A proton and an alpha particle are momentarily at rest at a distance r from each

Question

A proton and an alpha particle are momentarily at rest at a distance r from each other. They then begin to move apart. Find the speed of the proton by the time the distance between the proton and the alpha particle doubles.

Both particles are positively charged. The charge and the mass of the proton are, respectively, e andm. The charge and the mass of the alpha particle are, respectively, 2e and 4m.

A- Find the speed of the proton (vf)p by the time the distance between the particles doubles.

Express your answer in terms of some or all of the quantities e, m, r, and ?0.

B- The best way to check whether your result from Part A is correct is to check that it has the correct units. Which of the following expressions, where C stands for coulombs, N for newtons, kg for kilograms, and m for meters, represents the correct SI units for the expression found in part B?

Explanation / Answer

kinetic enrgy gained by proton = loss of electrostatic potential energy of the system

ie., 1 / 2 m v^2 = K x e x 2e ( 1 / r - 1 / 2r ), where 'v' is the required speed of proton and K=9x10^9

1 / 2 m v^2 = K e^2 / r or speed v = sqaue root of ( 2 K e^2 / m r )

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