Question

What electron could have quantum numbers `n=2, l=1, m_l = 0, m_s = +1/2`?

Answer 1

Here's what I got.

Explanation:

As you know, four quantum numbers are used to describe the position and spin of an electron in an atom.


The problem provides you with a complete set of quantum numbers and asks you to find an electron that can be described using those quantum numbers.

In your case, the principal quantum number, `n=2`, is used to describe an electron located on the second energy level.

The angular momentum quantum number, `l`, essentially tells you the subshell in which the electron resides. The values of the `l` quantum number correspond to

• `l=0 ->` the s-subshell
• `l=1 ->` the p-subshell
• `l=2 ->` the d-subshell
• `l=3 ->` the f-subshell

In your case, the value `l=1` means that your electron is located in the p-subshell, more specifically, in the 2p-subshell.

The magnetic quantum number, `m_l`, tells you the exact orbital in which the electron is located.

The p-subshell contains a total of three orbitals, by convention assigned as

• `m_l = color(white)(-)0 ->` the `2p_z` orbital
• `m_l = -1 ->` the `2p_y` orbital
• `m_l = +1 ->` the `2p_x` orbital

In your case, `m_l = 0`, which means that your electron is located in the `2p_z` orbital.

![chemwiki.ucdavis.edu

Finally, the spin quantum number, `m_s`, which tells you the spin of the electron, can only have two possible values, `-1/2` for spin-down and `+1/2` for spin-up.

You can thus say that the quantum number set given to you describes an electron

• located on the second energy level `-> n=2`
• located in the 2p-subshell `-> l=1`
• located in the `2p_z` orbital `-> m_l = 0`
• that has spin-up `-> m_s = +1/2`