Question

If in $3160$ years, a radioactive substance becomes one-fourth of the original amount, find its half-life period.

Answer 1

$\frac{N}{N_0}=\frac{1}{4}$
So, $\frac{1}{4}={\left(\frac{1}{2}\right)}^n$
or ${\left(\frac{1}{2}\right)}^2={\left(\frac{1}{2}\right)}^n$
or $n=2$
We know that, total time '$T$' $=n\times t_{1/2}$
So, $3160=2\times t_{1/2}$
or $t_{1/2}=\frac{3160}{2}=1580$ years
The half life period of the radioactive substance is $1580$ years.