# 8.9 Unit Conversions for Energy & Mass

## 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

#### Worked example

Show that the rest mass of a proton, 1.67 × 10–27 kg, is roughly equivalent to 1 GeV/c2

Step 1: Write the known quantities

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

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

Empc2

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

#### Exam Tip

In this worked example, we could have used the direct conversion between GeV/c2 and kg, because 1 GeV/c2 = 1.78 × 10–27 kg, but you should be super comfortable with using Einstein's energy-mass relation to find quantities of mass/energy in standard units, and converting to eV and eV/c2 the 'long way round'. Exam questions may require you to do this when the conversions are not so straightforward.

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