Question

In a sample of radioactive material, what fraction of the initial number of active nuclei will remain disintegrated after half of a half-life of the sample?

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

Answer 1

Answer: (C)

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

Answer 2

According to radioactive decay, $\frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{t / T_{1 / 2}}$
According to question, $t=\frac{T_{1 / 2}}{2}$
Then, $\frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{1 / 2}=\frac{1}{\sqrt{2}}$