- #1

nonequilibrium

- 1,439

- 2

## Homework Statement

I must be overlooking something very simple:

"A particle of mass M decays from rest into two particles. One particle has mass m and the other particle is massless. The momentum of the massless particle is..."

## Homework Equations

energy² = mass² c^4 + p² c²

momentum is conserved

## The Attempt at a Solution

a quick drawing makes clear that [itex]\vec p_{m}[/itex] and [itex]\vec p_{\gamma}[/itex] (with gamma denoting the massless particle) are on the same line, and since the initial momentum was zero, we get [itex]\vec p_{m} = - \vec p_{\gamma}[/itex] and thus [itex]p_m^2 = p_\gamma^2[/itex].

Using conservation of energy we get [itex]M^2 c^4 = m^2 c^4 + p_m^2 c^2 + p_\gamma^2 c^2 = m^2 c^4 + 2 p^2 c^2[/itex] with p the sought for momentum.

*However,*the answer should be [itex]p = \frac{M^2 - m^2}{2M} c[/itex]