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)

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, $\frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{1 / 2}=\frac{1}{\sqrt{2}}$