The interatomic spring stiffness for copper is determined from Young's modulus measurements to be 28 N/m. The mass of
one mole of copper is 0.064 kg. If we model a block of copper as a collection of atomic “oscillators” (masses on springs),
what is one quantum of energy for one of these atomic oscillators? Note that since each oscillator is attached to two
“springs,” and each “spring” is half the length of the interatomic bond, the effective interatomic spring stiffness for one of
these oscillators is 4 times the calculated value given above.
Use these precise values for the constants: = 1.0546 × 10−34 J s (Planck's constant divided by 2π), Avogadro's number =
6.0221 × 1023 molecules/mole, kB = 1.3807 × 10−23 J/K (the Boltzmann constant).
(a) What is one quantum of energy for one of these atomic oscillators?
(b) Figure 12.56 is a table containing the number of ways to arrange a given number of quanta of energy in a particular
block of copper. Fill in the blanks to complete the table, including calculating the temperature of the block and the
per-atom heat capacity C. The energy E is measured from the ground state. Nothing goes in the shaded boxes. Be
sure to give the temperature to the nearest 0.1 Kelvin.