Question

Identify the orbital which has lobes not orienting on the axis

• A. \(p_x\)
• B. \(p_y\)
• C. \(d_{x^2-y^2}\)
• D. \(d_{yz}\)

Hint:

A simple mnemonic for d-orbitals: if the subscript has two different letters (like xy, yz, xz), the lobes are *between* those axes. If the subscript involves squares (like \(x^2-y^2\), \(z^2\)), the lobes are *on* the axes.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We need to identify which of the given atomic orbitals has its electron density lobes located between the coordinate axes, rather than directly along them.

Step 2: Key Formula or Approach:
This requires knowledge of the standard shapes and orientations of p and d atomic orbitals.
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p orbitals (\(p_x, p_y, p_z\)): These are dumbbell-shaped, and their lobes lie directly along the corresponding axis (x, y, or z).
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d orbitals: There are five d orbitals with two main groups:
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Axial orbitals (\(d_{z^2}, d_{x^2-y^2}\)): Their lobes lie along the axes. \(d_{x^2-y^2}\) has lobes on the x and y axes. \(d_{z^2}\) has a main lobe along the z-axis and a torus in the xy-plane.
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Non-axial orbitals (\(d_{xy}, d_{yz}, d_{xz}\)): These are cloverleaf-shaped, and their lobes lie in the planes indicated by their subscripts, but positioned *between* the axes.

Step 3: Detailed Explanation:
Let's analyze the options:
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(A) \(p_x\): The two lobes of the \(p_x\) orbital lie directly on the x-axis.
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(B) \(p_y\): The two lobes of the \(p_y\) orbital lie directly on the y-axis.
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(C) \(d_{x^2-y^2}\): The four lobes of this orbital lie directly on the x and y axes.
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(D) \(d_{yz}\): The four lobes of this orbital lie in the yz-plane, but they are oriented at 45° to the y and z axes, i.e., between the axes.
Therefore, the \(d_{yz}\) orbital has lobes that are not oriented on the axes.

Step 4: Final Answer:
The orbital \(d_{yz}\) has lobes not orienting on the axis.