1-24. The proper mean lifetime of \( \pi \) mesons (pions) is \( 2.6 \times 10^{-8} \mathrm{~s} \). Suppose a beam of such particles has speed \( 0.9 c \). (a) What would their mean life be as measured in the laboratory? (b) How far would they travel (on the average) before they decay? (c) What would your answer be to part \( (b) \) if you neglected time dilation? \( (d) \) What is the interval in spacetime between creation of a typical pion and its decay?
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- Proper mean lifetime of \( \pi \) mesons, \( \tau_0 = 2.6 \times 10^{-8} \) s - Speed of the particles, \( v = 0.9c \) - Speed of light, \( c = 3 \times 10^8 \) m/s Show more…
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The proper mean lifetime of $\pi$ mesons (pions) is $2.6 \times 10^{-8}$ s. Suppose a beam of such particles has speed $0.9 c$. ( $a$ ) What would their mean life be as measured in the laboratory? (b) How far would they travel (on the average) before they decay? (c) What would your answer be to part $(b)$ if you neglected time dilation? $(d)$ What is the interval in spacetime between creation of a typical pion and its decay?
The Pi Meson An elementary particle called a pi meson (or pion for short) has an average lifetime of $2.6 \times 10^{-8} \mathrm{s}$ when at rest. If a pion moves with a speed of $0.99 \mathrm{c}$ relative to Earth, find (a) the average lifetime of the pion as measured by an observer on Earth and (b) the average distance traveled by the pion as measured by the same observer. (c) How far would the pion have traveled relative to Earth if relativistic time dilation did not occur?
The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is $2.6 \times 10^{-8} s.$ If the meson moves with a speed of 0.98$c,$ what is (a) its mean lifetime as measured by an observer on Earth, and (b) the average distance it travels before decaying, as measured by an observer on Earth? (c) What distance would it travel if time dilation did not occur?
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