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## Homework Statement

Electrons are allowed to be accelerated through a 300V potential difference.

a) Determine the electron's kinetic energy, total energy, and velocity.

b) Repeat for a proton instead of electron

c) Assume a potential difference of 1MV instead of 300V, repeat the above calculations

## Homework Equations

W=qdV

KE=(1/2)mv^2

KE=(mc^2)/(sqrt(1-(v/c)^2))-mc^2

## The Attempt at a Solution

It's been 2 years since a quantum mechanics course or physics course for that matter so bare with me if I missed something obvious.

**(Part A&B)**

KE is the same for both the electron and proton, 300eV

This translates to 4.8*10^-17J (from 1eV=1.6*10^-19J)

***What is the total energy?? I know it is PE+KE+U, but I can't remember how to find PE for electrons or protons. As the proton or electron is accelerated through the 300V, the KE gained=PE lost, correct? If so does that mean my total energy=2*KE or just KE?

I then used this and the mass of electron/proton to find V.

I calculated, for electron V=1.0271*10^7m/s, and for proton V=2.398*10^5m/s (from classical expression) what is the "threshold" where you must use relativistic equation? I know v<<c uses classical but what is considered much greater than c?

**(Part C)**

KE=10^6eV=1.6*10^-13J from same method as above.

Here I had to use relativistic equation for electron to find V=2.8228*10^8m/s, but used classical eq for proton and V=1.384*10^7m/s.

Is this the correct use of classical vs. relativistic equation?

If you made it to the end, thanks so much in advanced for the help!!!!