Question

Radioactivity of a sample $(Z=22)$ decreases $90\%$ after $10$ yr. What will be the half-life of the sample?

• A. $5$ yr
• B. $2$ yr
• C. $3$ yr
• D. $10$ yr

Answer 1

The correct option is C $3$ yr

$t=10$ yr, $t_{\frac{1}{2}}=?$

$\lambda =\frac{2.303}{t}log\frac{N_0}{N_t}$

Since, radioactivity decreases $90\%$ in $10$ yr.

$\Rightarrow N_0=100$

and $N_t=10$

Thus, $\lambda =\frac{2.303}{10}log\frac{100}{10}$

or $\lambda =\frac{2.303}{10}$

since, $t_{\frac{1}{3}}=\frac{0.693}{\lambda }$

$\Rightarrow t_{\frac{1}{2}}=\frac{0.693\times 10}{2.303}$

$\Rightarrow =3$ yr