Question

In a sample of a radioactive substance, what friction of the initial nuclei will remain undecayed after a time $t=T/2$, where $T=$ half-life of radioactive substance?

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

Answer 1

The correct option is A $\frac{1}{\sqrt{2}}$

Let $N_0$ be the number of initial nuclei,
After '$n$' half lifes it would decay to $\frac{N_0}{2^n}$.
If $n=0.5$, then number of nuclei would be $\frac{N_0}{2^{0.5}}=\frac{N_0}{\sqrt{2}}$
Hence, fraction of radioactive substance is $\frac{1}{\sqrt{2}}$.