How would the dx2−y2 orbital in the n=5 shell compare to the dx2−y2 orbital in the n=3 shell?
Determine which statement is true or false.

The orbital in the n = 5 shell is bigger than the orbital in the n = 3 shell.
The value of l would increase by 2 for the n = 5 shell.
The value of l for both orbitals would be the same.
The orientation of the n = 5 orbital would be rotated 45∘ along the xy plane.
The mâ„“ value for both orbitals would be the same.

TRUE; False; TRUE; False; TRUE

Explanation:

1. Orbital size

TRUE.

The orbital in the n = 5 shell is bigger than the orbital in the n = 3 shell.

The principal quantum number (n) determines the size of the orbital. A 5d orbital is bigger than a 3d orbital.

2. and 3. Orbital shape

The secondary quantum number (l) determines the shape of the orbital

If l = 2, the orbital is a d orbital. All d orbitals have l = 2.

2 is False. 3 is TRUE.

4. and 5. Orbital orientation

The magnetic quantum number (mₗ) determines the orientation of the orbital in a magnetic field.

The d(xy), d(xz), and d(yz) orbitals have four lobes oriented half-way (45°) between the xy-, xz-. and yz-axes, respectively.

The d(x²-y²) orbitals have four lobes oriented along the x- and y-axes.

The d(z²) orbital has two lobes oriented along the z-axis, with a torus (a ring-shaped doughnut) in the xy-plane.

These are each d(x²-y²) orbitals, so they have the same mₗ values.

4. is False. 5. is TRUE.

The 3d and 5d orbitals are shown below. The lobes are aligned along the x- and y-axes. The 5d orbital is bigger, and it also has two radial (spherical) nodes, which are absent in the 3d orbital.