Spectroscopic vibration-rotation transitions in the P- and R-branches of the high-resolution infrared spectrum of hydrogen iodide, HI, are observed to be separated by a wavenumber of 6.37 cm^-1. Calculate the length of the bond of a hydrogen iodide molecule.

Question

Quizplus · Accepted Answer

The separation between the P and R branches is approximately twice the rotational constant B. The rotational constant B is related to the bond length (r) by the formula B = h / (8π²cI), where I is the moment of inertia (I = μr², μ is the reduced mass). Solving for r using the given separation (2B = 6.37 cm⁻¹) and the known values for h, c, and μ for HI, we find r ≈ 1.03 Å.

Spectroscopic Vibration-Rotation Transitions in the P- and R-Branches of the High-Resolution