Question

From the equation expressing the law of radioactive decay, derive the following useful formulas for the decay constant and the half-life, in terms of the time interval $\Delta t$ during which the decay rate decreases from $R_{0}$ to $R$ : $$ \lambda=\frac{1}{\Delta t} \ln \left(\frac{R_{0}}{R}\right) \quad T_{1 / 2}=\frac{(\ln 2) \Delta t}{\ln \left(R_{0} / R\right)} $$

          From the equation expressing the law of radioactive decay, derive the following useful formulas for the decay constant and the half-life, in terms of the time interval $\Delta t$ during which the decay rate decreases from $R_{0}$ to $R$ :
$$
\lambda=\frac{1}{\Delta t} \ln \left(\frac{R_{0}}{R}\right) \quad T_{1 / 2}=\frac{(\ln 2) \Delta t}{\ln \left(R_{0} / R\right)}
$$

Added by John T.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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From the equation expressing the law of radioactive decay, derive the following useful formulas for the decay constant and the half-life, in terms of the time interval $\Delta t$ during which the decay rate decreases from $R_{0}$ to $R$ : $$ \lambda=\frac{1}{\Delta t} \ln \left(\frac{R_{0}}{R}\right) \quad T_{1 / 2}=\frac{(\ln 2) \Delta t}{\ln \left(R_{0} / R\right)} $$