Edexcel A Level (IAL) Physics-4.39 Unit Conversions for Energy & Mass- Study Notes- New Syllabus

Energy and Mass Units in Particle Physics: MeV, GeV and SI Conversions

In particle physics, energies and masses are very small when expressed in SI units. Therefore, larger and more convenient units such as MeV, GeV, MeV/\( c^2 \) and GeV/\( c^2 \) are commonly used.

Energy Units: eV, MeV and GeV

Definition:

• 1 electronvolt (eV) is the energy gained by an electron when it moves through a potential difference of 1 V.

\( 1\ \mathrm{eV} = 1.60\times10^{-19}\ \mathrm{J} \)

Larger units:

\( 1\ \mathrm{MeV} = 10^{6}\ \mathrm{eV} \)

\( 1\ \mathrm{GeV} = 10^{9}\ \mathrm{eV} \)

Conversions to joules:

\( 1\ \mathrm{MeV} = 1.60\times10^{-13}\ \mathrm{J} \)

\( 1\ \mathrm{GeV} = 1.60\times10^{-10}\ \mathrm{J} \)

Mass Units in Particle Physics

Using mass–energy equivalence:

\( E = mc^2 \)

Mass can be expressed in energy units divided by \( c^2 \).

Common mass units:

• MeV/\( c^2 \)
• GeV/\( c^2 \)

Converting MeV/\( c^2 \) and GeV/\( c^2 \) to kg

Using \( 1\ \mathrm{eV} = 1.60\times10^{-19}\ \mathrm{J} \) and \( c = 3.00\times10^{8}\ \mathrm{m\,s^{-1}} \):

\( 1\ \mathrm{eV}/c^2 = 1.78\times10^{-36}\ \mathrm{kg} \)

Therefore:

\( 1\ \mathrm{MeV}/c^2 = 1.78\times10^{-30}\ \mathrm{kg} \)

\( 1\ \mathrm{GeV}/c^2 = 1.78\times10^{-27}\ \mathrm{kg} \)

Why These Units Are Used

• Particle masses are extremely small in kg.
• Particle energies are very large in joules.
• MeV and GeV give manageable numerical values.
• Using MeV/\( c^2 \) links mass directly to energy.

Typical Particle Values

• Electron mass ≈ \( 0.511\ \mathrm{MeV}/c^2 \)
• Proton mass ≈ \( 938\ \mathrm{MeV}/c^2 \)
• High-energy accelerators operate at GeV and above.