An atom of mass M is initially at rest, in its ground state. A moving (nonrelativistic) electron of mass me collides with the atom. The atom+electron system can exist in an excited state in which the electron is absorbed into the atom. The excited state has an extra, "internal," energy E relative to the atom's ground state.
Find the kinetic energy that the electron must have in order to excite the atom.
Express your answer in terms of E, me, and M.
m1*v1 + m2*v2 = (m1+m2)Vf
[tex]\Delta[/tex]K = Ki - Kf
The Attempt at a Solution
What i've got so far:
m1*v1 + m2*v2 = (m1+m2)Vf -->
me*ve + (0) = (me + M)*Vf -->
Vf = (me*ve)/(me + M)
[tex]\Delta[/tex]K = Ki - Kf -->
Kf = (1/2)(me + M) * [(meve)/(me + M)]^2 --> simplified -->
Ki = just the Kinetic energy of the electron = (1/2)(me*ve^2 --> so..
(me*ve)^2/2(me+M) - (1/2)(me*ve^2) = E(?.. an assumption) --->
so K_e = (m_e * v_e)^2/2(m_e + M) - E --->
there's the problem, i have v_e in my solution. But first i need to know i'm on the right track which i think i am. Any advice?