How Do You Calculate the Effective Potential Energy in a Hydrogen Atom?

[rbnphlp]

An electron (of mass me and charge −e) in a hydrogen atom is located at position vector r
relative to the proton (of mass mp and charge +e) constituting the nucleus. It is attracted
to the proton by the electrostatic force
F =-\frac{e^2}{4\epsilon_0r^2}\hat{r},
where e_0 is a constant (the ‘permittivity of the vacuum’). Find the potential energy V (r)
associated with the force F, assuming that V -> 0 as r -> infty. Find also the reduced mass
associated with the two-body system of the electron and the proton.
Find an expression for the effective potential energy V_eff associated with the radial motion
of the electron and the nucleus when the system has angular momentum L.

Im stuck on how to do the last bit .

V_{eff}=V(r)+\frac{L^2}{2mr^2}but how do I find the combined Veff of electron and nucleus ?
Thanks ..

edit :wheter it says 872; should be a -

 

[kuruman]

Im stuck on how to do the last bit .

V_{eff}=V(r)+\frac{L^2}{2mr^2}


but how do I find the combined Veff of electron and nucleus ?
Thanks ..

edit :wheter it says 872; should be a -

Use the reduced mass for m. To find V_eff you need V(r). That's the electrostatic potential energy of the proton-electron system.

 

[rbnphlp]

Use the reduced mass for m. To find V_eff you need V(r). That's the electrostatic potential energy of the proton-electron system.

oh ok , thanks but why is that the case?

 

[kuruman]

Why is what the case?

 

[rbnphlp]

Why is what the case?

oh sorry ..I meant to ask why do we consider the reduced mass for both of them ?
Edit : a quick wike gave me the answer what I was looking for .thanks for your help !