Question

How would you determine the quantum number, ml, for an element?

Answer 1

`m_l` is the magnetic quantum number, corresponding to the projection of the angular momentum of an orbital, i.e. its orientation in space.

As the symbol suggests, it has to do with `l`, the angular momentum quantum number. `l` describes the shape of the orbital. Let's look at various values of `l` and their corresponding `m_l`.

• `l = 0 -> m_l = 0`, orbital = `s`
• `l = 1 -> m_l = -1,0,+1`, orbital = `p`
• `l = 2 -> m_l = -2,-1,0,+1,+2`, orbital = `d`
• `l = 3 -> m_l = -3,-2,-1,0,+1,+2,+3`, orbital = `f`

and so on.

The general pattern is that we have:

`m_l = -l, -l+1, -l+2, . . . , 0, +1, +2, . . . , +l-2, +l-1, +l`

or

`color(blue)(m_l = 0, pm1, pm2, . . . , pml)`

In short, we have `2l+1` values of `m_l` for a particular `l` for a particular orbital.

If, let's say, we chose boron (`Z = 5`), it has access to the valence orbitals `2s` and `2p`, but it also has the `1s` technically as a core orbital.

`1s`:

`(n, l, color(blue)(m_l)) = (1, 0, color(blue)(0))`

Hence, there is only one `1s` orbital.

`2s`:

`(n, l, color(blue)(m_l)) = (2, 0, color(blue)(0))`

So, there is only one `2s` orbital.

`2p`:

`(n, l, color(blue)(m_l)) = (2, 1, [color(blue)(-1,0,+1)])`

Therefore, there are only three `2p` orbitals (`2p_x`, `2p_y`, and `2p_z`).

For its valence orbitals, since it has one `2s` and three `2p` orbitals, it can have up to `2xx1 + 3xx2 = 8` valence electrons. Thus, it is not expected to exceed `8` valence electrons in its molecular structures.