Cosmic ray muons are produced high in the atmosphere (at 8000 m, say) and travel toward the earth at very nearly the speed of light (0.998 c, say). (a) Given the lifetime of the muon (2.2 × 10-6 sec), how far would it go before disintegrating, according to prerelativistic physics? Would the muons make it to ground level? (b) Now answer the same question using relativistic physics. (Because of time di- lation, the muons last longer, so they travel farther.) (c) Now analyze the same process from the perspective of the muon. (In its reference frame it only lasts 2.2 x 10-6 sec; how, then, does it make it to ground?)
Cosmic ray muons are produced high in the atmosphere (at 8000 m, say) and travel toward the earth at very nearly the speed of light (0.998 c, say). (a) Given the lifetime of the muon (2.2 × 10-6 sec), how far would it go before disintegrating, according to prerelativistic physics? Would the muons make it to ground level? (b) Now answer the same question using relativistic physics. (Because of time di- lation, the muons last longer, so they travel farther.) (c) Now analyze the same process from the perspective of the muon. (In its reference frame it only lasts 2.2 x 10-6 sec; how, then, does it make it to ground?)
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![3.4. Cosmic ray muons are produced high in the atmosphere (at 8000 m, say) and travel
toward the earth at very nearly the speed of light (0.998 c, say).
(a) Given the lifetime of the muon (2.2 x 10-6 sec), how far would it go before
disintegrating, according to prerelativistic physics? Would the muons make it
to ground level?
(b) Now answer the same question using relativistic physics. (Because of time di-
lation, the muons last longer, so they travel farther.)
(c) Now analyze the same process from the perspective of the muon. (In its reference
frame it only lasts 2.2 x 10-6 sec; how, then, does it make it to ground?)
+
(d) Pions are also produced in the upper atmosphere. [In fact, the sequence is
proton (from outer space) hits proton (in atmosphere) → p + p + pions. The
pions then decay into muons: ¯ → μ¯ + D µ; πt → μ† + vµ.] But the lifetime
of the pion is much shorter, a hundredth that of the muon. Should the pions
reach ground level? (Assume that the pions also have a speed of 0.998 c.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe44e7fdc-f850-4dc9-8247-4240983c667e%2Fa0355441-dcb6-401a-939b-8a149d60fff7%2F9hpmldn_processed.png&w=3840&q=75)
Transcribed Image Text:3.4. Cosmic ray muons are produced high in the atmosphere (at 8000 m, say) and travel
toward the earth at very nearly the speed of light (0.998 c, say).
(a) Given the lifetime of the muon (2.2 x 10-6 sec), how far would it go before
disintegrating, according to prerelativistic physics? Would the muons make it
to ground level?
(b) Now answer the same question using relativistic physics. (Because of time di-
lation, the muons last longer, so they travel farther.)
(c) Now analyze the same process from the perspective of the muon. (In its reference
frame it only lasts 2.2 x 10-6 sec; how, then, does it make it to ground?)
+
(d) Pions are also produced in the upper atmosphere. [In fact, the sequence is
proton (from outer space) hits proton (in atmosphere) → p + p + pions. The
pions then decay into muons: ¯ → μ¯ + D µ; πt → μ† + vµ.] But the lifetime
of the pion is much shorter, a hundredth that of the muon. Should the pions
reach ground level? (Assume that the pions also have a speed of 0.998 c.)
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