A particle known as a pion lives for a short time before breaking apart into oth

Question

A particle known as a pion lives for a short time before breaking apart into other particles. Suppose a pion is moving at a speed of 0.990c, and an observer who is stationary in a laboratory measures the pion's lifetime to be 3.2 x 10-8 s. (a) What is the lifetime according to a hypothetical person who is riding along with the pion? (b) According to this hypothetical person, how far does the laboratory move before the pion breaks apart?


At most, how many bright fringes can be formed on either side of the central bright fringe when light of wavelength 603 nm falls on a double slit whose slit separation is 4.17 x 10-6 m?

Explanation / Answer

the life time of the pion with respect to the labframe at rest
t = t' 1 -v2/c2

t' = 3.2 x 10^-8 s.
t = lab frame at rest.
v = 0.990c
c = velocity of light .

from the above realtion we can calcualte the time pertiod of the pion withrespect lab frame.

the distance ' d ' coverd by the pion moving with 0.987cvelocity and have a life period of tas calcuated above ,

d = v * t
v = 0.990c
t = t' 1-v2/c2)

t = 4.51 x 10^-9

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