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The radial probability density of finding an electron in the 3s orbital in a Hydrogen-like atom a distance from the nucleus is proportional to: where

The radial probability density of finding an electron in the 3s orbital in a Hydrogen-like atom a distance from the nucleus is proportional to: where is the radial part of the wavefunction of the Hydrogen-like atom in the 3s state. It turns out that to find the most likely radial position of the electron in the 3s state of the hydrogen like atom, it is sufficient to find the point where the function has a MINIMUM (You can convince yourself of this by sketching both and ). Given that where is the nuclear charge, and is the Bohr radius, find the most probable distance of the electron from the nucleus for the electron in the 3s state in the ion. Express your final answer in units of the Bohr radius .

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