First slide

Radio activity

Question

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

Moderate

A

$\frac{1}{2}$
B

$\frac{3}{4}$
C

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

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

Solution

Fraction remains after n half lives
$\frac{N}{N_{0}} = {(\frac{1}{2})}^{n} = {(\frac{1}{2})}^{t / T} ∴ \frac{N}{N_{0}} = {(\frac{1}{2})}^{\frac{T / 2}{T}} = {(\frac{1}{2})}^{1 / 2} = \frac{1}{\sqrt{2}}$

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