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

• unscientific
In summary: Oops. Then ##1s^2, 2s^2, 2s2p, 3s^2, 3s3p##?Alright, upon some thorough searches I can finally come up with a conclusion about the commonly used notation in the electronics structure to denote the electron binding energy. I will just give you the hint, the ordering of the electron binding energies follows exactly from one electron atom taking...1, 2, 3, 4, 5, 6... orbitals in the ground state.
unscientific

## Homework Statement

[/B]
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##.

## 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##?

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.

ArmanCham said:
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.
How can lowest energy level be 1 when the outermost orbital is at ##6s^2##?

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

ArmanCham said:
First three energy means n=1 n=2 and n=3 but lowest energy is ##6s^2##

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

Here you can find everything

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ArmanCham said:
Here you can find everything
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.

Yes I didnt understand your question and I assumed this

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.

blue_leaf77 said:
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.

The question is here:

bumpp

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

blue_leaf77 said:
then post the url

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

Send me a message I can help him maybe

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.

ArmanCham said:
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.
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}##.

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

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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.

blue_leaf77 said:
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.

Ok, but ##n## is defined as the number beside ##1s,2s,3s## right? So in that case the first 4 levels are ##1s^2, 1s1p, 2s^2, 2s2p, 3s^2##? So energy levels are ##n=1,1,2,2,3##.

where does 1p come from?

blue_leaf77 said:
where does 1p come from?
Oops. Then ##1s^2, 2s^2, 2s2p, 3s^2, 3s3p##?

Alright, upon some thorough searches I can finally come up with a conclusion about the commonly used notation in the electronics structure to denote the electron binding energy. I will just give you the hint, the ordering of the electron binding energies follows exactly from one electron atom taking into account fine structure effect. Are you familiar with fine structure of hydrogenic atoms? Unfortunately I cannot figure out why spectroscopists defined the notation this way.

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## 1. What is the meaning of the quantum numbers (n, L, J)?

The quantum numbers (n, L, J) are used to describe the energy levels, orbital shapes, and spin states of electrons in an atom. They provide a way to identify and distinguish between different electron configurations in an atom.

## 2. How are the quantum numbers (n, L, J) determined?

The quantum numbers (n, L, J) are determined by solving the Schrödinger equation for the electron in an atom. Each quantum number represents a different aspect of the electron's behavior, such as its energy, orbital shape, and spin.

## 3. What is the relationship between the quantum numbers (n, L, J)?

The quantum numbers (n, L, J) are related to each other in a specific way. The principal quantum number (n) determines the energy level, the azimuthal quantum number (L) determines the shape of the orbital, and the magnetic quantum number (M) determines the orientation of the orbital. The spin quantum number (J) is related to the spin of the electron.

## 4. How do the quantum numbers (n, L, J) affect the properties of an atom?

The quantum numbers (n, L, J) play a crucial role in determining the properties of an atom. They affect the energy levels, electron configurations, and chemical reactivity of the atom. The values of these quantum numbers can also be used to predict and explain the observed spectral lines of an atom.

## 5. Can the quantum numbers (n, L, J) change?

Yes, the quantum numbers (n, L, J) can change. The principal quantum number (n) can take on any positive integer value, the azimuthal quantum number (L) can take on any value from 0 to n-1, and the magnetic quantum number (M) can take on any value from -L to L. However, the spin quantum number (J) remains constant for a specific electron in an atom.

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