1. The problem statement, all variables and given/known data a) Express the total energy of an electron in the Coulomb potential of proton through the electron's angular momentum L and the shortest distance a between the proton and the electron's orbit. Hint: The electron's velocity is perpendicular to it's position vector whenever it is distance a away from the proton. b) For a fixed L, minimize the expression found in (a) with respect to a. Show that the minimum corresponds to the case of a circular orbit. State the minimum value of the total energy for fixed L. 2. Relevant equations L=sqrt(l2+l)ћ Lz=mlћ L=r x mv=Iω En=-mee4/[2(4πε0)2ћ2n2] n > l > |ml| > 0 KE=.5Iω2 3. The attempt at a solution E=U+KE => E= .5L*v/a - e^2/[4πε0a] I have little confidence in that as a solution. Either I've stopped short or I'm going in the wrong direction, I'm not sure. I really only want help with part (a)... Once I get that far I should be handle (b) somewhat easily, I just wanted to provide context for the problem.