Question

What are the quantum numbers for electrons in the `4d` orbitals?

Answer 1

Here's what I got.

Explanation:

As you know, the principal quantum number, `n`, tells you the energy shell in which the electron is located.

In your case, the electron is said to occupy the `"4th"` energy level, which is equivalent to saying that it is located in the `"4th"` energy shell, so

`n = 4`

The angular momentum quantum number, `l`, tells you the energy subshell in which the electron is located. For this quantum number, you have

• `l = 0 ->` the `s` subshell
• `l = 1 ->` the `p` subshell
• `l = 2 ->` the `d` subshell
  `vdots`

and so on. In your case, you have

`l = 2`

Now, the `d` subshell can hold a maximum of five `d` orbitals, which are denoted by the values of the magnetic quantum number, `m_l`.

For the `d` subshell, you have

`m_l = {-2, -1, 0, 1, 2}`

Finally, the spin quantum number, `m_s`, which denotes the spin of the electron, can take two possible values

`m_s = {+1/2, - 1/2}`

You now have all the information that you need to write the sets of quantum numbers that can describe an electron located on the `"4th"` energy level, in the `4d` subshell.

I'll show you four sets to start you off

• `n = 4, l =2, m_l = -2, m_s = +1/2`
• `n = 4, l = 2, m_l = 0, m_s = -1/2`
• `n = 4, l =2, m_l = 1, m_s = -1/2`
• `n = 4, l =2, m_l = 1, m_s = +1/2`