Proton electron mass ratio calculation

[Tsumi89]

Homework Statement

Hello! I've come upon this question and haven't been able to find it anywhere. The goal is to find Mp/Me with basis on the Bohr's atomic model and hydrogen emisson spectrum lines.

Homework Equations

l=rp=nh_ ; h_=h/2pi ; E=-K.e^2/2r ; r=(n^2.h_^2)/Me.e^2.k ; k=1/(4pi.ε0)

wave lengh for first line of Balmer series on the air= 656,279 nm

The Attempt at a Solution

My attempt was the following: I actually didn't use the spectral lines information cause I wasn't able to see how could they help me. So I used angular momentum quantification which leads to the equations above for E and r, but instead of using electromagnetic force between the proton and the electron I used the gravitational force between both. That led me to this: Me.Mp=2r.E/-G ; now, not only this gives Me.Mp instead of Mp/Me, but it also gives a wrong value of Me.Mp. ...Hope someone can help me ^^
Thx

 

[tsumi]

Thanks for helping...

 

[tsumi]

Could somebody point me in the right direction? An year has gone by and this question hits me again x) and I still can't solve it.