Question

A human body excretes (removes by waste discharge, sweating, etc.) certain materials by a law similar to radioactivity. If technitium is injected in some form in a human body, the body excretes half the amount in 24 hours. A patient is given an injection containing ${}^{99}$ Tc. This isotope is radioactive with a half-life of 6 hours. The activity from the body just after the injection is $6\mu Ci$. How much time will elapse before the activity falls to $3\mu Ci$?

Answer 1

Given $t_1=24,h{t}_2=6h$

$\therefore t_{\frac{1}{2}}=\frac{t_1{t}_2}{t_1+t_2}=\frac{24\times 6}{24+6}$

= $\frac{24\times 6}{30}$ = 4.8 h

Given $A_0=6\mu Ci,A=3\mu Ci$

$\therefore A=\frac{A_0}{2\frac{t}{t_2}}$

$\Rightarrow 3\mu Ci=\frac{6\mu Ci}{2\frac{t}{4.8}}$

$\Rightarrow \frac{6\mu Ci}{2\frac{t}{4.8}}=3\Rightarrow \frac{t}{4.8h}=1$

$\Rightarrow$ t= 4.8 h