An unstable particle with a mass equal to 3.34 x10 -27 kg is initially at rest.

Question

An unstable particle with a mass equal to 3.34 x10-27 kg is initially at rest. The particle decays intotwo fragments that fly off with velocities of 0.987c and -0.865c, respectively.
Find the masses of the fragments. (Hint: Conserve bothmass-energy and momentum.)
m0.987c = kg m-0.865c = kg An unstable particle with a mass equal to 3.34 x10-27 kg is initially at rest. The particle decays intotwo fragments that fly off with velocities of 0.987c and -0.865c, respectively.
Find the masses of the fragments. (Hint: Conserve bothmass-energy and momentum.)
m0.987c = kg m-0.865c = kg

Explanation / Answer

Conservation of linear momentum : m1*v1/(1-(v1/c)^2) = m2*v2/(1-(v2/c)^2) (1) => m2/(1-(v2/c)^2) = m1/(1-(v1/c)^2) *v1/v2 Conservation of mass-energy Mo.c^2 = m1/(1-(v1/c)^2) * c^2 + m2/(1-(v2/c)^2) *c^2= m1.c^2/(1-(v1/c)^2) *(1 + v1/v2) => m1 = Mo*(1-(v1/c)^2) /(1 + v1/v2) = 2.5x10^-28 kg (1)=> m2 = 9 x10^-28 kg

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