Question

Q10M.9 Consider an HCl molecule. The hydrogen atom irn this molecule has a mass we can look up (see the inside front cover), and the chlorine mass is enough larger that we can (to a first degree of approximation) consider it to be fixed. The bond between these atoms has a local minimum .13 nm, and for "small oscillations" around that minimum, the bond's potential energy can be modeled as a harmonic oscillator potential energy function. Suppose we find that the energy differ- ence between adjacent energy eigenvalues for a vibrating when the atoms are separated by 0 HCl molecule is 0.37 eV (a) What is the effective spring constant k, for the bond between these atoms? (b) The width of the energy eigenfunction is roughly equal to the distance between classical turning points for the eigenfunction's corresponding energy. Assuming that the HCl molecule is in its lowest vibrational energy state, what is this distance? (c) Does this qualify as a "small oscillation"? If so, how high would n have to become for the small-oscillation approximation to break down? Justify your reasoning (there is room for some debate here)

Answer 1

(c) lels calcnlate which is very lon than . So, a good approximation to use small os llaion Lels take 2xmax to be eto 5 for the small oscillation" approximahon to break doun. Here lies the rgom for de bate So 2. 2. 0 2 4 709 c 5

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