First slide

Radio activity

Question

In a radioactive sample, what fraction of the initial number of radio active nuclei will be decayed after a time $t = \frac{T}{2}$ , where T=half life of radio active substance?

Moderate

A

$(\sqrt{2} - 1)$
B

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

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

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

Solution

$\frac{N}{N_{0}} = \frac{1}{{(2)}^{t / T}} = \frac{1}{{(2)}^{\frac{T / 2}{T}}} = \frac{1}{\sqrt{2}}$
Fraction of sample decayed $= \frac{N_{o} - N}{N_{o}} = 1 - \frac{N}{N_{o}} = 1 - \frac{1}{\sqrt{2}} = \frac{\sqrt{2} - 1}{\sqrt{2}}$

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