General Physics, 2nd Edition
General Physics, 2nd Edition
2nd Edition
ISBN: 9780471522782
Author: Morton M. Sternheim
Publisher: WILEY
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Chapter 26, Problem 26E

(a)

To determine

The reduced mass of the OH group.

(b)

To determine

The characteristic vibrational frequency of the OH group.

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3. (a) One way of treating the vibrational modes of a linear diatomic solid is to assume that the atoms have the same masses, but the springs on either side of an atom have spring constants K and G, respectively. Show that the dispersion relation of such a lattice is given by (K+G` +G)' - 4KGsin ka M where M is the mass of the ion, G and K the lattice constants, a is the periodic distance between masses and k the lattice wave vector. (i) (ii) Sketch the dispersion relation Discuss what happens when K = G and K >> G. (b) In diatomic (linear) lattice, why do we assume same o and k.
Air is 21% oxygen. You measure the total translational kinetic energy of the molecules of oxygen in a container to be 75J at room temperature, what is the total vibrational energy of these molecules were they at a higher temperature?
Consider an isolated carbon atom being held in its equilibrium lattice site position by the mutual interaction with the neighboring atoms. If the spring constant driving the carbon atom back into its equilibrium lattice site is 21.71 N/m, what is the frequency of oscillation? The atomic mass of carbon is given in the periodic table. Give your answers in units of 1012 rad/s with 2 digits precision, rounding off to two decimal places, i.e. the nearest hundredths. (time budget 6min)
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