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An unstable particle is at rest and suddenly decays into two fragments. No external forces act...

An unstable particle is at rest and suddenly decays into two fragments. No external forces act on the particle or its fragments. One of the fragments has a speed of 0.76c and a mass of 6.68×10?27kg, while the other has a mass of 1.67×10?27kg.

What is the speed of the less massive fragment?

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Answer #1

The momentum of lighter particle in rest frame of reference

p1 = m1v1 / sqrt(1 - v1^2 / c^2)

The momentum of heavier particle in rest frame of reference

p2 = m2v2 / sqrt(1 - v2^2 / c^2)

p1 = p2

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

v1^2 / (1 - v1^2 / c^2) = (m2/m1)^2 x v2^2 / (1 - v2^2 / c^2)

v1^2 / (1 - v1^2 / c^2) = (6.68 x 10^-27 / 1.67 x 10^-27)^2

v1^2 = 21.88*c^2(1 - v1^2/c^2)

v1^2 = 21.88*c^2 - 21.88*v1^2

22.88*v1^2 =  21.88*c^2

v1^2 = 21.88*c^2 / 22.88

v1 = 0.978*c

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