The expansion of the universe means that select one:
a. as time goes by, galaxies move away from each other through empty space.
b. as time goes by, space itself expands, carrying the galaxies along with it.
c. each object in the universe expands its size.
d. the light from distant galaxies is doppler shifted as the galaxies move away from us.

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?