- #1
rbnphlp
- 54
- 0
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
[tex]F =-\frac{e^2}{4\epsilon_0r^2}\hat{r}[/tex],
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 .
[tex]V_{eff}=V(r)+\frac{L^2}{2mr^2}[/tex]but how do I find the combined Veff of electron and nucleus ?
Thanks ..
edit :wheter it says 872; should be a -
relative to the proton (of mass mp and charge +e) constituting the nucleus. It is attracted
to the proton by the electrostatic force
[tex]F =-\frac{e^2}{4\epsilon_0r^2}\hat{r}[/tex],
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 .
[tex]V_{eff}=V(r)+\frac{L^2}{2mr^2}[/tex]but how do I find the combined Veff of electron and nucleus ?
Thanks ..
edit :wheter it says 872; should be a -