In the absorption spectrum of the diatomic molecule HCl the central frequency is at 8.67 $\times$ 10¹³ Hz,while the absorption peaks on either side are separated by 5.9 $\times$ 10¹¹ Hz.What is the energy of the lowest vibrational state? A)0.18 eV B)0.27 eV C)0.36 eV D)2.4 meV E)1.2 meV

Question

Quizplus · Accepted Answer

The energy of the lowest vibrational state can be calculated using the separation between the absorption peaks, which corresponds to the energy difference between the first excited and ground vibrational states. This energy difference is given by $E = h\nu$, where $h$ is Planck's constant ($6.626 \times 10^{-34} \, \text{Js}$) and $\nu$ is the frequency separation ($5.9 \times 10^{13} \, \text{Hz}$). The energy of the lowest (ground) vibrational state is half of this value, as it is the zero-point energy. Calculating this gives a value close to 0.18 eV, making option A correct.

In the Absorption Spectrum of the Diatomic Molecule HCl the Central