Question

What quantum number defines a subshell? How do we label each subshell? How many orbitals in each subshell?

Answer 1

The angular momentum quantum number.

`l = 0, 1, 2, 3, . . . , n-1`

where `n` is the principal quantum number, the energy level. This maximum to `l` is why `1p`, `2d`, `3f`, `4g`, . . . etc. orbitals don't exist.

Each value of `l` designates a subshell, of a certain shape, labeled `s,p,d,f,g,h,i,k, . . .`, corresponding to `l = 0, 1, 2, 3, 4, 5, 6, 7, . . .`.

The `z`-projection of `l` is the magnetic quantum number `m_l`, which corresponds to EACH orbital in a given subshell designated by `l`.

`m_l = {-l, -l+1, . . . , 0, . . . , l-1, l}`

i.e. there are `2l+1` values of `m_l`, so there are `bb(2l+1)` orbitals in one subshell.

CHALLENGE: How many `d` orbitals are there in any given subshell?