Test on Molecular Rotational Spectroscopy

Question 1: The total classical energy of a rotating body is expressed as the sum of contributions from the angular velocities and moments of inertia along the x, y, and z axes.

A. Ano

B. Ne

Explanation: According to the study materials, the total classical energy is given by the expression E = 1/2 I_x ω_x^2 + 1/2 I_y ω_y^2 + 1/2 I_z ω_z^2, which is a sum of terms relating moment of inertia and angular velocity for each axis.

Question 2: The spacing between adjacent lines in the rotational spectrum of a linear rotor is equal to the rotational constant, B̄.

A. Ano

B. Ne

Explanation: For a linear rotor, the spacing between equally spaced lines in the rotational spectrum is 2B̄, not B̄.

Question 3: According to the provided study materials, which factors contribute to the moment of inertia of a rotating molecule?

A. The mass of the rotating atoms.

B. The perpendicular distance of the rotating atoms from the axis of rotation.

C. The total number of atoms in the molecule.

D. The mass of non-rotating atoms.

Explanation: The study materials explicitly state that inertia increases with the 'mass of rotating atoms' and the 'distance of rotating atoms from axis'. It also states that 'Non-rotating atoms do not contribute to inertia', making option 3 incorrect. The total number of atoms is not listed as a direct contributing factor.

Question 4: In rotational Raman spectroscopy, which statement accurately describes the characteristics of Anti-Stokes lines?

A. Anti-Stokes lines result from a photon emerging with lower energy, and have a ∆J = +2 selection rule.

B. Anti-Stokes lines show no change in photon frequency, and are associated with ∆J = 0.

C. Anti-Stokes lines result from a photon emerging with higher energy, and have a ∆J = -2 selection rule.

D. Anti-Stokes lines are only observed when the molecule is isotropically polarizable.

Explanation: According to the study materials (4.2.14. Rotational Raman spectroscopy – Spectra), Anti-Stokes lines occur when the photon emerges with higher energy, corresponding to a ∆J = -2 transition.

Question 5: The rotational energy level frequency for J = 1, K = 0 is 19.392 cm − 1 in Example 13.2.

A. Ano

B. Ne

Explanation: The study materials explicitly state: "For J = 1, K = 0: � 𝐹𝐹 1,0 = 19 . 392 cm − 1 = End to end rotation" in Example 13.2.