Total charge density of all electrons in the closed subshell n=3, l=2

[Dixanadu]

Homework Statement

Hey guys,

So the title pretty much says it. I have to find the total charge density produced by all the electrons in a closed subshell where n = 3 and l = 2. The charge density produced by a single electron is $(-e)|R_{32}(r)Y_{2,m}(\theta , \phi)|^{2}$

Homework Equations

So he gave an example in lectures, but that was for something that had n=2, l=1 subshell. This is what I've got written down:

$|P_{21}|^{2}=2(-e)\sum_{m=-1}^{+1}|Y_{lm}|^{2}=2(-e)|R_{21}|^{2}\frac{3}{4\pi}$

The Attempt at a Solution

I'm not sure that equation above is right for my situation...does it change when the quantum numbers change? of course the sum will now range from m = -2 -> +2 but is that all that changes? I can't even find any material on this, in my book or elsewhere...

thanks guys!

 

[clamtrox]

The charge distribution is just $$\rho = -e \sum |\Psi_{nlm}|^2$$ where the sum is over all the electrons you're interested in. In this case, they are the electrons with n=3, l=2 so you should sum is over m and m_s, for all values possible for this shell.