Question

If the half-life of a material is $10years$, then in what time, it becomes $\frac{1}{4}th$ part of the initial amount.

• A. $15yr$
• B. $20yr$
• C. $25yr$
• D. $30yr$

Answer 1

The correct option is B $20yr$

We know that, $N=N_0{e}^{\frac{-t}{T_{1/2}}}$
$\frac{1}{4}=e^{-t/10}$
${\left(\frac{1}{2}\right)}^2=e^{\frac{1}{t/10}}$
$t=20yr$.