calculate the height of the mountain as it is seen to pass by
10. Compare answer (9) with the height we normally ascribe to
Mount Washington (6,300 ft).
11. How far does the earth move towards the muons in a time of
1.5 μs. Comment on how many of the muons should be hit by the
earth.
12. Given the experimental fact that 412 muons reach the foot of
the mountain, calculate the fraction of one-half life that elapsed,
and so calculate the elapsed time in μs from the muon’s reference
frame. For us (at rest on the earth) the time is clearly 6.4
μs.
- 9 Use The Gamma Factor Gamma Factor Value Is 10 0125 Calculate The Height Of The Mountain As It Is Seen To Pass By 1 (43.25 KiB) Viewed 261 times
The muon is an elementary radioactive particle created when
cosmic rays crash into the upper atmosphere of the earth. It has a
half-life of 1.5 μs. = 1.5 x 10-6 s in its rest frame. Only muons
with a speed of 0.995c are stopped in the detector where they
remain until they decay. Muons with less speed are stopped in the
iron above the detector. Muons with greater speeds pass through the
detector into Mount Washington below. Here we are at rest alongside
the mountain and we observe the muons speeding towards us at a
speed of 0.995 c.
Muon Reference Frame 9. Use the gamma factor, y, calculate the height of the mountain as it is seen to pass by. 10. Compare answer (9) with the height we normally ascribe to Mount Washington. 11. How far does the earth move towards the muons in a time of 1.5 µs. Comment on how many of the muons should be hit by the earth. 12. Given the experimental fact that 412 muons reach the foot of the mountain, calculate the fraction of one-half life that elapsed, and so calculate the elapsed time in us from the muon's reference frame. For us (at rest on the earth) the time is clearly 6.4 μs.