Question

Question #64fc6

Answer 1

`"3 e"^(-)`

Explanation:

The idea here is that each individual orbital can hold a maximum of `2` electrons, one having spin-up, or `m_2 = +1/2`, and the other having spin-down, or `m_s = -1/2`.

This implies that in order to figure out how many electrons that are located in the `2p` subshell can have `m_2 = -1/2`, you must determine how many orbitals are present in this subshell.

As you know, the number of orbitals present in a given subshell `l` is given by the number of values that the magnetic quantum number, `m_l`, can take.

`m_l = {-l, -(l-1), ..., -1, 0, 1, ..., (l-1), l}`

In your case, you are dealing with a `p` subshell, so you should know that `l=1` since you have

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

and so on. This means that any `p` subshell, including the `2p` subshell, which is simply the `p` subshell located on the second energy level, will have

`m_l = (-1,0,1}`

So, three values for `m_l` give you `3` orbitals for any `p` subshell.

Now, you know that you get a maximum of `2` electrons per orbital, but that only `1` electron can have `m_2 = -1/2` in an orbital--the other electron located in the same orbital must have `m_2 = +1/2`.

This means that you have

`3 color(red)(cancel(color(black)("2p orbitals"))) * ("1 e"^(-)color(white)(.)"with m"_s = -1/2)/(1color(red)(cancel(color(black)("2p orbital")))) = "3 e"^(-)` `"with m"_s = -1/2`