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## Homework Statement

A hydrogen like ion (with one electron and a nucleus of charge Ze) is in the state

[tex] ψ = ψ_{2,0,0} - ψ_{2,1,0} [/tex]

What's the expectation value of

**\hat{r}**(position operator) as a function of Z?

Assuming origin at nucleus.

## Homework Equations

for Z=1

[tex] < ψ | \hat{r} | ψ > = -3 \frac{4 π ε_0 \hbar^2}{m e^2} n_z[/tex]

## The Attempt at a Solution

Using the values for

[tex] ψ = ψ_{2,0,0} - ψ_{2,1,0} [/tex]

I got

[tex] ψ = \frac{1}{4 \sqrt{2 π a_0 ^3}} e^{- \frac{r}{2 a_0}} ( 2 - \frac{r}{a_0} - \frac{r cos(\theta)}{a_0}) [/tex]

I wouldn't have a clue how to integrate this and I imagine there must be an easier way to find the expectation value.

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