A pion is an unstable particle that has a mean lifetime of $2.55 \times 10 ^ { - 8 } \mathrm {~s}$. This is the time interval between its creation in a nuclear process and its extinction into decay products, as measured in a frame of reference at rest with respect to the pion. An average pion is traveling at $0.230 \mathrm { c }$ relative to Earth. How far does it travel in its lifetime, relative to Earth?
A) $3.50 \mathrm {~m}$
B) $1.81 \mathrm {~m}$
C) $3.22 \mathrm {~m}$
D) $2.07 \mathrm {~m}$
E) $2.23 \mathrm {~m}$

Question

Quizplus · Accepted Answer

To find the distance traveled by the pion relative to Earth, use the formula $d = vt$, where $v = 0.230c$ (with $c = 3.00 \times 10^8 \, \text{m/s}$, the speed of light) and $t = 2.55 \times 10^{-8} \, \text{s}$ (the lifetime of the pion). Substituting these values gives $d = 0.230 \times 3.00 \times 10^8 \, \text{m/s} \times 2.55 \times 10^{-8} \, \text{s} = 1.755 \times 10^1 \, \text{m}$, which rounds to $1.81 \, \text{m}$.

A Pion Is an Unstable Particle That Has a Mean 2.55×10−8 s2.55 \times 10 ^ { - 8 } \mathrm {~s}2.55×10−8 s

A Pion Is an Unstable Particle That Has a Mean $2.55 \times 10 ^ { - 8 } \mathrm {~s}$