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Probing Deep Into Matter

Relativistic energy and the relativistic factor

  • 3 things to know
  • Components 01, 02 and 03

Overview

Recall questions on rest energy from rest mass, electron and proton values in MeV, evaluating the factor at high speeds, total and kinetic energy, and why no massive particle reaches light speed.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Key term

Write the relationship between the rest mass of a particle and its rest energy.

Numbers

Calculate the rest energy of an electron in joules.

Key term

Express the rest energy of an electron in MeV.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Write the relationship between the rest mass of a particle and its rest energy.

    Model answer

    The rest energy is Erest = mc², where m is the rest mass and c is the speed of light in a vacuum.

  2. 2

    Calculate the rest energy of an electron in joules.

    Model answer

    Erest = mc² = 9.11 × 10⁻³¹ × (3.00 × 10⁸)² = 8.2 × 10⁻¹⁴ J.

  3. 3

    Express the rest energy of an electron in MeV.

    Model answer

    Dividing 8.2 × 10⁻¹⁴ J by 1.60 × 10⁻¹⁹ gives about 5.1 × 10⁵ eV, which is 0.51 MeV.

  4. 4

    Calculate the rest energy of a proton in MeV.

    Model answer

    Erest = 1.673 × 10⁻²⁷ × (3.00 × 10⁸)² = 1.5 × 10⁻¹⁰ J, which is about 940 MeV.

  5. 5

    Write the expression for the relativistic factor of a particle moving at speed v.

    Model answer

    The relativistic factor is γ = 1/√(1 − v²/c²).

  6. 6

    What is the value of the relativistic factor for a particle at rest?

    Model answer

    The relativistic factor is 1, because v is zero and the square root reduces to 1.

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AThe neutron has lepton number 0.
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