Question 28.Q-Q.9: A particle is in a box of length L. Suddenly, the length of ...

(c). According to Equation 28.30, if the length L is increased, all quantized energies become smaller. Therefore, the energy levels move closer together. As L becomes macroscopic, the energy levels are so close together that we do not observe the quantized behavior.

\begin{aligned}E_{n} &=\frac{1}{2} m v^{2}=\frac{p^{2}}{2 m}=\frac{(n h / 2 L)^{2}}{2 m} \\&=\left(\frac{h^{2}}{8 m L^{2}}\right) n^{2} \quad n=1,2,3, \ldots\end{aligned}                      [28.30]