Muon evidence experiment

Question 1

How are muons created

Answer 1

Unstable muons are created when cosmic rays reach the ionosphere above the Earth’s surface

Can also be created in a laboratory

Question 2

What speeds do muons travel at

Answer 2

0.996c (0.99c)

Question 3

What is the half-life of low energy muons

Answer 3

Roughly 1.5 microseconds

Question 4

Decay equation for a muon

Answer 4

muon –> electron + muon neutrino + electron antineutrino

Question 5

Experiment:

Answer 5

1) Measure speed of muons ~ 0.996c
2) Place detector/Geiger counter at high altitude and measure the muon count rate
3) Use another detector to measure the count rate at sea/ground level
4) Compare the two figures

Question 6

What was expected from the experiment

Answer 6

Muons travelled a distance of 2km from a high altitude to sea level at 0.996c
This took about 6.7microseconds

As this time is greater than the half life (6.7>1.5) it was expected most muons would decay by the time they reached sea-level (<10% left)

Question 7

What did the experiment show

Answer 7

Around 76% did reach sea level - this can be explained by special relativity: time dilation or length contraction

Question 8

Explain the results of the experiment via time dilation

Answer 8

-To an Earth observer, time passes slower for cosmic muons because of their speed so they have a relativistic half life which is 17 microseconds which is much greater than the original half life of 1.5 microseconds
This enables them to cover 2km in 6.7/17 = 0.4 half lives and so intensity is 2^-0.4 x 100 = 76% of the original amount reach the second detector

• In the reference frame of the observer, the muons travel 6.7/1.5 = 4.5 half lives however in a muon’s own reference frame, the time taken between both detectors, t0 = 0.6 microseconds which is less than the original half life of 1.5 microseconds and so 0.6/1.5 = 0.4 half lifes occur meaning 2^-0.4 x 100 = 76% of the original amount reach the second detector

Question 9

Explain the results of the experiment via length contraction

Answer 9

Consider relativistic contraction of the distance 2km as seen by the muons. Distance contracts to L=2000/y = 179m in muon frame of reference so takes 179/0.996c = 0.6 microseconds which is 0.6/1.5 = 0.4 half lifes occur meaning 2^-0.4 x 100 = 76% of the original amount reach the second detector

Question 10

If speed of muons = 0.99c rather than 0.996c then will get very different numbers for the explanation

Answer 10

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