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13.Nuclei
normal
Activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at time $t_2(t_2 > t_1).$ Then the ratio $\frac{R_2}{R_1}$ is :
A
$\frac{t_2}{t_1}$
B
${e^{ - \lambda ({t_1} + {t_2})}}$
C
$e\left( {\frac{{{t_1} - {t_2}}}{\lambda }} \right)$
D
${e^{ \lambda ({t_1} + {t_2})}}$
Solution
$N=N_{0} e^{-\lambda t}$
$R=\frac{d N}{d t}=-\lambda N_{0} e^{-\lambda t}$
$R_{1}=-\lambda N_{0} e^{-\lambda t_{1}}$
$R_{2}=-\lambda N_{0} e^{-\lambda t_{2}}$
Dividing the two, we get:
$R_{2}=R_{1} e^{\lambda\left(t_{1}-t_{2}\right)}$
Standard 12
Physics
