Question

Radioactive substance becomes ${\left(\frac{1}{16}\right)}^{th}$ of the original in 80 minutes.Find half-life.

• A. $40min$
• B. $20min$
• C. $60min$
• D. $5min$

Answer 1

The correct option is B $20min$

$[A{]}_t=\frac{[A{]}_0}{2^n}$
Here,
$[A{]}_t=\text{Conc. at time t}$
$[A{]}_0=\text{Initial concentration}$
$n=\text{Number of half lives}$
Given
$[A{]}_t=\frac{[A{]}_0}{16}$
ao,

$\frac{[A{]}_0}{2^n}=\frac{[A{]}_0}{16}$
$\Rightarrow n=4$
For 4 half-lives, time taken is 80 min.
For 1 half-life, time taken is:
$t_{1/2}=\frac{80}{4}=20min$
Hence half-life is 20 min.