A muon is a lepton that is a higher-mass (rest mass 105 MeV/c^2 ) sibling to the

Question

A muon is a lepton that is a higher-mass (rest mass 105 MeV/c^2) sibling to the electron. Muons are produced in the upper atmosphere when incoming cosmic rays collide with the nuclei of gas molecules. As the muons travel toward the surface of the earth, they lose energy. A muon that travels from the upper atmosphere to the surface of the earth typically begins with kinetic energy 9.0GeVand reaches the surface of the earth with kinetic energy 4.5GeV . The energy decreases by a half of its initial value.

Part A

By what fraction does the speed of the muon decrease?

2 sig figs

(vi-vf)/(vi) = ?

Explanation / Answer

Ki = (gamma_i - 1) m c^2

==> Ki = (1/(1 - vi^2)^0.5 - 1) m c^2

==> 9e9 = (1/(1 - vi^2)^0.5 - 1) * 105e6

==> vi = 0.9999335028 c

Kf = (gamma_f - 1) m c^2

==> Kf = (1/(1 - vf^2)^0.5 - 1) m c^2

==> 4.5e9 = (1/(1 - vf^2)^0.5 - 1) * 105e6

==> vi = 0.999740016 c

(vi - vf)/vi * 100 = (0.9999335028 - 0.999740016 )/0.9999335028 * 100 = 0.019 %

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