Mass of an accelerated electron by 31 kV

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SUMMARY

The mass of an electron accelerated by an electric potential of 31 kV can be calculated using the equation qU = mc^2 - m0c^2, where m0 is the rest mass of the electron (9.1093826 x 10^-31 kg). After applying the principles of energy and relativistic mass, the calculated mass of the electron post-acceleration is approximately 9.66191907 x 10^-31 kg. It is important to note that the modern approach utilizes the Lorentz factor (gamma) to express mass, moving away from the traditional rest mass notation.

PREREQUISITES
  • Understanding of electric potential energy (E = qU)
  • Familiarity with Einstein's mass-energy equivalence (E = mc^2)
  • Knowledge of relativistic mass and the Lorentz factor (gamma)
  • Basic concepts of particle physics and electron properties
NEXT STEPS
  • Study the derivation and application of the Lorentz factor in relativistic physics
  • Learn about the implications of relativistic mass in high-energy particle physics
  • Explore the relationship between electric fields and particle acceleration
  • Investigate advanced topics in quantum mechanics related to electron behavior
USEFUL FOR

Students in upper-grade physics, educators seeking clarity on relativistic concepts, and anyone interested in the physics of particle acceleration and energy transformations.

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Homework Statement



My upper grade teacher in physics has lack of intelligence, and she's not in duty to help people. I would like to clear this out here.

"An electron is accelerated from rest by the electric tension 31.0 kV. Determine the mass of the electron after the acceleration."

Homework Equations



I've based my procedure from the principles:

E = qU

E = mc^2 - m0c^2

qU = mc^2 - m0c^2

m0 = is rest mass --> m0 = 9.1093826*10^-31 kg


The Attempt at a Solution



m0c^2 = (9.1093826*10^-31)c^2 --> m0 = 8.18751672*10^-14

q31000 = mc^2 - 8.18751672*10^-14

mc^2 = 8.68413672*10^-14

m = 9.66191907*10^-31 kg


Is this correct?
 
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That looks very good, aside from one typo (" m0 = 8.18751672*10^-14 ").

Be warned that the "modern" way is to let m = rest mass, then your m = (gamma)*m, gamma = 1/[sqrt(1 - (v^2/c^2)]. m0 is no longer used.

Don't ask me why.
 

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