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, $\lambda =\frac{0.693}{T_{1/2}}=0.0866$
Activity (A) at t = 4 days is given by
$$\begin{gathered} A=A_0{e}^{-\lambda t} \\ \Rightarrow A=20\times {10}^{-6}\times e^{-0.0866\times 4} \\ =1.41\times {10}^{-6}\mathrm{Ci}=14\mathrm{\mu Ci} \end{gathered}$$

(b) Decay constant is a constant for a radioactive sample and depends only on its half-life.
$$\begin{gathered} \lambda =\frac{0.693}{[8\times 24\times 3600]} \\ =1.0026\times {10}^{-6}{\mathrm{s}}^{-1} \end{gathered}$$