The diatomic radical, 160¹H, can be treated approximately as a harmonic oscillator, with a force constant of 780.7 N/m, mH = 1.007825 Dalton, and mo = 15.9949146 Dalton. (a) What is the harmonic angular frequency, w, of this oscillator (in sec-¹)? (b) Spectroscopic measurements are often used to characterize molecular oscillators, and in doing so, they relate a wavelength of light to its characteristic oscillation frequency through the relation, λω = 2πc. Use this to find in units of cm-1 (wavenumbers). λ - (c) If the force constant is the same, what would be in wavenumbers (cm-¹) for ¹60 2H (²H = deuterium), with mH = 2.014101778 Dalton?

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The diatomic radical, 160¹H, can be treated approximately as a harmonic oscillator, with a
force constant of 780.7 N/m, mH = 1.007825 Dalton, and mo = 15.9949146 Dalton.
(a) What is the harmonic angular frequency, w, of this oscillator (in sec¯¹)?
(b) Spectroscopic measurements are often used to characterize molecular oscillators, and
in doing so, they relate a wavelength of light to its characteristic oscillation frequency
through the relation, w = 2πc. Use this to find in units of cm-1 (wavenumbers).
λ
=
(c) If the force constant is the same, what would be in wavenumbers (cm-¹) for ¹60 ²H (²H
= deuterium), with mH = 2.014101778 Dalton?
Transcribed Image Text:The diatomic radical, 160¹H, can be treated approximately as a harmonic oscillator, with a force constant of 780.7 N/m, mH = 1.007825 Dalton, and mo = 15.9949146 Dalton. (a) What is the harmonic angular frequency, w, of this oscillator (in sec¯¹)? (b) Spectroscopic measurements are often used to characterize molecular oscillators, and in doing so, they relate a wavelength of light to its characteristic oscillation frequency through the relation, w = 2πc. Use this to find in units of cm-1 (wavenumbers). λ = (c) If the force constant is the same, what would be in wavenumbers (cm-¹) for ¹60 ²H (²H = deuterium), with mH = 2.014101778 Dalton?
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