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Unformatted text preview: at room temperature.
This is unusual for a diatomic molecule, due to the low force constant and the high reduced mass.
More commonly, only the ground state is populated.
12. Oscillator. Consider a 1H127I molecule (force constant 313.8 N m-1, equilibrium bond distance 161
pm) in its vibrational ground state
. What is the probability of finding the molecule with its bond length at least 20 percent longer than its equilibrium value? Hint: Use a computer program
(Excel, Matlab, etc.) or online resource to evaluate the error function.
The range of bond displacements x (deviation from the equilibrium bond distance) we look for is
from b = 0.2·161pm = +32.2 pm up to infinity. The ground state wave function is
The probability of finding the displacement between b and + is
∫ () With ∫ () [() √ , [ √
we get and
[ √ where erf(…) is the error function. The probability is almost negligible. √...
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- Fall '06