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Hooke's law (Read 2982 times)
Gerrit-Jan Linker
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Hooke's law
21.07.08 at 22:25:54
Hooke's law
The value of the potential energy for a bond between two atoms A and B can be determined at an arbitrary point by taking a Taylor expansion about req, the equilibrium bond length.
U(r) = U(req) + dU/dr|r=req] + 1/2! d2U/d2r|r=req (r-req)2) + 1/3!
d3U/d3r|r=req (r-req)3) + ...
The first term U(req) can be set to zero. By doing this we set the offset of the potential energy at U(req)
The second term dU/dr|r=req is also zero as U is minimum at req
If we truncate after the first non zero term we have the simpelest possible expression for the vibrational potential energy:
U(r) = 1/2! d2U/d2r|r=req (r-req)2)
= 1/2 kAB (rAB - rAB,eq)2
We replaced the second derivative with the symbol k, the force constant for the spring. This equation is Hooke's law.
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« Last Edit: 21.07.08 at 22:28:52 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
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