Before decaying, a specific particle produced in a nuclear reactor leaves a 1 cm track. Determine the life of the particle in the frame of the particle, assuming it travelled at 0.995c .

Step-by-step solution

The distance travelled by the particle in the laboratory frame is L = 1 cm = 10⁻² m . The speed of the particle is v = 0.995c . The time lived by the particle in the laboratory frame is given by: t = L v = 10⁻² 0.995 3 10^8 = 10⁻¹⁰ 2.985 33.5 10⁻¹² s The life of the particle in its own rest frame (proper time t₀ ) is related to the laboratory time by time dilation: t = t₀ 1 - v^2 c^2 t₀ = t 1 - v^2 c^2 Substituting the values: t₀ = 33.5 10⁻¹² 1 - (0.995)^2 t₀ = 33.5 10⁻¹² 1 - 0.990025 t₀ = 33.5 10⁻¹² 0.009975 t₀ 33