Momentum and kinetic energy through potential difference

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SUMMARY

An electron and a proton accelerated through a potential difference of 10 million volts will each gain kinetic energy equivalent to the energy provided by the voltage. The kinetic energy (KE) can be calculated using the formula KE = qV, where q is the charge and V is the potential difference. For an electron, the kinetic energy is approximately 10 MeV, and for a proton, it is also approximately 10 MeV, given their equal acceleration through the same potential difference. The momentum can be derived from the kinetic energy using the relation p = sqrt(2mKE), where m is the mass of the particle.

PREREQUISITES
  • Understanding of electric potential and energy conversion
  • Familiarity with the concepts of momentum and kinetic energy
  • Knowledge of particle physics, specifically electron and proton properties
  • Basic proficiency in using formulas involving mass-energy equivalence
NEXT STEPS
  • Calculate the momentum of an electron and proton using the formula p = sqrt(2mKE)
  • Explore the relationship between voltage and kinetic energy in particle accelerators
  • Study the mass-energy equivalence principle as described by Einstein's equation E=mc²
  • Investigate the effects of relativistic speeds on momentum and kinetic energy calculations
USEFUL FOR

Students in physics, particle physicists, and anyone interested in understanding the effects of potential difference on particle acceleration and energy transformation.

itsdanfreas
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An electron and a proton are each accelerated through a potential difference of 10 million volts. find the momentum (in MeV/c) and the kinetic energy (in MeV) of each.

----------------------------

I started by finding the masses of the proton and electron in MeV/c^2, but i don't know where to go from there.

I believe i need to find the velocities...but I'm not sure how to get the velocity just by looking at the potential difference.

Thanks!
 
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Welcome to PF!

itsdanfreas said:
An electron and a proton are each accelerated through a potential difference of 10 million volts. find the momentum (in MeV/c) and the kinetic energy (in MeV) of each.
…
I believe i need to find the velocities...but I'm not sure how to get the velocity just by looking at the potential difference.

Hi itsdanfreas! Welcome to PF! :smile:

Learn your electric units …

voltage = energy per charge = joules per coulomb :wink:​
 

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