Question

$t_{1/2}$ for $Kr$ is $10.6yr$. The time taken for $99.9\%$ decay of $Kr$ is

• A. 106 yr
• B. 1060 yr
• C. 1.06 yr
• D. 10.6 yr

Answer 1

Answer: (A)

$\frac{N}{N_0}={\left(\frac{1}{2}\right)}^n$
where $n=$ number of half-life periods
$N_0=$ initial concentration of substance
$N=$ amount of concentration left after $n$ half-life period.
Total time $(T)=n\times t_{1/2}$
Amount disintegrated $=99.9\%=\frac{999}{1000}$
Amount left $=1-\frac{999}{1000}$
$=\frac{1}{1000}\approx \frac{1}{1024}$
$\frac{N}{N_0}={\left(\frac{1}{2}\right)}^n$
$\frac{1}{1024}={\left(\frac{1}{2}\right)}^n$
${\left(\frac{1}{2}\right)}^{10}={\left(\frac{1}{2}\right)}^n$
$n=10$
Total time $=n\times t_{1/2}$
Here, $t_{1/2}=10.6yr$
Total time $=10\times 10.6$
$=106yr$