The exact fine-structure formula for hydrogen (obtained from the dirac equation without ecourse to perturbation theory) is: 21-1/2 enj mc 5+1/2)2 - a2 n - (j1/2) expand to order a4 (noting that a < < 1), and show that you recover: 13.6ev 3 enj 1+ n2 j+1/2 a handy relation, not necessarily needed for the exercises: e1 (6) mc2

Two charged particles, q1 and q2, are located on the x-axis, with q1 at the origin and q2 initially at x1 = 12.2 mm. in this configuration, q1 exerts a repulsive force of 2.62 µn on q2. particle q2 is then moved to x2 = 18.0 mm. what is the force (magnitude and direction) that q2 exerts on q1 at this new location? (give the magnitude in µn.)