The wavenumber (cm–1), the reciprocal of the wavelength, is often used as a measure of energy and is — Analytical Chemistry Chemistry Question
Vibrational states of Cl2
The wavenumber (cm–1), the reciprocal of the wavelength, is often used as a measure of energy and is equal to the energy of a photon with the corresponding wavelength. The following figure shows the emission spectrum of gaseous Cl2 excited at 73448 cm–1. The spectrum shows a sequence of peaks, and each peak corresponds to the fluorescence at the vibrational state with the quantum number v (= 0, 1, 2,...).
Calculate the approximate energy spacing between the adjacent vibrational energy levels at the ground electronic state of Cl2, Ev, in kJ mol–1. You can choose any pair of adjacent peaks for calculation.
Model Answer
From the figure, the interval between the peaks can be determined to be 500 [480 – 550] cm–1.
The corresponding wavelength λ = 1×10–2 / 500 [480 – 550] = 2.0 [1.82 – 2.08] × 10–5 m
Then, the corresponding energy Ev = NAhc / 2.0 [1.82 – 2.08]×10–5 = 6.0 [5.7 – 6.6] kJ mol–1.
Ev = 6.0 [5.7 – 6.6] kJ mol–1