Question

The half-life of ${}^{215}At$ is $100mus$. The time taken for the radioactivity of a sample of this nucleus to decay to $\frac{1}{16}th$ of its initial value is

• A. $6.3\mu s$
• B. $40\mu s$
• C. $300\mu s$
• D. $400\mu s$

Answer 1

Answer: (D)

$400\mu s$

Activity, $\left(\frac{R}{R_0}\right)={\left(\frac{1}{2}\right)}^n$
$\Rightarrow \frac{1}{16}={\left(\frac{1}{2}\right)}^n$
$\Rightarrow {\left(\frac{1}{2}\right)}^4={\left(\frac{1}{2}\right)}^n$
$\Rightarrow n=4$
$\Rightarrow \frac{t}{T}=4$ $[\because n=\frac{t}{T}]$
$\Rightarrow t=4T$
$t=4\times 100\mu s$
$\therefore t=400\mu s$.