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conantee
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« on: January 04, 2010, 04:24:38 AM »

51. One feature common to both the Debye theory and the Einstein theory of the specific heat of a crystal composed of N identical atoms is that the
(A) average energy of each atom is 3kT
(B) vibrational energy of the crystal is equivalent to energy of 3N independent harmonic oscillators
(C) crystal is assumed to be continuous for all elastic waves
(D) speed of the longitudinal elastic waves is less than the speed of the transverse elastic waves
(E) upper cutoff frequency of the elastic waves is the same
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« Reply #1 on: January 13, 2010, 09:59:48 AM »

If you know the motivation under both theories, you can eliminate some choices. These two theories use quantum effect to improve model of heat capacity in crystal. So, (A) is wrong, and (C) sounds wrong since they are not relevant to quantum treatment. Now, you have 3 choices left to guess. Well, according to both theories, they assume each atom can oscillate as harmonic oscillators. So, it is equivalent to 3N independent harmonic oscillators (crystal is in 3D). However, atoms in Einstein theory can oscillate in unlimited frequency, while Debye theory has a cutoff by size of atomic seperation (phonons in a box constrained by crystal sites is introduced in this model).

The correct answer then is (B). 30 of 100 people got the correct answer.
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