Atomic terms and quantum numbers?

In summary: The S and J you are concerned with are the spin and orbital quantum numbers, respectively. They are just two possible values that an electron can have. There are a total of 24 possible combinations of these two numbers, and those are what you specify when you write down an atomic term.
  • #1
jeebs
325
4
Hi,
I have a helium atom in the excited state of (1s,20p), and I am told that it has 4 corresponding atomic terms. I am supposed to "write down the quantum numbers of these 4 atomic terms".

As I understand it, an atomic term is specified by the 2S+1LJ notation, where S is the spin quantum number for the whole atom, L is the orbital angular momentum quantum number for the whole atom, and J is the total angular momentum quantum number for the whole atom.

So, looking at the individual electrons, the 1s electron has spin quantum number s=1/2, and orbital angular momentum quantum number l=0.
the 20p electron has s=1/2, l=1.

I think I am right in saying that only the 20p electron contributes any orbital angular momentum to the atom, so that for the whole atom, L = l = 1, therefore the atomic term should become 2S+1PJ.

However, this is where I start to get confused. My notes aren't that clear and there are a lot of L's, S's J's, l's, s's, j's etc. getting thrown around. How am I supposed to determine what S and J are?

I am assuming there are only 4 possible combinations of S and J. I thought of doing S = s1+s2 = s+s = 1/2 + 1/2 = 1, therefore Ms = -1,0,1 (not sure if this is relevant) but I was not sure about this and got the impression from my notes this was incorrect. The same goes for saying J=L+S. This would only give me the one atomic term, 3P2, where I need 4 terms.

I'd appreciate it if someone could help me out here.
Thanks.
 
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  • #2
First of all, when you add two spin-1/2 particles, s=1 is not the only possibility. Similarly, when you add l=1 to s=1, j=2 is not the only possibility. Remember that it's not regular numerical addition when you add angular momenta; you actually get multiple results. (The math is based on group theory, but don't worry about that for now)

Anyway, the point is, figure out what other results you can get from adding two angular momenta. I find 4 states in the end when you take them all into account.
 
  • #3
diazona - i am aware there are 2 possibilities for the orientation of a given s, but that is due to ms=+/-1/2, is it not? it is the capital letter quantum number S that I am interested in.
I get that for a given l you have ml=2l+1 possibilities, etc... I still don't get this.
 
Last edited:

Related to Atomic terms and quantum numbers?

1. What are atomic terms and quantum numbers?

Atomic terms and quantum numbers are concepts used in atomic physics to describe the energy levels and properties of atoms. They are used to explain the behavior and structure of atoms and their electrons.

2. What is the significance of atomic terms and quantum numbers?

Atomic terms and quantum numbers are important because they provide a way to understand and predict the behavior of atoms and their electrons. They also help us classify elements and their properties, which is crucial in understanding chemical reactions and the periodic table.

3. How do atomic terms and quantum numbers relate to each other?

Atomic terms and quantum numbers are related because atomic terms describe the overall energy state of an atom, while quantum numbers provide more specific information about the electrons in that energy state. Together, they give a complete picture of an atom's energy level and electron configuration.

4. What are the four quantum numbers and what do they represent?

The four quantum numbers are the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (ml), and the spin quantum number (ms). They represent the energy level, sublevel, orbital orientation, and spin direction of an electron, respectively.

5. How do atomic terms and quantum numbers help us understand the behavior of electrons in an atom?

Atomic terms and quantum numbers provide a framework for understanding the arrangement and movement of electrons in an atom. They explain why electrons occupy certain energy levels and how they are distributed among sublevels and orbitals. This understanding is crucial in explaining various chemical and physical properties of elements.

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