Question

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

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

Answer 1

The correct option is A $400\mu s$

$t_{1/2}=100\mu s$
$\lambda =\frac{ln2}{t_{1/2}}$

First order decay:
$N\left(t\right)=N_o{e}^{-\lambda t}$

Time for which:
$N\left(t\right)=\frac{N_o}{16}$
$\frac{N_o}{16}=N_o{e}^{-\lambda t}$
$\lambda t=4ln2$
$t=4t_{1/2}=400\mu s$