Final Velocity of Electron Accelerated from Rest Through Potential Difference

AI Thread Summary
An electron accelerated from rest through a potential difference of V volts requires the use of relativistic equations to determine its final velocity. The initial attempt to use non-relativistic energy resulted in an answer exceeding the speed of light, indicating a misunderstanding of the physics involved. The correct approach involves using the relativistic kinetic energy formula, which accounts for the significant potential difference. The discussion highlights the importance of recognizing when to apply relativistic principles in calculations. Ultimately, the key takeaway is the necessity of using the appropriate equations for high-energy scenarios.
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Homework Statement


An electron is accelerated from rest through a potential difference of V volts. What is the final velocity?

I did:
qV=\frac{mc^2}{\sqrt{1-\frac{v_f^2}{c^2}}}

And solve for v, but I get an unreal answer. What am I doing wrong?!

Homework Equations


The Attempt at a Solution

 
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Why are you using relativistic energy?
 
Because there is an high potential difference. If I use non-relativistic energy it gives a speed higher than the speed of light. :rolleyes:
 
Could you post more of the question and your work?
 
If I'm not mistaken(Memory sometimes betray me) qV=(Gamma-1)mc^2
 
ziiad this is the relativistic kinetic energy, what I need is the relativistic change in kinetic energy.
 
No, you are right. What a stupid mistake of mine. :( Thanks, mate.
 
Don't worry, we all make mistakes, they key part was "...accelerated from rest..."
 
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