Question

A subatomic particle X spontaneously decays into two particles, A and B, each of rest energy 1.40 × 10² MeV. The particles fly off in opposite directions, each with speed 0.827c relative to an inertial reference frame S.

Use energy conservation to determine the rest energy of particle X.

thank you for your help

Answer 1

However, connection of the total or relativistic energy (Er) with the rest or invariant mass (m0) requires consideration of the system total momentum, in systems and reference frames where momentum has a non-zero value. The formula then required to connect the different kinds of mass and energy, is the extended version of Einstein's equation, called the relativistic energy–momentum relationship:

(E_r)^2 - |P|^2 c^2 = m_0^2 c^4

(E_r)^2 - (pc)^2 = (m_0 c^2)^2

or

E_r = sqrt{ (m_0 c^2)^2 + (pc)^2 }
total relativistic energy=140+140=280Mev
p=m_0c for the second mass also
E_r=?(pc)^2+(pc)^2

E_r=?2(pc)^2

p=sqrt[(E_r)^2/2*c^2]

    =E_r/c?2

    =206MeV/c