Question

The activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at time $t_2$ where $t_2>t_1$.Its decay constant is $\lambda$.Then the number of atoms decayed between the time interval $t_1$ and $t_2$ are

• A. $\frac{ln\left(2\right)}{\lambda }\left(R_1{R}_2\right)$
• B. $R_1{e}^{-\lambda t_2}-R_2{e}^{-\lambda t_2}$
• C. $\lambda (R_1-R_2)$
• D. $\left(\frac{R_1-R_2}{\lambda }\right)$

Answer 1

Answer: (D)

$\left(\frac{R_1-R_2}{\lambda }\right)$

b'

Let $N_1$ be the number of atoms at $t_1$

$\therefore R_1=\lambda N_1$

Let $N_2$ be the number of atoms at $t_2$

$\therefore R_2=\lambda N_2$

$\Rightarrow R_1-R_2=\lambda N_1-\lambda N_2$

$\Rightarrow N_1-N_2=\frac{R_1-R_2}{\lambda }$

$\therefore$ number of atoms decayed between the time interval $t_1$ and $t_2$ are $\frac{R_1-R_2}{\lambda }$

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