-2
$\begingroup$

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?

$\endgroup$
3
$\begingroup$

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

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.

| improve this answer | |
$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.