+e. -e An electron (charge -e, mass m) and a positron (charge te, mass m) revolv

Question

+e. -e An electron (charge -e, mass m) and a positron (charge te, mass m) revolve around their common center of mass under the influence of their attractive coulomb force. This bound state is sometimes called Wikipedia: http://www.wikipedia.org/wiki/positronium and can actually be created for very brief periods of time in the laboratory (it is very unstable quantum mechanically as the positron and electron rapidly anihillate one another)- Find the speed of each particle v in terms of e, m, k and their separation d. Note well that the circle of their motion has a radius r d/2

Explanation / Answer

here Centripetal force = Couloumbs force of attraction

i.e F = mv^2/R = Kq1q2/d^2

here R = d/2 and q1 = q2 = e

so

2mv^2/d = Ke^2/d^2

v^2 = K e^2 d/2md^2

v^2 = Ke ^2 /2md

or

v = Sqrt {1/2*(K e^2/dm) }

We can neglect gravitational force because it is so much smaller than the Coulomb force .

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