I was solving the following problem the following way: In a solid the atoms are regularly arranged in space. The potential seen by an electron is thus periodic and the energy levels are arranged in bands in which the energy of a state k is given by: ek= Eat + 2t cos(ka) The relevant band structure of the metal Silver (Ag) can be roughly modelled with a band of that form with t= 4 eV and a= 0.409 nm. Assume Ag has one conduction electron per atom. a) Calculate the maximum velocity of an electron. ek= Eat + 2t cos(ka) with: a= 0.409* 10 -9 m t= 4 eV= 4* 1.6*10-19= 6.4*10-19 J Therefore: ek= Eat + 1.28*10-18 cos(0.409* 10 -9k) vg= 1/hwith line * (d ek/dk) d ek/dk= -1.28*10-18 *0.409* 10 -9 sin(0.409* 10 -9k) vg=-4.96*106 sin(0.409* 10 -9k) The velocity is maximal when the sine is maximal, therefore when the sine=1. In that case the velocity is -4.96*106 m/s. b) Calculate the drift velocity (average velocity) of electrons in a silver wire of 1mm2 cross-sectional area through which a current of 1A is flowing, knowing vdrift= I/nAq and n= 5.85*1028 electrons per m3. vdrift= I/nAq vdrift= 1/5.85*1028* 1*10-6* 1.6*10-19 = -1.069*10-4 m/s Now my question is: why are the velocities calculated in a and b so different from each other?!