If an electron of 40 eV had a head-on collision with a Hg atom at rest, what wou

Question

If an electron of 40 eV had a head-on collision with a Hg atom at rest, what would be the kinetic energy of the recoiling Hg atom? Assume an elastic collision.

Explanation / Answer

Mass of e = 0.00055 amu (m) initial speed u final speed v Mass of Hg = 200.59 amu (M) final speed V Since this is a very large difference we can assume that Let m/M = a Momentum conservation mu = mv+ MV =>V = m(u-v)/M = a(u-v) eq1 By energy conservation we have .5mu^2 = .5mv^2 + .5 MV^2 =>V^2 = m(u^2- v^2)/M = a(u^2- v^2) eq2 eq1^2/Eq2 we have a(u-v) = (u+v) =>v = u(a-1)/(a+1) using this in eq1 we have V= a(u -v) = a(u- u(a-1)/(a+1)) = a*u(a+1-a+1)/(a+1) = 2au/a+1 ˜ 2au (since a+1 ˜a as a is very small) Now the kinectic energy of M = .5MV^2 = .5 M (2ua)^2 we know that .5mu^2 = 40 .5M*4*u^2*m^2/M^2 = (.5mu^2) * 4*m /M = 40*4*m/M = 0.000435492651 ev

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