The wave function for the ground state of hydrogen (n=1) is [psi(r)=frac{1}{sqrt{a_{0}^{3} pi}} e^{-frac{r}{a_{0}}}] Take the reduced

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The wave function for the ground state of hydrogen \(n=1\) is

\[\psi(r)=\frac{1}{\sqrt{a_{0}^{3} \pi}} e^{-\frac{r}{a_{0}}}\]

Take the reduced mass to be \(\approx m_{e}\).

(a) Show that this wave function is normalized.

(b) What is the expectation value \(\langle rangle\) of \(r\) ?

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