# What are the quantum numbers (n, L, J)?

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1. May 30, 2015

### unscientific

1. The problem statement, all variables and given/known data

I'm supposed to find the quantum numbers (n, L, J) for the first 3 energy levels in Iridium (Z=77), given that the first 4 ionization energies are $76.1, 13.4, 12.8, 11.2 keV$.

2. Relevant equations

3. The attempt at a solution
I know that the electronic configuration is $[Xe] 4f^{14} 5d^7 6s^2$.
I suppose lowest level is $n=6, l=0, S=0,J=0$.
Is the next level $6s^1 6p^1$?

2. May 31, 2015

### ArmanCham

I want to help you but I didnt understand your question.Example you said "first 3 energy levels" you know first energy level is n=1 l=0 and J=0 so can you be more spesific.I might be understand your question false too.

3. May 31, 2015

### unscientific

How can lowest energy level be 1 when the outermost orbital is at $6s^2$?

4. May 31, 2015

### ArmanCham

First three energy means n=1 n=2 and n=3 but lowest energy is $6s^2$

5. May 31, 2015

### unscientific

Ok, so n = 1,2,3,4. What are the L and J for each?

6. May 31, 2015

### ArmanCham

Here you can find everything

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7. May 31, 2015

### unscientific

Thanks for your input, but you just said first 3 levels are n=1,2,3 and that directly contradicts what's in the picture.

8. May 31, 2015

### ArmanCham

Yes I didnt understand your question and I assumed this

9. May 31, 2015

### blue_leaf77

I think you should check again the problem, you said first 4 ionization energies but the values you gave stands in keV range which doesn't make sense for large atom like Ir, plus they are in the order of lowering values, which should be the other way around. There is a good discussion about many electron atoms in Physics of Atoms and Molecules by Bransden and Joachain, you might want to check this out.

10. May 31, 2015

### unscientific

The question is here:

11. Jun 1, 2015

### unscientific

bumpp

12. Jun 2, 2015

### ArmanCham

I want to help.Is there any equation between energy level and n I found this but I am not sure

13. Jun 2, 2015

### blue_leaf77

14. Jun 2, 2015

### ArmanCham

then post the url

15. Jun 2, 2015

### blue_leaf77

The forum rule forbids helpers to give directly the final answer. Very unfortunate that I can't help with physical arguments.

16. Jun 2, 2015

### ArmanCham

Send me a message I can help him maybe

17. Jun 2, 2015

### ArmanCham

Electron binding energy means electron ionization energy.Now there wrote most tightly,it means we have to give a lot of energy to ionize electron.Think this way If Ir has one electron then we should use this formula to find binding energy of electron.Put the values and you will find n there.Find it and tell me the answer then I will explain the other energies and you will understand the question.

18. Jun 17, 2015

### unscientific

We can't assume that, as each level has a shielding effect such that $E_n = -hcR_{\infty}\frac{(Z-\sigma_n)^2}{n^2}$.

19. Jun 17, 2015

### unscientific

Ok, I think I got it. Are the first 4 energy levels $1s^2, 2s^2, 3s^2, 4s^2$?

Last edited: Jun 17, 2015
20. Jun 17, 2015

### blue_leaf77

For such heavy atom, I suspect the relativistic effect which manifests itself in the coupling between orbital and spin angular momenta will be too big to be neglected, due to which the J quantum number may have to appear in certain form in the notation of the states.