A moving electron of mass me and initial speed v 1 collides head on with an init

Question

A moving electron of mass me and initial speed v
1
collides head on with an initially stationary
Hydrogen atom of mass mp. If the collision is elastic and 1-dimensional and if mp/ me = 1840:
(a) What is the center of mass velocity?
(b) What does this collision look like from the center of mass reference frame?
Draw two pictures (before and after ) to depict the collision from this frame.
(c) When viewed entirely from the center of mass frame, what fraction of the
electron’s initial kinetic energy is transferred to the Hydrogen atom ?
(d) Viewed from the original LAB frame, what final velocity does the Hydrogen atom recoil with

Explanation / Answer

a) vG=mv/(M+m)=m*v/1841m=v/1841 b) in the center of mass reference frame, the atom and the electron ll head to each other. v_atom=v/1841 and v_elec=v*1840/1841. c)zero. Because in the center of mass frame, after collision, they ll move away from each other but with the same velocity. d) v_hydro=vG+v/1841=2v/1841.

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