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Physics / Physics with MasteringPhysics 4 / Chapter 29 / Problem 12P

Physics with MasteringPhysics | 4th Edition | ISBN: 9780321541635 | Authors: James S. Walker

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•• The Pi Meson An elementary particle called a pi meson

Chapter 29, Problem 12P

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QUESTION:

Problem 12P

•• The Pi Meson An elementary particle called a pi meson (or pion for short) has an average lifetime of 2.6 × 10–8 s when at rest. If a pion moves with a speed of 0.99c 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?

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QUESTION:

Problem 12P

•• The Pi Meson An elementary particle called a pi meson (or pion for short) has an average lifetime of 2.6 × 10–8 s when at rest. If a pion moves with a speed of 0.99c 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?

ANSWER:

Step 1 of 3:-

a)

Here, we have to find the average lifetime of pion in the frame of reference of earth.

At its rest frame, the average lifetime is,

$\Delta{}t=2.6\times{}1{0}^{-8}\ s$ .

$v=0.99\ c$ .

We know that,

$\Delta{}t'=\gamma{}\Delta{}t$

Where,

$\gamma{}=\frac{1}{\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}}$

$=\frac{1}{\sqrt{1-\frac{0.9{9}^{2}\ {c}^{2}}{{c}^{2}}}}$

$=7.09$

So,

$\Delta{}t'=7.09\times{}2.6\times{}1{0}^{-8}$

$=1.84\times{}1{0}^{-7}s\$

So, the average lifetime of the pions in earth’s frame of reference is $1.84\times{}1{0}^{-7}s$ .

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