Question

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

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

Answer 1

Answer: (A)

$400\mu s$

First order decay reaction:
$N\left(t\right)=N_o{e}^{-\lambda t}$
Given: $t_{1/2}=\frac{ln2}{\lambda }$
$\frac{1}{16}=e^{-\frac{ln2}{100}t}$
$\Rightarrow t=400\mu s$