Question

${\text{Bi}}^{210}$ has a half-life of $5$ days. The time taken for $\frac{7}{8}$ of a sample to decay is :

• A. $15\text{days}$
• B. $20\text{days}$
• C. $10\text{days}$
• D. $3.4\text{days}$

Answer 1

The correct option is A $15\text{days}$

Half life of ${\text{Bi}}^{210}=5$ days

$\therefore \text{k}=\frac{0.693}{\text{t1/2}}=\frac{0.693}{5}{\text{day}}^{-1}$

Using $\text{k}=\frac{2.303}{\text{t}}log\frac{\text{a}}{\text{a-x}}$

(where ${\text{a = a}}_0$, (let) $\Rightarrow \text{x}=\frac{7}{8}{\text{a}}_0$, $\text{t}$ is time taken in decay and $\text{k}$ is rate constant)

We get, $\text{t}=\frac{2.303\times 5}{0.693}\text{log}\frac{{\text{a}}_0}{\frac{1}{8}{\text{a}}_0}$

= $\frac{2.303\times 5}{0.693}\text{log}8=15\text{days}$