Question

$16$g of a radioisotope reduces to one gram in one hour. Its half life period in minutes is-

• A. $15$
• B. $30$
• C. $45$
• D. $60$

Answer 1

The correct option is A

$15$

Step 1: Given data and formula are used:

$16\mathrm{g}$ of radioisotope reduces to $1\mathrm{g}$ in $1$hour.

Formula used:

$Kt=2.303\log \frac{{\mathrm{R}}_0}{\mathrm{R}}$

Step 2: Substitute values in the formula used-

$\begin{array}{rcl}\mathrm{K}\times 60\mathrm{minutes}& =& 2.303\log \frac{16}{1}\\ & =& \frac{2.303}{60}\log 16\\ & =& 0.038\times 1.2041\\ & =& 0.04621{\mathrm{minutes}}^{-1}\end{array}$

Step 3: Calculate half life period of radioisotope-

$$\begin{gathered} t^{\frac{1}{2}}=\frac{0.693}{\mathrm{k}} \\ {\mathrm{t}}^{\frac{1}{2}}=\frac{0.693}{0.04621} \\ {\mathrm{t}}^{\frac{1}{2}}=14.99=15\mathrm{minutes} \end{gathered}$$

Final answer:

Hence, option (A) is correct.