Using the quantum particle in a box model, describe how the possible energies of the particle are related to the size of the box.

In this exercise, we are going to relate the energy of a particle in the quantum particle in a box to the length of the box. To begin, we will discuss the quantum particle in a box model. Basically, this model consists of a quantum particle bound in a box with impenetrable walls. The particle can only travel in one dimension inside the box, which means it can only travel along the length of the box.