- #1
steely
- 1
- 0
Homework Statement
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.
Homework Equations
L=sqrt(l2+l)ћ
Lz=mlћ
L=r x mv=Iω
En=-mee4/[2(4πε0)2ћ2n2]
n > l > |ml| > 0
KE=.5Iω2
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.