Question

a. The Tau Lepton has a proper lifetime of 0.3 picoseconds. What speed must tau particles have in order to travel an average distance of 1 mm.

b. Repeat this calculation with a distance of 10⁷m.

Answer 1

(a)

We know that,

t = to / sqrt (1 - v² / c²)

Speed of tau particles,

v = x / t

v = x / [to / sqrt (1 - v² / c²)]

= (x / to) * sqrt (1 - v² / c²)

= (10^-3 / 0.3*10^-12) sqrt (1 - v² / (3*10⁸)²)

v = 2.99*10⁸ m/s

(b)

x = 10⁷ m

v = x / [to / sqrt (1 - v² / c²)]

= (x / to) * sqrt (1 - v² / c²)

= (10⁷ / 0.3*10^-12) sqrt (1 - v² / (3*10⁸)²)

v = 2.99*10¹⁸ m/s