The IR spectra for the hydrogen chloride molecule (HCl) display a peak at 2886 cm^(-1). Assuming the diatomic vibration can be treated as a harmonic oscillator, calculate the energy for the first vibrational excited state of HCl.

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The IR spectra for the hydrogen chloride molecule (HCl) display a peak at 2886 cm^(-1). Assuming the diatomic vibration can be treated as a harmonic oscillator, calculate the energy for the first vibrational excited state of HCl.