Complete Question
The positive [tex]muon (^+)[/tex], an unstable particle, lives on average [tex]2.20 * 10^{-6}\ s[/tex] (measured in its own frame of reference) before decaying.
If such a particle is moving, with respect to the laboratory, with a speed of 0.950 c , what average lifetime is measured in the laboratory?
Answer:
The value is [tex]\Delat t = 7.046 *10^{-6} \ s[/tex]
Explanation:
From the question we are told that
The the average live time of [tex]muon (^+)[/tex] is [tex]\Delta t_o = 2.20 *10^{-6} \ s[/tex]
The speed of of [tex]muon (^+)[/tex] in the laboratory is [tex]v = 0.950 c[/tex]
Generally the average life time of the positive [tex]muon (^+)[/tex] measured in the laboratory is mathematically represented as
[tex]\Delat t = \frac{\Delta t_o }{ \sqrt{1 - \frac{v^2}{c^2} } }[/tex]
[tex]\Delat t = \frac{2.20 *10^{-6}}{ \sqrt{1 - \frac{(0.950 c)^2}{c^2} } }[/tex]
[tex]\Delat t = \frac{2.20 *10^{-6}}{ \sqrt{1 - \frac{0.9025 c^2}{c^2} } }[/tex]
[tex]\Delat t = \frac{2.20 *10^{-6}}{ \sqrt{1 - 0.9025 } }[/tex]
[tex]\Delat t = \frac{2.20 *10^{-6}}{ \sqrt{ 0.0975 } }[/tex]
[tex]\Delat t = 7.046 *10^{-6} \ s[/tex]
