Question

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

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

Answer 1

Answer: (C)

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

Answer 2

Fraction remains after n half lives

$\frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{n} = \left( \frac{1}{2} \right)^{t/T}$

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