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Naya [18.7K]
3 years ago
15

The positive muon (?+), an unstable particle, lives on average 2.20×10?6s (measured in its own frame of reference) before decayi

ng. a. If such a particle is moving, with respect to the laboratory, with a speed of 0.910 c , what average lifetime is measured in the laboratory? b. What average distance, measured in the laboratory, does the particle move before decaying?
Physics
1 answer:
Debora [2.8K]3 years ago
4 0

Answer:

4.82383\times 10^{-6}\ s

1316.90559 m

Explanation:

\Delta T' = Time measured in the laboratory

\Delta T = Time measured in its own frame of reference = 2.2\times 10^{-6}\ s

c = Speed of light = 3\times 10^8\ m/s

v = 0.91 c

Time dilation is given by

\Delta T'=\dfrac{\Delta T}{\sqrt{1-\dfrac{v^2}{c^2}}}\\\Rightarrow \Delta T'=\dfrac{2\times 10^{-6}}{\sqrt{1-\dfrac{0.910^2c^2}{c^2}}}\\\Rightarrow \Delta T'=4.82383\times 10^{-6}\ s

The average lifetime is measured in the laboratory is 4.82383\times 10^{-6}\ s

Distance measured would be

L=v\Delta T'\\\Rightarrow L=0.91\times 3\times 10^8\times 4.82383\times 10^{-6}\\\Rightarrow L=1316.90559\ m

The distance is 1316.90559 m

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