Question

An unstable particle is at rest and suddenly breaks up into two fragments. No external forces act on the particle or its fragments. One of the fragments has a velocity of +0.772c and a mass of 2.81 × 10-27 kg, and the other has a mass of 4.32 × 10-27 kg. What is the velocity of the more massive fragment (as a multiple of c)?

Answer 1

Relativistic momentum is given by:

P = mv/sqrt (1 - v^2/c^2)

Since particle beaks from rest So it's total momentum will be zero, which means

P1 + P2 = 0

|P1| = |P2|

m1v1/sqrt (1 - v1^2/c^2) = m2v2/sqrt (1 - v2^2/c^2)

Using given values:

Suppose v2 = n*c

2.81*10^-27*0.772*c/sqrt (1 - 0.772^2) = 4.32*10^-27*n*c/sqrt (1 - n^2)

n/sqrt (1 - n^2) = (2.81*0.772/4.32)*1/sqrt (1 - 0.772^2) = 0.790

n^2 = 0.79^2*(1 - n^2)

n^2*(1 + 0.79^2) = 0.79^2

n = 0.79/sqrt (1 + 0.79^2)

n = 0.620

Speed of second particle = 0.620c