How far does the electron move before reaching its turning point?

[rushton_19]

1. The hydrogen molecular ion, with one electron and two protons, is the simplest molecule. The equilibrium spacing between the protons is 0.11 nm. Suppose the electron is at the midpoint between the protons and moving at 1.5*10^6 m/s perpendicular to a line between the protons.

How far (in nm) does the electron move before reaching a turning point? Because of their larger mass, the protons remain fixed during this interval of time.



2. K = 1/2 m*v^2
V = Uelec/q
W = q*E*L



3. I think this problem has to do with conservation of energy, but I don't know how to approach it.

[Delphi51]

Find the electric potential due to the two protons along the electron's path. Find out where the electron's kinetic energy is completely converted to electric potential energy.

[rushton_19]

Okay, but how do you find the electric potential due to the two protons?

[Delphi51]

The potential at distance R from charge Q is V = kQ/R.
Potentials from multiple charges add.
Potential is energy per unit charge.

An alternative approach would be to find the electric field due to the 2 charges, then the force on the electron due to the E field. You could then do an integral over F*dx to find the work done. This look like more work because the electric field is a vector, but the symmetry should clear that up early on.

[rushton_19]

Okay, thank you.