Question

A carbon nanoparticle (very small particle) contains 7400 carbon atoms. (a) According to the Einstein model of a solid, how many oscillators are in this particle? (b) If the particle contains 1.5 x 10^8 units of energy, what is the entropy of the particle?

Answer 1

a) According to Einstein model of solid, each atom behave as independent oscillator. So number of oscillators is equal to 7400.

b) Number of units of energy, q = 1.5 *10^8

these many units have to be distributed among 7400 oscillators (N). The number of ways (microstates) it can be done is

Entropy is defined as

Here k is Boltzmann coefficient. k=1.38 *10^-23 J/K

Now q is very large, so we can use Stirling approximation