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13.Nuclei
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In a radioactive material the activity at time $t_1$ is $R_1$ and at a later time $t_2$ it is $R_2$. If the decay constant of the material is $\lambda$ then
A
$R_1=R_2$
B
$R_1=R_2 {e^{ - \lambda \left( {t_1- t_2} \right)}}$
C
$R_1=R_2{e^{\lambda \left( {t_1 - t_2} \right)}}$
D
$R_1=R_2 \left( {\frac{{t_1}}{{t_2}}} \right)$
(AIPMT-2006)
Solution
According to activity law, $R = {R_0}{e^{ – \lambda t}}$
$\therefore $ ${R_1} = {R_0}{e^{ – \lambda {t_1}}}$ and ${R_2} = {R_0}{e^{ – \lambda {t_2}}}$
$\therefore \,\,\frac{{{R_1}}}{{{R_2}}} = \frac{{{R_0}{e^{ – \lambda {t_1}}}}}{{{R_0}{e^{ – \lambda {t_2}}}}}$ $ = {e^{ – \lambda {t_1}}}{e^{\lambda {t_2}}} = {e^{ – \lambda \left( {{t_1} – {t_2}} \right)}}$
or, ${R_1} = {R_2}{e^{ – \lambda \left( {{t_1} – {t_2}} \right)}}$
Standard 12
Physics
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