Finding speed of two electrons initially at rest

AI Thread Summary
Two electrons, initially at rest and separated by 5.0 x 10^-12 m, accelerate away from each other due to electrostatic repulsion. The energy conservation equation is applied, where the initial electrostatic energy equals the final kinetic energy of both electrons. The calculation initially provided a speed of approximately 1.0 x 10^7 m/s, but the correct answer is 7.1 x 10^6 m/s. The discussion highlights the importance of considering the kinetic energy of both electrons and whether they achieve the same speed upon separation. Accurate calculations require accounting for the shared kinetic energy of both particles.
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Homework Statement


Two electrons start at rest with a separation of 5.0 x 10^-12 m. Once released, the electrons accelerate away from each other. Calculate the speed of each electron when they are a very large distance apart (Ee = 0).

Homework Equations


EE = kQq/r
Ek = (1/2)mv2

The Attempt at a Solution


EE2 - EE1 = - (Ek2 - Ek1)
- EE1 = - Ek2
(kq2) / r = (1/2)mv2
v = sqrt[ 2(8.99 x 109)(-1.6 x 10-19)2 / (9.11 x 10-31)(5.0 x 10-12) ]
v ≅ 1.0 x 107 m/s

The answer is apparently 7.1 x 106 m/s
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Hello, and welcome to PF!

Do both electrons end up with some kinetic energy? Did you take that into account?
 
TSny said:
Hello, and welcome to PF!Do both electrons end up with some kinetic energy? Did you take that into account?
Thanks for replying!
Oh I don't think I did. So it would be Ee1 = (1/2)mv^2 + (1/2)mv^2.
 
Yes. Are you assuming that the two electrons end up with the same speed? Can you justify that?
 
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