A nanoparticle containing 6 atoms can be modeled approximately as an Einstein solid of 18 independent oscillators. The
evenly spaced energy levels of each oscillator are 4 × 10−21 J apart.
(a) When the nanoparticle's energy is in the range 5 × 4 × 10−21 J to 6 × 4 × 10−21 J, what is the approximate
temperature? (In order to keep precision for calculating the heat capacity, give the result to the nearest tenth of a
Kelvin.)
(b) When the nanoparticle's energy is in the range 8 × 4 × 10−21 J to 9 × 4 × 10−21 J, what is the approximate
temperature? (In order to keep precision for calculating the heat capacity, give the result to the nearest tenth of a
degree.)
(c) When the nanoparticle's energy is in the range 5 × 4 × 10−21 J to 9 × 4 × 10−21 J, what is the approximate heat
capacity per atom?
Note that between parts (a) and (b) the average energy increased from “5.5 quanta” to “8.5 quanta.” As a check, compare
your result with the high temperature limit of 3kB.