Question

What do quantum numbers describe?

Answer 1

The energy level, shape of orbital, orientation of the orbital and the spin of an electron, for a given electron.

Explanation:

The quantum numbers are represented as: `(n,l,m_l,m_s)`

`n` represents the energy level of the electron, where `n=1,2,3,4,...`. `n` also indicates the row on the periodic table.

`l` determines what orbital shape it is, where `l=0,1,2,...(n-1)`.
`l=0=>text(s-orbital)`
`l=1=>text(p-orbital)`
`l=2=>text(d-orbital)`
`l=3=>text(f-orbital)`

`m_l` determines the orientation of the orbital, where `-l <= m_l <= l`. This shows that an s-orbital has 1 orientation, a p-orbital has 3 orientations, d-orbital has 5 orientations, and an f-orbital has 7 orientations.

`m_s` is the spin of the electron which can only be `-1/2` or `+1/2`
It tells whether a electron is spin-up or spin-down.

The video below explains how quantum numbers describe the position of an electron. The video also discusses how to determine the quantum numbers for four different electrons (#1, 6, 29).

Video from: Noel Pauller

Hope this helps!