Question

Which of the following is a `2p` orbital?

`A)`

`B)`

`C)`

`D)`

Answer 1

The `2p` orbital is `D`.

• `A` is an `ns` orbital, probably `3s` or `4s`, though it depends on their size.
• `B` is a `3d_(z^2)` orbital.
• `C` is a `3d_(xz)` orbital.

However, do not trust the image. `B`, `C`, and `D` are wrong because all the lobe signs are presented to be the same whereas they aren't.

The `3d_(z^2)` orbital ring is the opposite sign, the `3d_(xz)` has diagonal lobes of the same sign (`yz` and `xy` nodal planes), and the `2p_z` orbital's second lobe is the opposite sign.

---

The `2p` orbital has:

• `n = 2`, for the principal quantum number. `n` can be one number in the set `{1,2,3, . . . }`.
• `l = 1`, for the angular momentum quantum number since `l = {0,1,2,3, . . . } harr {s,p,d, f, . . . }`.

If you recall:

• The total number of nodes (radial or angular regions of zero electron density) is equal to `n - 1`.
• The total number of angular nodes (nodal planes or conic nodes) is `l`.
• The total number of radial nodes is `n - l - 1`.

Since `l = 1`, there is one angular node, and since `n - 1 = 1`, it is the only node.

On either side of a nodal plane is a lobe of the opposite sign, and thus, there are two lobes on a `2p` orbital. That means it has to be either `B` or `D`.

The `B` orbital has `2` conic nodes, which are angular nodes, and corresponds to how `l = 2` corresponds to a `d` orbital.

`B` is actually a `bb(3d_(z^2))` orbital, like so:

Both lobes on `B` are actually the same sign, whereas it's the ring that is the opposite sign.

The `2p` orbital is `color(blue)(D)`.