(adapted from Schroeder, Thermal Physics). A water molecule can vibrate in may w

Question

(adapted from Schroeder, Thermal Physics). A water molecule can vibrate in may ways, but the "Flexing" mode, where the angle between the OH bonds oscillates about its central value of 104 degrees, is the vibrational mode whos excited energies are the smallest. We can model this vibrational modeas if we were a simple one dimensional quantum harmonic oscillator (mathematically, the situation are equivalent); so we saw in unit Q, the energy levels are 1/2hw, (5/2)hw, and so on, where w is the angular frequency of the oscillation. The measured value of w for this mode is 3.0 x 10^12 s^-1. Calculate the absolute probabilities that a water molecule at room temperature will be in its flexing ground state and its first two excited states (hint: calculate Z by adding up as many boltzmann factors you think you need to get a result accurage to within 4 significant digits.)

Explanation / Answer

we can find the the probability by heisenberg uncertainty principle that is delta x * delta p is greater and equalt to h/4pie

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