Question

Which of the following pairs of d-orbitals will have electron density along the axes?
A.${d_{{z^2}}}$, ${d_{xz}}$
B.${d_{xz}}$, ${d_{yz}}$
C.${d_{{z^2}}}$, ${d_{{x^2} - {y^2}}}$
D.${d_{xy}}$, ${d_{{x^2} - {y^2}}}$

Answer 1

The d orbitals are arranged in the three planes according to their shapes. ${d_{{z^2}}}$ is vertical along the z-axis while the ${d_{{x^2} - {y^2}}}$ is also vertical.

Complete step by step solution:
The orbital is defined as the area in the atom, where the probability of finding the electron is maximum. There are five d-orbitals known as the ${d_{xz}}$, ${d_{yz}}$, ${d_{xy}}$, ${d_{{z^2}}}$ and ${d_{{x^2} - {y^2}}}$ orbitals. The d-orbitals are what gives the transition metals its properties.
The ${d_{{z^2}}}$ is the vertical probability of finding the electrons and has a donut like shape with a lobe above and a lobe below. The other four orbitals, ${d_{xz}}$, ${d_{yz}}$, ${d_{xy}}$ and ${d_{{x^2} - {y^2}}}$ have a clover like structure or a daisy like structure with the lobes lying in the axes mentioned in the subscript.
For the ${d_{xz}}$, ${d_{yz}}$, ${d_{xy}}$ orbitals, the lobes lie in between the axes and not directly along them. But for the ${d_{{x^2} - {y^2}}}$, the lobes lie directly along the x and the y axes.
On the other hand, the lobes of the ${d_{{z^2}}}$ orbitals also lie along the z axis.

Hence, the correct answer is option C.

Note:
The d-orbitals can be seen from principal quantum number 3 onwards and the azimuthal quantum number 2, the magnetic quantum number ranges from $- 2{\text{ to }} + 2$ and hence we get 5 orbitals. The magnetic quantum numbers do not correlate to a specific orbital, rather the orbitals are a linear combination of different ${m_l}$ values.