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A hydrogen atom is in a cubic box with side lengths equal to $\require{mediawiki-texvc}\pu{100 \AA{}}$. For what value of $n$ (principal quantum number) will the expectation value of the radius be equal to one-half the box size?

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closed as off-topic by Satwik Pasani, Klaus-Dieter Warzecha, Ben Norris, jonsca Feb 14 '14 at 20:31

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\[ \left< r_{nl} \right> = n^2\cdot a_0\ \left\{ 1+ \frac{1}{2} \left[1-\frac{l(l+1)}{n^2}\right] \right\} \]

should be close to what is applicable to solve to problem in a simple way. If the value is a bit off, blame it on Niels Bohr or the cabinetmaker who built the box.

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