Find the speed of an electron accelerated through a potential difference

[Miri]

Homework Statement

In a color television tube, electrons are accelerated through a potential difference of 20 000 volts. With what speed do the electrons strike the screen?
mass of electron=9.109*10^-31kg or 0.51099 MeV/c^2

Homework Equations

I don't know which formula I have to use. When I use E=mc^2/sqrt(1-v^2/c^2) I first have to add the kinetic energy (20 000eV) and the rest energy of the electron (0.51099MeV) and than solve for x (which is v^2/c^2). The solution should be 0.27c but I never get it...Thank you!

 

[Redbelly98]

You have the right formula. Can you show your math? It sounds like there is a simple arithmetic error somewhere.

p.s. if instead you use the nonrelativistic expression for kinetic energy, the answer will not be very different.

 

[Miri]

Ok. For E I use 20 000.51099MeV (KE+rest energy)
For mc^2 I use 0.51099MeV and for v^2/c^2 I use x because that's the thing I want to know. Then I put everything into the solver like this: solve(20000.51099=0.51099/sqrt(1-x^2),x) and my calculator says x is -1 or 1 (exact nr.: 0.99999999967363) I really don't know why I always get the wrong result...

 

[Redbelly98]

Okay. The kinetic energy is

KE = 20 000 eV ≠ 20 000 MeV​

 

[Miri]

Thank you. But it doesn't change nothing when I use 20 000*10^6 eV + 0.51099MeV...Heeelp :S

 

[Born2bwire]

I think you need to double-check your conversion of 20,000 eV to MeV. 1,000,000 eV = 1 MeV

 

[Matterwave]

The rest energy is .511MeV = 511,000eV

The kinetic is 20,000eV

You see how the kinetic energy is not larger than the rest energy? It is in fact smaller by about 25 times. This is why Redbelly said you can use non-relativistic mechanics because the kinetic energy is only a small fraction of the rest energy.

The way you have it now, your kinetic energy is 40,000 times larger than your rest energy...which is why you get an answer ridiculously close to c.

 

[Redbelly98]

Thank you. But it doesn't change nothing when I use 20 000*10^6 eV + 0.51099MeV...Heeelp :S

And it shouldn't change, because you are just repeating the same mistake.

20 000 eV is not, I repeat not, 20 000*10⁶ eV.

To do the units conversion from eV to MeV:

20000 eV * (^{1 MeV}/_{10^6 eV}) = ____ ?

 

[Miri]

oh yes..thank you very much..I forgot the minus: 20000*10^-6 eV=0.02MeV...Thank you for your patience :)