Question

How to describe the electrons defined by the following quantum numbers?

n=3, l=0, `m_l=0`
n=2, l=1 `m_l=1`
Do I just have to say that it has for example one 3s orbital with 3 subshells or do I have to add other information as well? I am struggling a bit with this one. Thanks in advance.

Answer 1

Here's how you can do that.

Explanation:

You have values for three our of the four quantum numbers that we use to describe the location and the spin of an electron inside an atom.

• the principal quantum number, `n`
• the angular momentum quantum number, `l`
• the magnetic quantum number, `m_l`.

This means that in order to describe the electrons defined by these two incomplete quantum number sets, you must mention

• the energy shell in which the electron is located because you know the value of `n`
• the energy subshell in which you can find the electron because you know the value of `l`
• the orientation of the orbital in which the electron resides because you know the value of `m_l`

For the first set, you have

`n = 3, l=0, m_l = 0`

This set describes an electron that

• is located in the third energy shell because `n = 3`
• is located in the `s` subshell because `l = 0`
• is located in the `s` orbital because `m_l = 0`

So for this first electron, you have the third energy shell, the `3s` subshell, and the `3s` orbital. You don't know the value of the spin quantum number, `m_s`, so you can't specify the spin of the electron.

For the second set, you have

`n = 2, l =1, m_l = 1`

This time, the set describes an electron that

• is located in the second energy shell because `n = 2`
• is located in the `p` subshell because `l = 1`
• is located in one of the three `p` orbitals because `m_l = 1`

So for this electron, you have the second energy shell, the `2p` subshell, and one of the three `2p` orbitals, let's say `2p_x`. Once again, you don't have the value of `m_s`, so you can't say anything about the spin of the electron.