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tashkent

• Guest vibrational frequency inquiry
« on: October 14, 2004, 11:27:30 AM »
Greetings!

I'm having a problem figuring out the reason for the answer in # 70 of the GRE Chemistry Book:

70) Which of the following hydrogen molecules has the highest vibrational frequency?  (D = deuterium, T = tritium).

a) H2
b) HD
c) D2
d) HT
e) T2

The answer is A, but I don't know why.  Can you cite me references or books on this topic?  Thanks!

Sincerely,
Tashkent

Demotivator

• Guest Re:vibrational frequency inquiry
« Reply #1 on: October 14, 2004, 11:53:28 AM »
Those ar all isotopes of hydrogen. They would all have the same frequency if it weren't for the different masses. The vibrational freq is inversely related to the reduced mass of the atom pair. Since H2 has the smallest reduced mass (obviously lightest), it has the greatest freq.

vib freq =(1/2pi)(sqrt(k/u))  u is reduced mass
u = m1m2/(m1 + m2)
« Last Edit: October 14, 2004, 12:01:19 PM by Demotivator » Donaldson Tan Re:vibrational frequency inquiry
« Reply #2 on: March 10, 2005, 10:19:31 AM »
Hooke's Law is used to approximate the vibrational behavior
"Say you're in a [chemical] plant and there's a snake on the floor. What are you going to do? Call a consultant? Get a meeting together to talk about which color is the snake? Employees should do one thing: walk over there and you step on the friggin� snake." - Jean-Pierre Garnier, CEO of Glaxosmithkline, June 2006 2810713 Re:vibrational frequency inquiry
« Reply #3 on: March 17, 2005, 04:45:26 PM »

masss of proton=mass of neutrn[app]
mass of electron=1/1847*mass of proton
forces which are established in the example are attractive force[gravitational force beetwen the nucleus of H [/isotope]]
Consider the molecule D-D  ,
For, D2 molecule, gravitational force bet. those two atoms is 4 times greater than in H2 - Newton's law of gravitation.
For D---D
R=Repulsion force
F' = Attractive force  in d-d

For
H---H
F=attractive  force in H---H
R= repulsive force

For D---D ,
F'=k'x'         ..[x' =relative displacement of D atom ]
For
H---H,
F=kx

net outword force in D---D= R-F'
k'= R-F'/x'  = [Const.] * R-F' / F'  ..as motion is oscilatory
F'=[const] * x'
net outword force in H----H = R-F
k= R-F/x = [Const.] * R-F / F  ..as motion is oscilatory

[(R-F)/F] > [(R-F')/F'] ....obviously

hence k>k' and  frequency = [const] * sqrt k
thus , n > n' i.e. frequency of vibration for H---H molecules is more than that of D---D  .