A hydrogen atom when in its lowest energy state consists of a proton of charge +e and an electron of charge -e and mass 9.1x10-31 kg. In the Bohr model of the atom, the electron moves around the nucleus in a circular orbit of radius 0.51x10-10 m. Determine the speed that another electron, starting very far away from the hydrogen atom, must have in order to ionize the atom during a collision. In the final state, all three particles (proton and two electrons) are considered at rest very far from each other.
(a) Construct a pictorial representation showing clearly the initial and final situations.
(b) Choose a system. Construct work-energy bar graphs for this process, showing Initial Energy + Wout = Final energy. (Hint do not ignore the circular velocity of the orbiting electron).
(c) Based on your work-energy bar graphs, write down the work-energy theorem for this problem. Use Newton's laws to find the orbital velocity of the atomic electron.
(d) Solve for the initial velocity of the second electron.