Question

A human body excretes [removes by waste discharges, sweating etc] certain material by a law similar to radio activity. If technitium is injected in some form in the human body, the body excrets half of the amount in $24$ hours. A patient is given an injection confaining $T{c}^{99}$. This isotope is radioactive with a half life 6 hrs. The activity from the body just after the injection is $20\mu Ci$. How many hours will elapse before the activity falls to $5\mu Ci$?

Answer 1

${\lambda }_{1}N+{\lambda }_{2}N=\lambda N$
${\lambda }_1=\frac{\ln 2}{24}{\lambda }_2=\frac{\ln 2}{6}$
$\lambda N_o=20$
$\lambda N_o{e}^{-\lambda t}=5$
$e^{\lambda t}=4$
$\lambda t=2\ln 2$
$(\frac{\ln 2}{24}+\frac{\ln 2}{6})t=2\ln 2$
$t=9.6\text{hours}$