The proper mean lifetime of a muon is 2.2ms. Muons in a beam are traveling through...

The proper mean lifetime of a muon is 2.2ms. Muons in a beam are traveling through a laboratory at 0.95c.

1. What is their mean lifetime as measured the laboratory?

2. How far do they travel, on average, before they decay?

Please show expressions, work, and a proper explination!!!

Expert Solution

Given, muon proper mean life time 'to' = 2.2 ms

velocity 'v'= 0.95C ( C is the velocity of light in vaccum = 3 x 10^8m/s)

a) mean life time = (r )* (to) where, r = 1/[square root(1 - v^2/c^2)

therefore, r = 1/squareroot(1- (0.95)^2)

= 1/ 0.31224 = 3.2

mean life time = 3.2 * 2.2 = 7.04 ms

b) distance = velocity * mean life time

= 0.95C * (7.04 x10^-3)

= 0.95 * (3 x 10^8)*(7.04 x 10^-3)

= 20.06 x 10^5 m

= 2006 km

genius_generous answered 3 months ago

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