Understanding the Question: Which Statement is Correct?

The question asks which statement about the number of planes of symmetry (POS) in a CH₄ (methane) molecule is correct. Methane has a tetrahedral geometry, and we need to determine how many planes of symmetry it possesses.

Step 1: Understand What a Plane of Symmetry Is

A plane of symmetry is an imaginary plane that divides a molecule into two halves that are mirror images of each other. If a molecule has a plane of symmetry, it is symmetrical with respect to that plane.

Step 2: Recall the Geometry of Methane (CH₄)

Methane has a tetrahedral structure. The carbon atom is at the center, and four hydrogen atoms are at the corners of a tetrahedron. This geometry is highly symmetric.

Step 3: Identify the Planes of Symmetry in a Tetrahedron

In a regular tetrahedron, there are multiple planes of symmetry. Each plane passes through one vertex (hydrogen atom) and the midpoint of the opposite face. Since there are 4 vertices, there are 4 such planes. Additionally, there are planes that pass through midpoints of edges, but in a regular tetrahedron, these are not distinct symmetry planes; the only planes are the ones through a vertex and the center of the opposite face.

Therefore, methane has 6 planes of symmetry. Wait, that might seem contradictory. Let me clarify:

Actually, for a regular tetrahedron, the number of planes of symmetry is 6. Each plane is defined by one carbon-hydrogen bond and the midpoint of the opposite face? No, that is incorrect. The correct way is: a plane of symmetry can be defined by any two vertices and the midpoint of the opposite edge? Actually, the standard result is that a regular tetrahedron has 6 planes of symmetry.

Let me derive it properly:

In a tetrahedron, for each pair of opposite edges (edges that do not share a vertex), there is a plane that contains these two edges. Since there are 3 pairs of opposite edges, that gives 3 planes? But wait, a tetrahedron has 6 edges, and the number of pairs of opposite edges is 3. However, that is not the complete set.

Actually, the full set of symmetry planes in a regular tetrahedron is 6. Each plane is defined by one vertex and the midpoint of the opposite edge? That would give 4 planes? But that is not symmetric.

The correct mathematical count: a regular tetrahedron has 6 planes of symmetry. Each plane passes through one edge and the midpoint of the opposite edge. Since there are 6 edges, and each plane is associated with a pair of opposite edges, but actually, each plane contains two edges? Let's think differently.

Standard knowledge: The tetrahedral point group (T_d) has 6 planes of symmetry. So, methane, being a perfect tetrahedron, has 6 planes of symmetry.

Therefore, the statement "CH₄ molecule have 6 POS" is correct.

Step 4: Verify the Options

The first option says: "CH₄ molecule have 6 POS." This matches our analysis.

The other options are images. Without seeing the images, we cannot be sure, but since the first option is text and correct, and the question is to choose the correct statement, the first one is likely correct.

Assuming the images show other numbers (like 3, 4, or 9), they would be incorrect.

Final Answer

The correct statement is: CH₄ molecule have 6 POS.

Related Topics

Molecular Symmetry
Point Groups (T_d for tetrahedral molecules)
Symmetry Elements: Planes, Axes, Center of Symmetry
Geometry of Molecules: Tetrahedral, Trigonal Planar, Linear, etc.

Formulae and Theory

Plane of Symmetry (σ): A plane that divides the molecule into two mirror-image halves.

Number of Planes in Common Geometries:

Tetrahedral (e.g., CH₄): 6 planes
Octahedral (e.g., SF₆): 9 planes
Square Planar (e.g., XeF₄): 5 planes
Linear (e.g., CO₂): ∞ planes (infinite)

Point Group of Methane: T_d, which has: $6 σ_{d}$ (dihedral planes) planes of symmetry.