SPECIAL RELATIVITY

An Experiment With Mu - Mesons

HALL and ROSSI'S  EXPT
Student Solutions
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USEFUL EQUATIONS


You should read through all the article on Rossi and Hall's experiment before you attempt the following questions.

1) What is a Mu Meson and where and how are Mu Mesons produced ?

2) Here is the data for Mu Meson decay as measured in a laboratory rest frame:
 
 
 

(i) Calculate the decay constant lm for muons at rest.

(ii) Using this constant , calculate the time that should have elapsed in the muon'srest frame for the count rate to have fallen from 563 hr-1 to 400 hr-1
 
 

 3) Show that mesons should take about 6.5 x 10-6 seconds to reach sea level from an altitude of 2000 metres. Show also that 'the muon count rate should have fallen to 'about 25 hr-1 ' by the time the mesons had reached sea level.

4)Deduce that the Time Dilation factor ( To / t ) is approximately 1/9.

Hence establish that the muons travel at a speed of roughly 0.994c.

 5)Explain fully the statement that 'If we take two groups of unstable particles of the same type, giving one a group speed of v and letting the other remain at rest with respect to our frame of reference, the radioactive clock represented by the decay in the moving group will run slow compared to that of the stationary group.'

6) From the article , calculate the % age of muons which are measured by the earthbound observer to have reached sea level.Calculate also the % of muons that would reach the observer if there was a ' Universal Newtonian Time '.

7)If muons moving at speed v travel a distance H in time Dt as measured by an observer on earth,postulate that from their frame of reference, they travel a distance H' in time Dt'.

(i) Show that this leads to the equation :
H' = H ( 1 - v2 /c2 )1/2          *

(ii) Interpret this equation physically.
 

(iii)Calculate the distance H' that the muons in Rossi and Hall's experiment cover as measured in their own rest frame.
 
 

 8) Equation * is the Lorentz - Fitzgerald contraction of length.
 
  (i) Do objects appear longer in a frame at rest , or a moving frame ?

(ii) Which is correct ?

L = Lo ( 1 - v2 / c2 )1/2
or
Lo = L ( 1 - v2 /c2 )1/2

where Lois the ' rest length ' or ' proper length '

(iii)Plot a graph of L / Lo against v/c and comment.
 
 

 9) An unstable particle has a half life of 2 m sec and travels at speeds within 0.2% of lightspeed. (i) Calculate the distance that it appears to cover before decay in its own rest frame.
 

(ii)Calculate the distance that it would appear to travel relative to a fixed observer on earth. Would a significant number of these particles reach the ground if they were created at an altitude of 10km ?

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