How Does Doubling Molecular Mass Affect Vibration Frequency?

[GX255]

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.

Homework Equations

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

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?

 

[Noein]

w=sq root (k/m) = sq root [( 7.19x10^29m)/1.439x10^30m)]=w=0.707

The denominator should be 2m, since the deuterium is twice as massive as the hydrogen.

 

[GX255]

H2:
k=m(w^2)=7.19x10^29(m)
D2:
m=2k=2(7.19x10^29)m=1.439x10^30(m)