In 1906, in what is arguably the first paper in theoretical condensed matter physics [3], Albert Einstein postulated that…

Question:

Transcribed Image Text:

In 1906, in what is arguably the first paper in theoretical condensed matter

physics [3], Albert Einstein postulated that vibrational excitations of a solid are

quantized with energy ho, just like photons in the vacuum. Repeat his calculation

for diamond: calculate the energy E(T) of one mole of simple harmonic oscillators

with characteristic frequency w at temperature T and show that the specific heat

capacity is

where

dE

Cy(T) = = RF

dT

F(x):

ha

KBT

(2) ²

x/2

(sinh(x/2).

and R = NAVKB, the product of Avagadro’s number NAV and Boltzmann’s constant

kB. Plot C(T) and show that it deviates from Dulong and Petit’s law, Cy = (R/2) per

quadratic degree of freedom, at temperatures T << hw/kB.
Expert Answer:
Answer rating: 100% (QA)
To calculate the energy E T of one mole of simple harmonic oscillators with characteristic frequency at temperature T we can use the formula E T N Avo
View the full answer