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








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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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\[
\left< r\_{nl} \right> = n^2\cdot a\_0\ \left\{ 1+ \frac{1}{2} \left[1-\frac{l(l+1)}{n^2}\right] \right\}
\]


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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