- #1
aaj92
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Homework Statement
Consider an electron (charge -e and mass m) in a circular orbit of radius r around a fixed proton (charge+e). Remembering that the inward Coulomb force ( ke[itex]^{2}[/itex]/r[itex]^{2}[/itex]) is what gives the electron its centripetal acceleration, prove that the electron's KE is equal to -[itex]\frac{1}{2}[/itex] times it's PE; that is, T = -[itex]\frac{1}{2}[/itex]U and hence E = [itex]\frac{1}{2}[/itex]U. (This result is a consequence of the so called virial theorem. Now consider the following inelastic collision of an electron with a hydrogen atom: Electron number 1 is in a circular orbit of radius r around a fixed proton. Electron 2 approaches from afar with kinetic energy T[itex]_{2}[/itex]. When the second electron hits the atom, the first electron is knocked free and the second is captured in a circular orbit of radius r'.
Homework Equations
coulomb force : ke[itex]^{2}[/itex]/r[itex]^{2}[/itex]
virial theorem T = nU/2
The Attempt at a Solution
I'm not really worried about the second part of this problem quite yet. Right now I'm not really sure how to go about proving that the kinetic energy is -[itex]\frac{1}{2}[/itex] times the potential energy... can someone get me started on the right track?