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SHM - Molecules Vibration

  1. Dec 16, 2007 #1
    1. The mass of the deuterium molecule D2 is twice the mass of Hydrogen molecule H2. If the vibrational frequency of H2 is 1.35x10^14 Hz, what is the vibrational frequency of D2, assuming the "spring constant" of attracting forces is the same for two species? Answer in unit of Hz.



    2. Relevant equations

    f=(w)/(2pie)
    w=sq root (k/m)
    k=m(w^2)
    w is phrased as omega

    3. The attempt at a solution

    H2 :
    f=1.35x10^14
    (f)(2pie)=w = 8.48x10^14
    k=m(w^2)=7.19x10^29(m)

    D2 :
    f=? <--solve
    m=2k=2(7.19x10^29)m=1.439x10^30(m)
    k=7.19m
    w=sq root (k/m) = sq root [( 7.19x10^29m)/1.439x10^30m)]=w=0.707
    f = 0.707/2pie = 0.1125 Hz
    check?
     
  2. jcsd
  3. Dec 16, 2007 #2
    The denominator should be 2m, since the deuterium is twice as massive as the hydrogen.
     
  4. Dec 16, 2007 #3
    H2:
    k=m(w^2)=7.19x10^29(m)
    D2:
    m=2k=2(7.19x10^29)m=1.439x10^30(m)
     
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