The linear expansivity of a metal, P is twice that of another metal Q. When these metals are heated through the same temperature change, their increase in length is the same.
Calculate the ratio of the original length of P to that of Q.

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?