Calculating Final Speed: Electrons & Potential Difference

[NikkiNik]

Homework Statement

Electrons are accelerated from rest through a potential difference of 250000 V. What is the final speed predicted classically?

What is the final speed predicted relativistically?

Homework Equations

KE=0.5mv^2
KE=mc^2-m0c^2

The Attempt at a Solution

a.2.96×108 m/s

b. I keep ending up with the speed of light which I know is incorrect...for m I know I use m0/sqrt (1-v^2/c^2) so the final equation is KE which I found to be 4.005e-14 J= m0/sqrt (1-v^2/c^2)*c^2 -m0c^2

 

[Geezer]

Your working equations are incomplete.

1. Yes, that's the correct classical kinetic energy, but how does that relate to an electric potential difference V?

2. Yes, that's the correct equation for relativistic kinetic energy, but you'll need it in a form that include relativistic momentum, since you need to compare the two speeds. After all, the equation as you have it written down doesn't allow us to solve for the electron's speed (it just includes masses and the speed of light).

 

[ideasrule]

b. I keep ending up with the speed of light which I know is incorrect...for m I know I use m0/sqrt (1-v^2/c^2) so the final equation is KE which I found to be 4.005e-14 J= m0/sqrt (1-v^2/c^2)*c^2 -m0c^2

I came up with 2.22 * 10^8 m/s. Are you sure you calculated correctly?