Question

What is the set of four quantum numbers that represent the electron lost to form the `"K"^(+)` ion from the `"K"` atom?

Answer 1

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

Explanation:

Your goal here is to find the values of the four quantum numbers that are used to describe the location and spin of an electron inside an atom.

Start by writing the electron configuration of a neutral potassium atom, `"K"`

`"K: " 1s^2 2s^2 2p^6 3s^2 3p^6 color(red)(4)color(darkgreen)(s)^color(blue)(1)`

When potassium forms the potassium cation, `"K"^(+)`, it does so by losing its valence electron, which as you know is the electron located in potassium's outermost shell.

As you can see, the electron lost when potassium becomes as ion comes from the `color(red)(4)color(darkgreen)(s)` orbital.

The principal quantum number, `n`, tells you the energy level on which the electron resides. In this case, the electron is located on the fourth energy level, and so you have

`n = color(red)(4)`

The angular momentum quantum number, `l`, tells you the subshell in which the electron is located. For an electron located on the fourth energy level, the angular momentum quantum number can take the following values

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

In your case, the electron comes from the `color(darkgreen)(s)` subshell, and so

`l = 0`

The magnetic quantum number, `m_l`, tells you the specific orbital in which you can find the electron resides. The s-subshell can only hold one orbital, the s-orbital, and so

`m_l = 0 ->` designates the s-orbital

Finally, the spin quantum number, `m_s`, gives you the spin of the electron. Since the electron is unpaired, you can assign it

`m_s = +1/2 ->` designates spin-up

Therefore, the quantum number set that describes potassium's valence electron looks like this

`color(green)(|bar(ul(color(white)(a/a)color(black)(n=4, l=0, m_l = 0, m_s = +1/2)color(white)(a/a)|)))`

This set describes an electron located on the fourth energy level, in the s-subshell, in the 4s-orbital, that has spin-up.