Step 1: Understanding the Concept:
This question asks to identify which of the given atomic orbitals has its lobes (regions of high electron probability) located between the Cartesian axes, rather than along them. This requires knowledge of the shapes and orientations of p and d orbitals.
Step 2: Detailed Explanation of Orbital Shapes:
Let's describe the orientation of the lobes for each option:
- (A) $p_x$ orbital: This is one of the three p orbitals. It has a dumbbell shape with its two lobes oriented directly along the x-axis.
- (B) $p_y$ orbital: This p orbital is identical in shape to the $p_x$ orbital but is oriented along the y-axis. (The third p orbital, $p_z$, is oriented along the z-axis).
- (C) $d_{x^2-y^2}$ orbital: This is one of the five d orbitals. It has a cloverleaf shape with its four lobes pointing directly along the x and y axes.
- (D) $d_{yz}$ orbital: This is also one of the d orbitals. It has a cloverleaf shape, but its four lobes are located in the yz-plane, pointing {between} the y and z axes. The other two similar orbitals are $d_{xy}$ (lobes between x and y axes) and $d_{xz}$ (lobes between x and z axes). These three orbitals ($d_{xy}, d_{yz}, d_{xz}$) are often called the non-axial d orbitals.
Step 3: Conclusion:
Based on the descriptions, the $p_x$, $p_y$, and $d_{x^2-y^2}$ orbitals all have their lobes oriented along the axes. The $d_{yz}$ orbital is the one whose lobes are oriented between the axes.
Step 4: Final Answer:
The $d_{yz}$ orbital has lobes that are not oriented on the axes. Therefore, option (D) is correct.