Explanation:

The three rotational constants obtained from the microwave spectrum of a molecule can be used to identify the shape of the molecule. The different shapes of molecules include prolate symmetric top, spherical top, asymmetric top, and oblate symmetric top.

Rotational Constant:

The rotational constant is a measure of the energy required to rotate a molecule about its axis. It is given by the formula:

B = h / (8π²cI)

where B is the rotational constant, h is Planck's constant, c is the speed of light, and I is the moment of inertia of the molecule.

Identification of the Shape of the Molecule:

The shape of the molecule can be identified based on the values of the three rotational constants obtained from the microwave spectrum.

Prolate Symmetric Top:

A prolate symmetric top molecule is one in which the molecule has a long axis of symmetry and two equal short axes perpendicular to the long axis. The rotational constants for a prolate symmetric top molecule are given by:

B₁ < b₂="" />

Spherical Top:

A spherical top molecule is one in which the molecule has no axis of symmetry. The rotational constants for a spherical top molecule are given by:

B₁ = B₂ = B₃

Asymmetric Top:

An asymmetric top molecule is one in which the molecule has no axis of symmetry and all three rotational constants are different. The rotational constants for an asymmetric top molecule are given by:

B₁ < b₂="" />< />

Oblate Symmetric Top:

An oblate symmetric top molecule is one in which the molecule has a short axis of symmetry and two equal long axes perpendicular to the short axis. The rotational constants for an oblate symmetric top molecule are given by:

B₁ = B₂ < />

The given molecule yields three rotational constants and the values of the rotational constants are not equal, which indicates that the molecule is an asymmetric top. Therefore, the correct option is C.