Question

If an electron has a spin quantum no. of `"+1/2"` and a magnetic quantum no. of `-1`, it cannot be present in?

(a) d-orbital
(b) f-orbital
(c) p-orbital
(d) s-orbital

Answer 1

(d) `s` orbital

Explanation:

The trick here is to realize that an `s` orbital cannot be described by a magnetic quantum number equal to `-1`.

The `s` subshell contains a single `s` orbital, which implies that the magnetic quantum number, which tells you the orientation of the orbital that holds a given electron, can only take `1` possible value.

More specifically, for an `s` subshell, you have

`l = 0`

The angular momentum quantum number, `l`, describes the energy subshell in which the electron resides.

For a given subshell, the relationship between the angular momentum quantum number and the magnetic quantum number is given by

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

This means that for the `s` subshell, you have

`m_l = 0`

as the only value that the magnetic quantum number can take.

Consequently, you can say that

`m_l = -1`

cannot describe an electron located in an `s` orbital because an `s` orbital can only be described by `m_l = 0`.