This problem explores under what conditions the classical limit is reached for a macrosc...

This problem explores under what conditions the classical limit is reached for a macroscopic cubic box of edge length a. A nitrogen molecule of average translational energy 3/2k_BT is confined in a cubic box of volume V = 1.250 m³ at 298 K. Use the result from Equation (15.25) for the dependence of the energy levels on a and on the quantum numbers n_x, n_y, and n_z.

Reference equation 15225

a. What is the value of the “reduced quantum number” for

b. What is the energy separation between the levels and (Hint: Subtract E_{α + 1} from E_α before plugging in numbers.)

c. Calculate the ratio and use your result to conclude whether a classical or quantum mechanical description is appropriate for the particle.