Calculating Electron Velocity and Kinetic Energy in a Television Tube

[Delzac]

Homework Statement

In a typical television tube, the electrons are accelerated through a potential difference of 25,000 volts. a) What speed do the electrons have when they strike the screen? And b) What is their kinetic energy in joules?

Homework Equations

$$K_m_a_x = hf - \varphi$$
$$KE = \gamma mc^2 - mc^2$$

The Attempt at a Solution

Well, i don't know where to start. How do you use the volts to obtain the velocity of the electron, so far, i haven't encountered any formula that can do that.(at least i didn't notice in the lecture)

Any help will be appreciated. Thanks

 

[Warr]

First off, the photoelectric effect is not part of the problem at all.

The energy gained by an electron moving through a 1 volt potential is 1 eV (electron volt). So then how much energy is gained moving through a 25,000 V potential? Also a constant may be useful is the rest mass of an electron, $${m_0}=511 \frac{KeV}{c^2}$$. Can you solve for v now, using your kinetic energy relationship?

 

[Delzac]

Ok, so i am going to use this equation : $$KE = \gamma mc^2 - mc^2$$

And then since the electrons are accelerated through 25,000 Volts it gains 25,000 eV. This 25,000eV = KE in the above equation is that correct?

so i obtain :
$$\gamma mc^2 = 25,000eV + mc^2$$
$$v = 9.055*10^7$$

Is this correct can anyone confirm?

 

[Dick]

Aside from the fact you should specify units on v, it is correct.

 

[Delzac]

Thanks for the help.