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  • The activity of a sample of radioactive material is <img alt="\mathrm{2 A_1at \, \, time\, \, t_1\, \, and\, \, 2 A_2at\, \, \, time \, \, t_2\left(t_2>t_1\right)}" src="https://entrancecorner.o

The activity of a sample of radioactive material is \mathrm{2 A_1at \, \, time\, \, t_1\, \, and\, \, 2 A_2at\, \, \, time \, \, t_2\left(t_2>t_1\right)}. If mean life is T, the the Value of \mathrm{ A_2} _

Option: 1

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


Option: 2

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


Option: 3

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


Option: 4

A_1 e^{\left(t_2+t_1\right) / 2 T}


Answers (1)

best_answer

Use,

\mathrm{\begin{aligned} A_1 & =A_0 e^{-\lambda t_1} \\ A_2 & =A_0 e^{-\lambda t_2}, \text { also } \lambda=\frac{1}{T} \end{aligned} but A_1=2 A_1, A_2=2 A_2 }
Now.
\mathrm{\begin{aligned} & \frac{2 A_2}{2 A_1}=\frac{e^{-\lambda t_2}}{e^{-\lambda t_1}} \Rightarrow e^{\left(-\lambda t_2+\lambda t_1\right)} \\ & A_2=A_1 e^{\lambda\left(t_1-t_2\right)}=A_1 e^{\left(t_1-t_2\right) / T} \end{aligned} }
 

Posted by

Ritika Kankaria

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