steely Posted December 2, 2009 Share Posted December 2, 2009 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. My only attempt so far has been: 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), looking for a point in the right direction... Once I get that far I should be handle (b) somewhat easily, I just wanted to provide extra context for the problem. Link to comment Share on other sites More sharing options...
swansont Posted December 2, 2009 Share Posted December 2, 2009 You probably want to drop v from your equation. Can you express KE in terms of L, m and a? Link to comment Share on other sites More sharing options...
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