I have a homework problem where I am getting the wrong answer and I just want advice on the route I took.
So I am told that electrons in a television set are accelerated through a potential difference of 50 000 volts. I am to find speed of the electrons using relativistic kinetic energy and classical Kinetic energy. The answer I found relativistically is correct. Since $E_K=W$ and $W=qV$, I know work, so I know $E_K$, then I solved for speed, 0.412c. All good.
So here's the question. I want to use $E_K = (1/2)mv^2$ to solve it again, and I am supposed to get 0.422c. I use the same $E_K$ as the first time, based on my $qV$. (I suspect this is the problem, but please tell me why or why not is it the correct value to be used here. If it is the incorrect value, I don't know then what I should have for $E_K$). When I solve for $v$ now, I get 0.44c.
I have ruled out sig fig problems. Thanks for your help.
Oh, and then I'm supposed discuss if this difference (0.412 vs. 0.422) makes a difference in designing television sets. I suppose it must, but I don't know how tvs work. Some guidance here would help too. Thanks.