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We find the radius at which the radial distribution function of the hydrogenic 1s orbital has a maximum value by solving $\mathrm dP/\mathrm dr = 0.$ If there are several maxima, then we choose the one corresponding to the greatest amplitude (the outermost one). The radial distribution function is given by $$P(r) = \frac{4Z^3r^2}{a_0^3}\exp\left(\frac{-2Zr}{...

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