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  • The rate of decay of a radio active sample is given by  at time <img alt="t_1" src="https://entrancecorner.oncodecogs

The rate of decay of a radio active sample is given by A_1 at time t_1 and A_2 at a later time t_2. The decay constant of this radio active sample is:

Option: 1

\lambda=\frac{\mathrm{A}_1}{\mathrm{~A}_2} \times \frac{\mathrm{t}_2}{\mathrm{t}_1}


Option: 2

\lambda=\frac{\ln \frac{A_1}{A_2}}{t_2-t_1}


Option: 3

\lambda=\frac{t_2-t_1}{\ln \frac{A_2}{A_1}}


Option: 4

\lambda=\frac{\ln \frac{A_2}{A_1}}{t_2-t_1}


Answers (1)

best_answer

\mathrm{A}_1=\lambda \mathrm{A}_{\mathrm{t}_1}

                \mathrm{A}_1=\lambda \mathrm{A}_0 \mathrm{e}^{-\lambda t_1} \quad \ldots \text { (i) }

                \mathrm{A}_2=\lambda \mathrm{A}_{\mathrm{t}_2}

                \mathrm{A}_2=\mathrm{A}_0 \mathrm{e}^{-\lambda, t_2} \quad \ldots \text { (ii) }

                 Equation (i) by (ii)

                \frac{A_1}{A_2}=e^{\lambda\left(t_2-t_1\right)}

                \lambda=\frac{1}{\mathrm{t}_2-\mathrm{t}_1} \ln \frac{\mathrm{A}_1}{\mathrm{~A}_2}

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Rishi

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