Particle Mass Units and Relativistic Lifetimes

An electronvolt is the energy transferred when a particle with elementary charge crosses a potential difference of one volt. One MeV is one million eV; one GeV is one billion eV. Multiplying by 1.60×10⁻¹⁹ J per eV converts to joules.

MeV/c² and GeV/c² are units of mass because rest energy is mc². A particle with mass quoted as 100 MeV/c² has rest energy 100 MeV; its mass is not 100 MeV and its total energy need not equal its rest energy if it is moving. Divide the converted rest energy by c² to obtain kilograms.

To investigate a very small feature, a probe needs a sufficiently short de Broglie wavelength, λ=h/p. Increasing particle momentum reduces the wavelength and makes smaller structure accessible. A higher-energy accelerator also permits creation of more massive particles when conservation laws allow.

For relativistic particles, do not automatically use p=mv with the rest mass or Ek=p²/(2m). That kinetic-energy expression is non-relativistic. Edexcel requires understanding why high energies are useful; a question must supply any additional relativistic quantitative relation it expects you to use.

Unstable particles have a characteristic mean lifetime in their rest frame. Particles moving very fast relative to a laboratory can have a longer mean lifetime measured in the laboratory. This relativistic effect helps explain why some high-speed particles survive much farther than a rest-lifetime estimate would suggest.

Atmospheric muons provide an example: many reach the ground despite their short rest-frame lifetimes. The prediction must distinguish the particle rest frame from the Earth frame; it does not mean every individual particle decays after exactly its mean lifetime. For 9PH0 statement 139, the significance is qualitative and relativistic lifetime equations are not required.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.