# Radial expectation value for particle in a cubic box [closed]

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?

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

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