A beam of particles have a measured life time of 1.5 x 10-8 s when traveling 2.0 x 108 m/s. What would their lifetime be if they were at rest?
My Answer:
tm= tp/√(1-(v2/c2))
(1.5*10-8) = tp/√(1-((2*108)2/(3*108)2))
(1.5*10-8) = tp/√(1-((4*1016)/(9*1016))
(1.5*10-8) = tp/√(1-(4/9))
(1.5*10-8) = tp/√(5/9)
tp =(√(5)/3)(1.5*10-8)
tp =1.118033989*10-8
The lifetime of the particles if they were at rest would be 1.1*10-8s.
Is this correct? Thanks.
yes; good work!
tm= tp/√(1-(v2/c2))
(1.5*10-8) = tp/√(1-((2*108)2/(3*108)2))
(1.5*10-8) = tp/√(1-((4*1016)/(9*1016))
(1.5*10-8) = tp/√(1-(4/9))
(1.5*10-8) = tp/√(5/9)
tp =(√(5)/3)(1.5*10-8)
tp =1.118033989*10-8
on the 6th line, why does it become √(5)/3)? Is it not supposed to be √(5/9) from the line before?
yes this is right
in anwser to mike, they square rooted 3 but not 5
so it because (√(5)/3) = (√(5/9))
Your calculation is correct. The equation you used to calculate the lifetime of the particles at rest is
tm = tp/√(1-(v2/c2))
where
tm is the measured lifetime of the particles,
tp is the proper (rest) lifetime of the particles,
v is the velocity of the particles, and
c is the speed of light.
You correctly plugged in the values into the equation and obtained the result tp = 1.118033989*10^-8 s, which can be approximated as 1.1*10^-8 s.
Therefore, your answer is correct. The lifetime of the particles, if they were at rest, would be 1.1*10^-8 s.