Question

The half life period of a certain radioactive material is $1$ hour. If the initial sample weighed $500$ gm, find the mass of the sample remaining at the end of $5$th hour.

Answer 1

Given : $a=500,r=\frac{1}{2},n=6[$After $5$ hours number of terms are to be $6$ including first term$]$

We know, $T_n=a{r}^{n-1}$

$\therefore T_6=a{r}^{6-1}$

$\therefore T_6=a{r}^5$

$\therefore T_6=500{\left(\frac{1}{2}\right)}^5$

$\therefore T_6=\frac{500}{32}$

$\therefore T_6=15.625$

Hence, the mass at the end of $5$th hour will be $15.625$ gm.