2020 H2 Chem P1 Q1 — Atomic structure Solution

The answer is C (4).

There are five 3d orbitals: \(d_{xy}\), \(d_{xz}\), \(d_{yz}\), \(d_{x^2-y^2}\) and \(d_{z^2}\).
• \(d_{xy}\), \(d_{xz}\) and \(d_{yz}\) each have four lobes, lying between the two named axes.
• \(d_{x^2-y^2}\) has four lobes, lying along the x- and y-axes.
• \(d_{z^2}\) has only two lobes (along the z-axis) with a ring of electron density around the centre.

So 4 of the 3d orbitals have four lobes.

• A is wrong: 2 leaves out two of the four-lobed orbitals; \(d_{xy}\), \(d_{xz}\), \(d_{yz}\) and \(d_{x^2-y^2}\) all have four lobes.
• B is wrong: 3 counts only \(d_{xy}\), \(d_{xz}\) and \(d_{yz}\) and misses \(d_{x^2-y^2}\), whose four lobes lie along the axes instead of between them.
• D is wrong: 5 counts every 3d orbital, but \(d_{z^2}\) has two lobes and a ring, not four lobes.