Dipole and Angular Momentum

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1. Homework Statement
Show that the magnetic dipole moment M of an electron orbiting a proton nucleus of a hydrogen atom is related to the orbital angular momentum M=(e/2m)L

2. Homework Equations
M=NIA, Torque =MB, F=qvB=v^2/r, L=Iw=mrv=rp (where p=mv)

N=1 in this case I assume?

3. The Attempt at a Solution
I've tried every combination of everything I can think of. I started with solving for L as L=2mM/q (where q=e). Then I tried substituting everything I could think of in for L and nothing made sense. I also tried starting with M=Torque/B and substituting I*(angular acceleration) for torque but you just end up with vqr. I think I'm approaching this wrong, can anyone help.
 

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