Question

If the half-life of any sample of radioactive substance is $4$ days, then the fraction of sample will remain undecayed after $2$ days, will be?

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

Answer 1

Answer: (B)

$\frac{1}{\sqrt{2}}$

Answer 2

From Rutherford-Soddy law, the fraction left after $n$ half-lives is $N=N_{0}\left(\frac{1}{2}\right)^{n}$ where $n$ is number of half-lives. $n=\frac{\text { time }(t)}{\text { half-life }\left(T_{1 / 2}\right)}=\frac{2}{4}=\frac{1}{2}$ $\therefore \frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{1 / 2}$ $\Rightarrow \frac{N}{N_{0}}=\frac{1}{\sqrt{2}}$