Muons are subatomic particles that have the negative charge of an electron but a

Question

Muons are subatomic particles that have the negative charge of an electron
but are 206.77 times more massive. They are produced high in the atmosphere
by cosmic rays colliding with nuclei of oxygen or nitrogen, and muons are
the dominant cosmic-ray contribution to background radiation at the earth's
surface. A muon, however, rapidly decays into an energetic electron, existing,
from its point of view, for only 2.20 /^s. on the average. Cosmic-ray generated
muons typically have speeds of about 0.998c and thus should travel only a
few hundred meters in air before decaying. Yet muons travel through several
kilometers of air to reach the earth's surface. Using the results of special
relativity explain how this is possible. HINT: consider the atmospheric travel
distance as it appears to a muon, and the muon lifetime as it appears to an
observer on the earth's surface.

Explanation / Answer

= 1/(1-(v/c)^2) = 1/(1-0.998*0.998) = 15.819

t = tp = 15.819 * 2.2 = 34.8018 s

distance = d = v t = 0.998*3e8 * 34.8018 = 1.042e10 m = 1.042e7 Km

This is big enough for muons travel through several kilometers of air to reach the earth's surface.

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