First slide

Radio activity

Question

Activity of radioactive element decreased to one third of original activity $R_{0}$ in 9 years. After further 9 years. its activity will be

Easy

A

$R_{0}$
B

$\frac{2}{3} R_{0}$
C

$\frac{R_{0}}{9}$
D

$\frac{R_{0}}{6}$

Solution

$Activity R = R_{0} e^{- λt} \frac{R_{0}}{3} = R_{0} e^{- λ x 9} \Rightarrow e^{- 9 λ} = \frac{1}{3} . . . . . . . (i)$
After further 9 years $R' = {Re}^{- λt} = \frac{R_{0}}{3} x e^{- λ x 9} . . . . . . (ii)$
$From equation (i) and (ii) R' = \frac{R_{0}}{9} .$

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