Hydroelectric power plants convert the gravitational potential energy of falling water into electrical power, typically by allowing the water to flow through a pipe called a penstock to rotate a generator located below it. let the bottom of the penstock be the origin of a cartesian coordinate system and the point at which the gravitational potential energy is zero.

Materials will have different energies associated with the electrons inside them. this is related to how strongly bound they are by their work function. if we sandwich a material with a very low energy between two materials with a high energy, we create a trap for an electron. if this trap is very narrow in one direction in comparison to the others, this is approximately a 1-dimensional box that confines the electron. what is the lowest energy of an electron in the box if the thinnest direction across the materials is 4.81 nm?