Question

What is a combination of four quantum numbers that could be assigned to an electron occupying a 5p orbital?

Answer 1

`n=5, l=1, m_l = -1, m_s = +1/2`

Explanation:

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

![figures.boundless.com]()

So, you know that you must find a valid combination of quantum numbers that can describe the position and spin of an electron located in a 5p-orbital.

In your case, the principal quantum number, `n`, which tells you on which energy level the electron resides, will be equal to `5`, since a 5p-orbital is located on the fifth energy level.

As you an see, the angular momentum quantum number, `l`, which tells you on which subshell the electron resides, can take values ranging from `0` to `n-1`, with

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

and so on. IN your case, you need `l` to describe the p-subshell, since a 5p-orbital is located in the 5p-subshell, i.e. the p-subshell located on the fifth energy level. Therefore, you can say that `l=1`.

The magnetic quantum number, `m_l`, which specifies the exact orbital in which you can find the electron, can only take `3` possible values for an electron located in the p-subshell

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

In your case, all three values for `m_l` are possible.

Finally, the spin magnetic quantum number, `m_s`, can only take two possible values

• `m_s = +1/2 ->` spin-up electron
• `m_s = -1/2 ->` spin-down electron

Both values for `m_s` are possible for your electron. This means that a total of six sets can describe an electron located in a 5p-orbital.

I'll give you two such sets, and leave the other four to you as practice

`n=5, l=1, m_l = -1, m_s = +1/2`

This electron is located on the fifth energy level, in the 5p-subshell, in the `5p_x` orbital, and has spin-up.

`n=5, l=1, m_l = +1, m_s = -1/2`

This electron is located on the fifth energy level, in the 5p-subshell, in the `5p_z` orbital, and has spin-down.