1. For what kinetic energy is the de Broglie wavelengthof an electron equal to its Compton wavelength? Express your answerin units of mc2 in doing the calculation, and then use mc2 = 0.5MeV.(Answer: 0.2 MeV)
2. A beam of electrons with energy 1.0 eV approaches apotential barrier with U = 2.0 eV, whose width is 0.10 nm (see afigure below). Estimate the fraction of electrons that tunnelthrough the barrier. (Hint: use the relation of probability and thewave function, and the expression for wave function for barrierpenetration)
3. Calculate the Fermi energy of sodium (n= 2.65·10^28m^-3). This metal has a single valence electron per atom.(Answer:3.25 eV.)
