In how many different ways can the four quantum numbners designate a `3p` electron?

Options

A. Three
B. Six
C. Five
D. Just one

Answer

B

Explanation

The four quantum numbers `n, l, m_(l)`, and `m_(s)` enable us to tabel completely an electron in an orbital in any atom. To start with, we know that the principle quantum number `n` is `3` and the azimuthal quantum number `l` must be `1` (because we are dealing with a `p` orbital electron). for `l = 1`, there are three values of `m_(l)` gives as `-1, 0, 1`. Since the electron spin quantum number `m_(s)` can be either `.+1//2` or `.-1//2`, we conclude that there are six possible ways to designate the electron:
`(3, 1, -1, +1//2) (3,1, -1, -1//2)`
`(3, 1, 0, +1//2) (3, 1, 0, -1//2)`
`(3, 1, 1, +1//2) (3, 1, 1, -1//2)`