**Hmm...**
**1. The problem statement, all variables and given/known data**

A beam of electrons, with kinetic energy of 500eV, enters mid-way into the space between two oppositely charged parallel plates with a potential difference of 100V

**2. Relevant equations**

Determine the velocity of the electrons

**3. The attempt at a solution**

KE=0.5mv^2

500(1.60x10^-19)=0.5(500 x 9.11 x 10^-31)(v^2)

v=5.93x10^5

This is a tough one because you are assuming that there are 500 electrons. An electron-volt is the kinetic energy an electron obtains passing through a potential difference of 1 volt.

It is not said there are 500 electrons, but rather an electron beam with an energy of 500 eV. That could be 250 electrons that moved through a 2 volt potential, or 100 electrons that moved through a 5 volt potential, etc...

Furthermore you did not do anything with the 100 volt difference the electrons are now within.

I am thinking they are "shot" from one plate and midway between have an energy of 500 eV. Now midway between the two plates the voltage is 50 V. So they have moved through a potential difference of 50 V, gaining 500eV of energy.

That implies there are only 10 electrons each with 50 eV of energy, for a total of 500 eV of energy.

So,

500(1.60x10^-19)=0.5(10 x 9.11 x 10^-31)(V^2)

V = 4.191E+6 only a fraction of light speed, but about a factor of 10 faster than what you had. Electrons have so little mass, it does not take much energy/force to get them moving at great speeds.

I am pretty sure this is correct. Halfway between two plates with a 100 volt difference the voltage is 50 V, because V = Ed, and E is relatively constant between two plates, so the voltage must be about 1/2 of 100, or 50 V. Since 1 eV is the energy an electron obtains moving through a 1 volt difference, from 0 to 1 volt, and the energy the electrons obtain moving from 0 to 50 volts is 500 eV, that implies there need be 10 electrons in the middle to yield that energy (500eV), each with a 50 eV energy.

From there I just did what you did, converted the energy into Joules, and the mass of 10 electrons is 10 times that of one, divided each side by that and 1/2, took the square root and got a velocity. I think this is correct.

Many Smiles,

Craig