = 4 days, the activity (A) is shown as

A = A0e – λt

$\Rightarrow A=20 \times e-0.0866 \times 10-6 \times 4$

$=1.0026 \times 10-6 \mathrm{s}-1$

(b) Decay constant is dependent only on the half-life of the radioactive sample. And, it is the radioactive sample’s constant.

$\Lambda=0.693[8 \times 3600 \times 24]$

$=1.0026 \times 10-6 \mathrm{s}-1$