Question 41.1: A Hockey Puck in a Box Suppose that a hockey puck’s mass is ......
A Hockey Puck in a Box
Suppose that a hockey puck’s mass is 0.160 kg and it is in a box of length 6.35 m (Fig. 41.1). Find the system’s zero-point energy and the energies of the first three excited states. In CHECK and THINK, comment on the difference between the third excited state and the ground state.
INTERPRET and ANTICIPATE
A hockey puck in a box is a classical (macroscopic) system. So we expect to find results that seem familiar.
SOLVE
Find the zero-point energy by setting n = 1 in Equation 41.7.
The first three excited states have quantum numbers 2, 3, and 4. Write the energy of the excited states in terms of E_1.
\begin{aligned}& E_n=n^2 E_1 \\& E_2=2^2 E_1=3.41 \times 10^{-68} J \\& E_3=3^2 E_1=7.66 \times 10^{-68} J \\& E_4=4^2 E_1=1.36 \times 10^{-67} J\end{aligned}CHECK and THINK
The lowest energy level is not zero, but it is so small that we would not distinguish it from zero. Also, keep in mind that we derived the energy levels for the ideal situation in which there are no dissipative forces, and that any real hockey puck would experience dissipative forces. Furthermore, the energy difference between the third excited state and the ground state is about 10^{-67} J. Again, this is too small to be distinguished from zero.