One of the many fundamental particles in nature is the muon ? . This particle ac

Question

One of the many fundamental particles in nature is the muon ?. This particle acts very much like a "heavy electron." It has a mass of 106MeV/c2, compared to the electron's mass of just 0.511MeV/c2. (We are using E=mc2 to obtain the mass in units of energy and the speed of light c).

Unlike the electron, though, the muon has a finite lifetime, after which it decays into an electron and two very light particles called neutrinos (?). We'll ignore the neutrinos throughout this problem.

If the muon is at rest, the characteristic time that it takes it to decay is about 2.2?s(??=2.2

Explanation / Answer

(a)

??   =   2.2*10^-6 s

velocity    v    = 0.7 * c    ==>   v /c =   0.7

according to relativity

time deliation

??'     =   ?? / sqrt ( 1 - (v/c)2)       =   3.081*10-6 s

(b) if velocity of moun   v = 0.999 * c ==> v/ c =   0.999

??'     =   ?? / sqrt ( 1 - (v/c)2)       =   49.20*10-6 s

-----------------------------------

(c)

If there were no time delaiation effect

life time of the moun =   2.2*10^-6 s

velocity of the moun v   =   0.999943*c =   0.999943*3*10^8 m/s  

= 2.999829*10^8 m/s

distance travelled by the moun

d?   =   velocity * time =    2.999829*10^8 m/s )( 2.2*10^-6 s )

= 6.5996238*10^2 m

------------------------------------

(d) According to time delation

v = 0.999943*c    ==> v / c =   0.999943

??'     =   ?? / sqrt ( 1 - (v/c)2)     = 206. 05*10^-6 s

d?   =   velocity * time =  (  2.999829*10^8 m/s )( 206.05*10^-6 s )

= 618.11476545*10^2 m

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