A particle with rest energy 9000 GeV decays at rest into two

A particle with rest energy 9.000 GeV decays at rest into two daughter particles, one with rest energy 6.860 GeV and the other with rest energy 280.000 MeV.

(a) What is the mass of the parent particle? in kg

(b) How much energy is released in the decay? in Mev

(c) What is the momentum of the lighter daughter particle? in MeV/c

(d) What is the energy of the lighter daughter particle? in MeV

Solution

a) m*c² =9*10⁹*1.6*10^-19

m=9*10⁹*1.6*10^-19 / (3*10⁸)² =1.6*10^-26kg

b) energy released =9-6.86-0.28= 1.86GeV =1860MeV

c) mass of lighter particle = 280*10⁶ *1.6*10^-19/ (3*10⁸)² = 4.98*10^-28kg

from momentum energy relation

p² / (2m) = energy =280*10⁶

p² =280*10⁶ *2*4.98*10^-28 = 2.78*10^-19

momentum = 5.28*10^-9 *3*10⁸= 1.584MeV/C

d)energy of lighter daughter particle=280MeV