Chemical Forums
Chemistry Forums for Students => Physical Chemistry Forum => Topic started by: tashkent on October 14, 2004, 11:27:30 AM
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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
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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)
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Hooke's Law is used to approximate the vibrational behavior
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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 .