Question

Radioactivity ${}^{131}\text{I}$ has a half-life of 8.0 days. A sample containing ${}^{131}\text{I}$ has activity $20\mu \text{Ci}$ (a) What is its activity at t = 4.0 days ? (b) What is its decay constant at t = 4.0 days ?

Answer 1

Given

$t_{\frac{1}{2}}=8.0\text{days,}$

${\text{A}}_0=20\mu \text{Ci}$

(a) $t=4.0\text{days},\lambda =\frac{0.693}{8}$

$\therefore A=A_0{e}^{-\lambda t}$

=$20\times {10}^{-6}\times e^{-\frac{0.698}{8}\times 4}$

=$1.41\times 1^{-6}\text{Ci}=14\mu Ci$

(b) $\lambda =\frac{0.693}{[8\times 24\times 3600]}$

= $1.0026\times {10}^{-6}$