Question

The molecule(s) that follow(s) 𝐼_𝑎< 𝐼_𝑏=𝐼𝑐 (𝐼_𝑎, 𝐼_𝑏, and 𝐼_𝑐 are the principal moments of inertia) is/are

• A. HCN
• B. CH₃Cl
• C. CH₃C≡CH
• D. C₆H₆

Answer 1

The Correct Option is A, B, C

To determine which molecules follow the condition \( I_a < I_b = I_c \), where \( I_a \), \( I_b \), and \( I_c \) are the principal moments of inertia, we need to understand the geometry and symmetry of each molecule.

The principal moments of inertia are representations of how mass is distributed with respect to rotation about three orthogonal axes through the center of mass of the molecule. The condition \( I_a < I_b = I_c \) typically corresponds to a linear molecule, since for a linear molecule, rotation about the axis along the molecule (linear axis) will have a very small moment of inertia \( (I_a) \), and the two perpendicular axes will have the same moment of inertia \( (I_b = I_c) \). 

1. **HCN (Hydrogen cyanide):**
   • HCN is a linear molecule with the structure H-C≡N.
   • This linear geometry makes \( I_a \) (along the internuclear axis) negligibly small compared to \( I_b \) and \( I_c\), which are equal. Hence, HCN follows \( I_a < I_b = I_c \).
2. **CH₃Cl (Methyl chloride):**
   • CH₃Cl has a pyramidal (approximate tetrahedral) geometry around the central carbon atom.
   • For such molecules, the principal moments of inertia do not satisfy \( I_a < I_b = I_c \), as the rotational symmetry is not linear.
3. **CH₃C≡CH (Propyne):**
   • CH₃C≡CH is also known as methylacetylene. It has a linear geometry along the C≡C axis.
   • Thus, it follows the condition \( I_a < I_b = I_c \) due to its linear structure.
4. **C₆H₆ (Benzene):**
   • Benzene is a planar molecule with a hexagonal shape.
   • It is not linear and has a more complex set of moments of inertia, generally not satisfying \( I_a < I_b = I_c \).

Based on the analysis above, the molecules that follow the given condition \( I_a < I_b = I_c \) are:

• HCN
• CH₃C≡CH

Therefore, the correct answers are HCN and CH₃C≡CH.