Step 1: Understanding the Concept:
The five d-orbitals are classified into two groups based on their orientation in space: those that lie between the axes ($t_{2g}$ set) and those that lie along the axes ($e_g$ set).
Step 2: Key Formula or Approach:
1. Non-axial orbitals: $d_{xy}, d_{yz}, d_{xz}$ (lobes lie at 45° to the axes).
2. Axial orbitals: $d_{x^2-y^2}, d_{z^2}$ (lobes lie directly on the axes).
Step 3: Detailed Explanation:
The $d_{x^2-y^2}$ orbital has four lobes pointing along the X and Y axes. The $d_{z^2}$ orbital has two lobes pointing along the Z-axis and a "doughnut" of electron density in the XY plane. In contrast, $d_{xy}, d_{yz},$ and $d_{xz}$ have lobes situated between the respective coordinate axes.
Step 4: Final Answer:
The orbitals with electron density along the axes are $d_{z^2}$ and $d_{x^2-y^2}$.