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Lesson: Relativistic Energy

Worksheet: Relativistic Energy • 7 Questions


A Van de Graaff accelerator utilizes a 50.0 MV potential difference to accelerate charged particles such as protons. The kinetic energy provided by such a large potential difference is sufficiently great that relativistic effects need to be taken into account when finding the velocity of accelerated particles.

What is the velocity of a proton accelerated by such a potential?

  • A
  • B
  • C
  • D
  • E

What is the velocity of an electron accelerated by such a potential?

  • A
  • B
  • C
  • D
  • E


A -meson has a rest mass of 135 MeV. The proper lifetime of the -meson is s and an observer in a laboratory measures its lifetime as s. What is the kinetic energy of the -meson as measured by the observer?


K mesons have an average lifetime in their rest frame of s. Plans for an accelerator that produces a secondary beam of K mesons to scatter from nuclei, for the purpose of studying the strong force, call for them to have a kinetic energy of 500 MeV.

What would the relativistic quantity be for these particles?

What would be the average lifetime of these particles, as measured by a laboratory based observer?

  • A s
  • B s
  • C s
  • D s
  • E s

How far would these particles travel during their average lifetime, as measured by a laboratory based observer?


What is the rest energy of an electron, given its mass is kg?


Determine the difference in the rest masses of a proton and a neutron from their rest energies. Use a value of 938.3 MeV for proton rest energy and 939.6 MeV for the neutron rest energy.

  • A kg
  • B kg
  • C kg
  • D kg
  • E kg