4.39 Unit Conversions for Energy & Mass

Units of Energy

• The electronvolt is a unit of energy
• It is equivalent to the amount of energy transferred to an electron accelerated across a potential difference of 1 V:

1 eV = 1.6 × 10^–19 J

• In order to convert between electronvolts and joules:
  • Multiply electronvolts by 1.6 × 10^–19 to get the equivalent energy in joules
  • Divide joules by 1.6 × 10^–19 to get the equivalent energy in electronvolts

Converting between electronvolts and joules

• Sometimes, units of MeV or GeV are used
  • These are given by: 

1 MeV = 1 × 10⁶ eV = 1.6 × 10^–13 J

1 GeV = 1 × 10⁹ eV = 1.6 × 10^–10 J

Units of Mass

• Energy and mass are related by Einstein's energy-mass relation

• Therefore, units of mass can be related to units of energy by division of c²
  • This provides particle physicists convenient units of calculation to work with
  • This is especially useful in experiments involving particle collisions, where annihilation and creation is common

• Possible units of mass are therefore:

, or,

• The following conversions are used to convert into S.I. units: 

= 1.78 × 10^–30 kg

= 1.78 × 10^–27 kg

Step 1: Write the known quantities

• • Rest mass of a proton, m_p = 1.67 × 10^–27 kg
  • Speed of light c = 3 × 10⁸ m s^–1

Step 2: Substitute quantities into Einstein's energy-mass relation

E = m_pc²

E = (1.67 × 10^–27) × (3 × 10⁸)² = 1.50 × 10^–10 J

Step 3: Convert joules to electronvolts

• • To convert a quantity of energy in joules to electronvolts, divide by 1.6 × 10^–19

= 9.4 × 10⁸ eV = 0.94 GeV

Step 4: Convert electronvolts to GeV/c²

• • 0.94 GeV is equivalent to a mass of 0.94 GeV/c², which is roughly 1 GeV/c²