How Fast Do Electrons Travel in a TV Tube?

AI Thread Summary
Electrons in a TV tube start at near-zero speed and are accelerated by a potential of 10,000 volts, resulting in a calculated speed of approximately 4.2 x 10^7 m/s, or about 2/15 the speed of light. The initial poster used the energy conservation principle to derive this speed, but there was a noted error in the potential energy formula. While the approach is valid for those not familiar with relativity, correcting the formula is essential for accuracy. The discussion also highlighted that this question would be better suited for a specific homework forum. Overall, the calculations need verification and correction for precise results.
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I am not sure if this is the right place to post this question but here it is any way...

Electrons leave the cathode of a TV tube at essentially zero speed and are accelerated toward the front by 10,000v potential. At what speed do they strike the screen? Express this value also as a faction of the speed of light.

OK so here is what I did does it look right?

PE1 + KE1 = PE2 + KE2
KE1 = PE2 = 0
so
PE1 = KE2

PE = 1/2QV
KE = 1/2mv^2

therefore

1/2QV = 1/2mv^2

Rearrange for velocity

v = sqroot(QV/m)
v = sqroot(1.6 x 10^-19 x 10,000 V / 9.11 x 10^-31)
v = 4.2 x 10^7 m/s

c 3.00 x 10^8 m/s

Therefore the speed of the electron equals approximately 2/15c

Does this look right or am I way off base?
thanks for your help...
 
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1. The correct place to post this would be the Homework and Coursework subforum (near the top of the main page). Keep that in mind for your next thread.

2. Recheck the formula you've used for PE - there's an error in it.

3. If you haven't yet had any Relativity, then this approach is correct. If you fix the error in 2 you should be good.

4. I haven't actually checked the numbers.
 

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