Calculating Final Speed: Electrons & Potential Difference

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SUMMARY

The discussion focuses on calculating the final speed of electrons accelerated through a potential difference of 250,000 V, comparing classical and relativistic predictions. The classical speed is calculated as 2.96 × 108 m/s, while the relativistic approach requires using the equation for relativistic kinetic energy, KE = mc² - m₀c², leading to a final speed of 2.22 × 108 m/s. Participants emphasize the need to incorporate relativistic momentum for accurate calculations, as the initial equations presented were incomplete.

PREREQUISITES
  • Understanding of classical mechanics, specifically kinetic energy equations.
  • Familiarity with relativistic physics concepts, including mass-energy equivalence.
  • Knowledge of the relationship between electric potential difference and kinetic energy.
  • Ability to manipulate equations involving relativistic momentum and speed of light.
NEXT STEPS
  • Study the derivation of kinetic energy from electric potential difference in classical mechanics.
  • Learn about relativistic momentum and its application in speed calculations.
  • Explore the implications of mass-energy equivalence in particle physics.
  • Investigate the limitations of classical physics when applied to high-speed particles.
USEFUL FOR

Physics students, educators, and anyone interested in understanding the differences between classical and relativistic calculations of particle speeds in high-energy contexts.

NikkiNik
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Homework Statement



Electrons are accelerated from rest through a potential difference of 250000 V. What is the final speed predicted classically?

What is the final speed predicted relativistically?

Homework Equations



KE=0.5mv^2
KE=mc^2-m0c^2

The Attempt at a Solution



a.2.96×108 m/s

b. I keep ending up with the speed of light which I know is incorrect...for m I know I use m0/sqrt (1-v^2/c^2) so the final equation is KE which I found to be 4.005e-14 J= m0/sqrt (1-v^2/c^2)*c^2 -m0c^2
 
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Your working equations are incomplete.

1. Yes, that's the correct classical kinetic energy, but how does that relate to an electric potential difference V?

2. Yes, that's the correct equation for relativistic kinetic energy, but you'll need it in a form that include relativistic momentum, since you need to compare the two speeds. After all, the equation as you have it written down doesn't allow us to solve for the electron's speed (it just includes masses and the speed of light).
 
NikkiNik said:
b. I keep ending up with the speed of light which I know is incorrect...for m I know I use m0/sqrt (1-v^2/c^2) so the final equation is KE which I found to be 4.005e-14 J= m0/sqrt (1-v^2/c^2)*c^2 -m0c^2

I came up with 2.22 * 10^8 m/s. Are you sure you calculated correctly?
 

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