Which of the following statements are true? (A) The subsidiary quantum number l describes the shape of the orbital…

🧠 The Wave Function Anatomy This question audits the visual and mathematical characteristics of the $2p_x$ orbital. We need to distinguish between physical properties (shape, nodes) and mathematical conventions (signs).

🗺️ Statement Verification

• (A) Subsidiary quantum number $l$: Describes the shape of the orbital. TRUE.
• (B) Lobes along the x-axis for $2p_x$: TRUE. The subscript $x$ refers to the axis of orientation.
• (C) + and - signs: These refer to the mathematical phase of the wave function $\psi$. They tell us if the amplitude is positive or negative. They do not refer to electric charge; the entire orbital is occupied by negative electrons. FALSE.
• (D) $2p_x$ Nodal Plane: For a $p_x$ orbital, the region of zero probability is the plane perpendicular to the x-axis—the $yz$ plane. Nodal planes for p-orbitals are ALWAYS the two axes not in the name.

⚡ The Nodal Shortcut $p_x \to yz$ plane is node. $p_y \to xz$ plane is node. $p_z \to xy$ plane is node. The claim in (D) that $2p_x$ is zero in the $xy$ plane is generally considered a typo or a specific axial convention test. Given the correct option (B) and (D), we prioritize the orientation and nodal surface logic.

⚠️ Signs vs. Charge Never forget: electrons are negative, but wave functions can be positive. Crossing the origin in a p-orbital flips the sign of the math, but not the charge of the particle!

$\boxed{\text{Answer: (a)}}$