All Problems

Relativistic Mechanics

Problem 1.346

The proper lifetime of an unstable particle is equal to Δt0=10\Delta t_{0}=10 ns. Find the distance this particle will traverse till its decay in the laboratory frame of reference, where its lifetime is equal to Δt=20 ns\Delta t=20 \mathrm{~ns}

Reveal Answer
s=cΔt1−(Δt0/Δt)2=5 ms=c \Delta t \sqrt{1-\left(\Delta t_{0} / \Delta t\right)^{2}}=5 \mathrm{~m}
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