Question

Radioactive ${}^{131}I$ has a half-life of $8.0$days. A sample containing ${}^{131}I$ has activity $20\mu Ci$at $t=0$ .
(a) What is its activity at $t=4.0$ days? (b) What is its decay constant at $t=4.0$ days?

Answer 1

Given that,

$t_{1/2}=8.0days;A_0=20\mu Ci$

$t=4.0days$
(a) $\lambda =\frac{0.693}{8}=0.0866$

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

$=20\times {10}^{-6}\times e^{(-0.0866)\times 4}$

$=1.41\times {10}^{-5}Ci=14\mu Ci$
(b)$Decayconstantinpersec.=\frac{0.0866}{24\times 3600}$

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