Full set of Notes with Fill-Ins - San Jose State University

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Chem 155 Unit 13 Page 244 of 316Group frequencies can be calculated approximately:Interatomic forces are approximated by Hooke’s Law:F =k · ySince F = mA (Newton’s Law)d 2 yF = mA = m = ky(t)y(t) is proportional to its own second derivative.This differential equation has a sinusoid solution:dt 2y(t) = A cos(2πν m t) ν m =1 k2π μμ =m 1 m 2m 1 + m 2reduced massUnits of μ are:Page 244 of 316units of mass
Chem 155 Unit 13 Page 245 of 316Classical calculations (above) tell you the natural frequencyof a classical oscillator.Quantuum mechanical calculations tell you the allowedenergy levels (E). From Planck and Einstein’s equationE=hν we can calculate the light frequencies (ν).E = (v + ½ )h ν mv = vibrational quantuum number = 0,1,2…Δv = 0,±1 = the selection rule for vibrational transitionsagain: ν m =12πkμso:ΔE = Δv h ν m = ±1h2πkμ= hνnote:ν m is the oscillator frequency andν is the light frequencyWhat is the relationship between ν and ν m ?the light frequency equals the oscillatorfrequencyWhat is the relationship between light frequency, ν, and lightwavenumber, ν (cm -1 )? (ν = 1/λ(cm)).ν = cνPage 245 of 316
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Full set of Notes with Fill-Ins - San Jose State University

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