Unit Conversions for Energy & Mass (Edexcel International A Level Physics)

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Katie M

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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

8-9-electronvolts-to-joules_edexcel-al-physics-rn

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

capital delta E equals c squared capital delta m

capital delta m equals fraction numerator capital delta E over denominator c squared end fraction

  • 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:

fraction numerator M e V over denominator c squared end fraction, or, fraction numerator G e V over denominator c squared end fraction

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

1 fraction numerator M e V over denominator c squared end fraction= 1.78 × 10–30 kg

1 fraction numerator G e V over denominator c squared end fraction= 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

fraction numerator 1.50 cross times 10 to the power of negative 10 end exponent over denominator 1.6 cross times 10 to the power of negative 19 end exponent end fraction= 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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Katie M

Author: Katie M

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