Question

If $T$ is the half-life of a radioactive material, then the fraction that would remain after time $\frac{T}{2}$ is,

• A. $\frac{1}{4}$
• B. $\frac{3}{4}$
• C. $\frac{1}{\sqrt{2}}$
• D. $\frac{\sqrt{2} - 1}{\sqrt{2}}$

Answer 1

Answer: (C)

$t=\frac{T_{1/2}}{2}$
$n=\frac{t}{T_{\frac{1}{2}}}$
$\Rightarrow n=\frac{1}{2}$
$\Rightarrow N=\frac{N_{0}}{2^{n}}=\frac{N_{0}}{\sqrt{2}}$
$\Rightarrow \frac{N}{N_{0}}=\frac{1}{\sqrt{2}}$