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  • The activity of a simple of radioactive material is  at time <img alt="t_{1}" src="https://entrance

The activity of a simple of radioactive material is A_{1} at time t_{1} and A_{2} at time t_2\left(t_2>t_1\right). If mean life is T , then the value of A_2 is -

Option: 1

\mathrm{A_1 e^{\left(t_1+t_2\right) / }T}


Option: 2

\mathrm{A_1 e^{\left(t_2-t_1\right) / }T}


Option: 3

\mathrm{A_1 e^{\left(t_1-t_2\right) / }T}


Option: 4

\mathrm{A_1 e^{2 t_1 / }T}


Answers (1)

best_answer

Use, \mathrm{A_1=A_0 e^{-\lambda t_1}}

\mathrm{\begin{aligned} A_2 & =A_0 e^{-\lambda t_2}, \text { also } \lambda=\frac{1}{T} \\ \therefore \quad \frac{A_2}{A_1} & =\frac{e^{-\lambda t_2}}{e^{-\lambda t_1}}=e^{\left(-\lambda t_2+\lambda t_1\right)} \\ \text { of } A_2 & =A_1 e^{\lambda\left(t_1-t_2\right)}-\text { (1) } \end{aligned}}

put the value of  \lambda=\frac{1}{1} in equation (1)

A_2=A_1 e^{\left(t_1-t_2\right) / }T

Posted by

Pankaj Sanodiya

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