Find the final speed of an electron

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SUMMARY

The final speed of an electron, starting from rest and passing between two parallel plates with a potential difference of 5000V, is calculated using the formula v=sqrt(2qV/m). With the charge of the electron (q) at 1.6*10^-19C and its mass (m) at 9.1*10^-31kg, the resulting speed is 4.2*10^7 m/s. While this calculation is valid under Classical Physics, it does not account for relativistic effects at higher potential differences, such as 30,000V, where the electron's speed would exceed the speed of light, violating physical laws.

PREREQUISITES
  • Understanding of Classical Physics principles
  • Familiarity with the formula for kinetic energy and potential difference
  • Knowledge of electron properties, including charge and mass
  • Basic grasp of relativistic physics concepts
NEXT STEPS
  • Study the implications of relativistic effects on particle speeds
  • Learn about the Lorentz factor and its role in high-speed particle physics
  • Explore the differences between classical and quantum mechanics regarding particle behavior
  • Investigate the applications of electric fields in particle accelerators
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Students in physics, educators teaching classical mechanics, and anyone interested in the behavior of charged particles in electric fields.

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Find the final speed of an electron, starting from rest, passing between two parallel plates with a potential difference of 5000V.

m=9.1*10^-31kg
q=1.6*10^-19C

v=sqr root of [2(1.6*10^-19)(5000)]/9.1*10^-31 = 4.2*10^7 m/s

Is this answer valid, why?
 
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Yes and No

The calculation is correct and in Classical Physics all is fine. However, if you increase the PD to say 30,000V you will find the electron traveling faster than the speed of light!

Your calculation doesn't account for the mass increase of the electron as it approaches the speed of light. For most School work it is fine though.
 


Yes, this answer is valid. The final speed of an electron can be calculated using the equation v=sqrt(2qV/m), where q is the charge of the electron, V is the potential difference, and m is the mass of the electron. Plugging in the given values for q, V, and m, we get a final speed of 4.2*10^7 m/s. This answer is valid because it follows the correct formula and uses the correct unit conversions. Additionally, the calculated speed is within a reasonable range for the speed of an electron in this scenario.
 

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