Question

Which d-orbitals have a different shape from the rest of all d-orbitals?
A. $d_{x^2-y^2}$
B. $d_{z^2}$
C. $d_{xz}$
D. $d_{xy}$
E. $d_{xy}$

Answer 1

Hint:An orbital is the quantum mechanical refinement of Bohr’s orbit. In contrast to his concept of a circular orbit with a fixed radius, orbitals are mathematically derived regions of space with different probabilities of containing an electron. The d orbital contains 10 electrons. The d orbital is a clover shape because the electron is pushed out four times during the rotation.

Complete step by step answer:
The d orbital has ten protons to complete a fourth level of tetrahedral structure. With three spin aligned protons, it would have a spherical shape, yet four times during the rotation will have gluons that align with protons of the opposite spin to force an electron.
Now, we see the figure of all d-orbitals except $d_{z^2}$ because it has four lobes and has only two lobes.

From the above figure, we see that the d-orbitals are in different shapes. $d_{z^2}$orbital has a different shape from rest of all d-orbitals.
 $d_{z^2}$ degenerate with other d orbitals, it has no nodal planes, instead it has 2 nodal cones. Instead of having 4 lobes, it has 2 lobes and 1 ring. That’s why this orbital is so different from the rest.
Hence, option (B) is the correct answer.

Note:The standard procedure in differential calculus is to use a linear combination of two functions to produce one independent one. So $d_{z^2}$ looks different because it is a linear combination of two functions. In this orbital, 2 lobes lie on the z-axis as we see.