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Lecture 5

PHYS 242 Lecture 5: PHYS242_Lecture_07-09

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Department
Physics
Course
PHYS 242
Professor
Wolfgang Rau
Semester
Fall

Description
23 ENPHPHYS 242 Fall 2014 L 07 Cosmic Ray Muons and Length Contraction For a change we now will discuss a real experiment as performed in 1963 by Frisch and Smith, two US American physicists. This experiment is concerned with the measurement of cosmic ray muons. Muons () are very similar to electrons but ~200 times more massive and instable. Like for radioactive decay the probability for a muon to decay is the same at any time. This leads to an exponential decay law: ex (14) where is the time, is the number of muons at time is the initial number of muons and 2.2 s is their mean live time. This decay law follows from fundamental properties of the decaying particle and as such should be according to Einsteins second postulate identical in all inertial reference frames. Therefore the decay can be used to measure the time: ln (15) Muons are produced when high energetic cosmic particles hit the atoms in the upper atmosphere. Frisch and Smith used a muon detector at Mt. Washington at a height of 1910 m above sea level. In one hour they detected 560 muons. Since the muons have very high energy their velocity is almost . Consequently they pass the vertical distance from top of Mt. Washington to sea level in 6.4 s . With help of equation (14) we can now calculate the expected number of muons at sea level: 560 exp 6.4 s 2.2 s30 This means we would expect that at sea level they would have measured 30 muons per hour. The result of their measurement however was 410 muons per hour. This can be explained by time dilation: the time passes slower for the muons since their frame has a high velocity as seen from the Earth surface. Using the measured numbers, the decay law (14), the time dilation equation (13) and the definition of (12) we can calculate what the actual velocity of the muons is (use frame for the laboratory and frame for the muons): (14): ln NN 0.69 s (proper time of muons!) (13): (12) 1 1 1 0.994 This confirms our initial assumption that the velocity of the muons is very close to . W. Rau
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