First slide

Radio activity

Question

The activity of a radio active sample decreases to one third of its original value in 9 years, what will be the activity after further 9 years?

Easy

A

$\frac{A_{o}}{3}$
B

$\frac{A_{o}}{6}$
C

$\frac{A_{o}}{9}$
D

$\frac{A_{o}}{18}$

Solution

$(\frac{\frac{A_{o}}{3}}{A_{o}}) = \frac{1}{{(2)}^{\frac{9}{T_{^{\frac{1}{2}}}}}} \Rightarrow \frac{1}{{(2)}^{\frac{1}{T_{\frac{1}{2}}}}} = {(\frac{1}{3})}^{\frac{1}{9}}$
$A^{'} = A_{o} \frac{1}{{(2)}^{\frac{18}{T_{\frac{1}{2}}}}} = A_{o} {(\frac{1}{3})}^{\frac{18}{9}} = \frac{A_{o}}{9}$

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