How Fast Do Electrons Travel in a TV Tube?

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SUMMARY

Electrons in a TV tube are accelerated from rest by a potential difference of 10,000 volts, resulting in a calculated speed of approximately 4.2 x 107 m/s, which is about 2/15 the speed of light (c). The discussion highlights the use of the energy conservation principle, specifically the equations for potential energy (PE) and kinetic energy (KE). A correction was noted regarding the formula for potential energy, indicating a need for accuracy in calculations. The approach is valid for those without a background in relativity.

PREREQUISITES
  • Understanding of basic physics concepts such as potential energy (PE) and kinetic energy (KE)
  • Familiarity with the equation for energy conservation
  • Knowledge of electron charge and mass values (1.6 x 10-19 C and 9.11 x 10-31 kg)
  • Basic understanding of the speed of light (c = 3.00 x 108 m/s)
NEXT STEPS
  • Review the derivation of the kinetic energy formula in classical mechanics
  • Study the implications of relativistic effects on electron speeds
  • Explore the principles of electron acceleration in cathode ray tubes
  • Investigate the relationship between voltage and electron velocity in different vacuum environments
USEFUL FOR

Students studying physics, particularly those focusing on electromagnetism and energy conservation, as well as educators and anyone interested in the mechanics of cathode ray tubes.

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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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