Question

Why do `2d`, `1d`, and `3f` orbitals not exist?

Answer 1

Each energy level listed does not contain the given sublevels in the ground state.

Explanation:

In the ground state for each energy level:

In the 2nd energy level, electrons are located only in the s and p sublevels, so there are no d orbitals.

In the 1st energy level, electrons occupy only in the s sublevel, so there is no d sublevel.

In the 3rd energy level, electrons occupy only the s, p, and d sublevels, so there is no f sublevel.

Answer 2

Because those angular momenta are too high for the given quantum levels.

---

Recall that the first two quantum numbers are:

• `n = 1, 2, 3, . . .`

• `l = 0, 1, 2, . . . , n-1` `harr` `s, p, d, f, g, h, i, k, . . .`

where `n` is the principal quantum number indicating the energy level, and `l` is the angular momentum quantum number indicating the shape of the orbital.

Since `l` can be no greater than `n-1` (i.e. `l_(max) = n-1`), it follows that the maximum `l` for each energy level is:

`n = 1 => l_(max) = 0 => s`

`n = 2 => l_(max) = 1 => p`

`n = 3 => l_(max) = 2 => d`

`n = 4 => l_(max) = 3 => f`

`vdots" "" "" "" "" "" "" "vdots`

As a result, the highest angular momentum orbitals we have are `1s`, `2p`, `3d`, `4f`, etc. We cannot have `1p`, `2d`, `3f`, `4g`, etc.

In other words, we have only:

`1s`

`2s, 2p`

`3s, 3p, 3d`

`4s, 4p, 4d, 4f`

`vdots" "" "" "" "ddots`