# Protons and Electrons

Cyto
Hey there guys... I got a question for are you whiz's... Let's say you place an electron and proton a certain distance from each other and allow them to accelerate towards each other. Just before the collision, which is moving faster?

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In the original reference frame (both initially at rest), the center of mass (of the two particles) is very close to the proton, since it is almost 2000 times as massive. Once they start moving, the center of mass doesn't move. As a result the elctron is moving much faster than the proton when they collide. The velocities are in the inverse ratio of the masses - conservation of momentum.

scientist0
relative masses:
mass of a proton = 1
mass of an electron = 1/1840

relative charges:
proton= +1
electron= -1

clearly the electron is far much lighter than the proton,so it will be moving faster.

Thanks for the number. Therefore conservation of momentum makes the electron speed 1840 times the proton speed.

FZ+
On a simpler level, consider that the forces on each particle is the same, as they have the same charge. But the electron has less mass, so by:

F = ma
a = F/m: the electron undergoes much more acceleration.

Damn... still can't get hang of latex...

Staff Emeritus
Gold Member
$$a = \frac{F}{m}$$

Click my image, or quote my post, to see how it's done.

Or, if you want to be a purist, you can make your vectors bold.

$$\renewcommand{\vec}[1]{\mbox{\boldmath  #1 }} \vec{a} = \frac{\vec{F}}{m}$$

Or, if that's not clear enough, you can use little arrows -- which is the default behavior for LaTeX's \vec command.

$$\vec{a} = \frac{\vec{F}}{m}$$

- Warren