Most probable radial distance for 4f state and selection rules for photon absorption

[schattenjaeger]

Well, I guess I didn't do that bad, but we'll see. I'll try and remember the questions of ones that gave me trouble

First and foremost, what's the most probable radial distance of an electron from the nucleus in a H atom in the 4f state? I was given R(r)

I just plain wasn't sure how to do this, so I basically did a bunch of stupid stuff, like I plugged that function for R into the radial wave equation thingy(that long 1/r^2 d/dr(r^2dR/dr)... and all that, then I tried to solve for r, well whatever it was it was dumb I think

then let's see, if an atom with an electron in the, um, 3d state I think, absorbs a photon that excites it to the n=6 state, what are the possible orbital angular momentum values? For starters I only found l, not L, oops, but as is does that selective transition stuff apply when you ABSORB a photon? So it could only be l=3 or l=1? Maybe?

That's really all I wasn't sure on I guess, so I didn't do too bad. Hopefully. *knocks on wood

 

[siddharth]

First and foremost, what's the most probable radial distance of an electron from the nucleus in a H atom in the 4f state? I was given R(r)
I just plain wasn't sure how to do this, so I basically did a bunch of stupid stuff, like I plugged that function for R into the radial wave equation thingy(that long 1/r^2 d/dr(r^2dR/dr)... and all that, then I tried to solve for r, well whatever it was it was dumb I think

The probability density when you are given the radial wavefunction $$R(r)$$ is $$P(r) = r^2 R(r)*R(r)$$. So the most probable distance is when $$\frac {dP(r)}{dr} = 0$$. Solve for that when the solution is for maximum value. How did you get 1/r^2 d/dr(r^2dR/dr)?