To calculate the number of free electrons in sodium, the resistivity value of 4.2 x 10^-6 ohm-cm is used alongside the Drude model. The first part of the calculation, determining free electrons per cubic centimeter, can be solved using the resistivity formula. For the second part, to find the number of free electrons per atom, one must calculate the number of atoms per cubic centimeter using sodium's density and atomic mass. Units are essential for accuracy in these calculations. The discussion emphasizes the importance of using proper formulas and values to arrive at the correct results.