If one large particle splits into two

[kimsworld]

If one large particle splits into two is that inelastic or elastic in terms of momentum?

 

[HallsofIvy]

I don't know what you mean by "inelastic or elastic in terms of momentum". A collision (and we can think of this as the two parts of the particle as two objects colliding) is "elastic" or "inelastic" if the energy is conserved or not conserved.

 

[Matterwave]

Both elastic and inelastic processes conserve momentum. Momentum is always conserved. Whether a collision is elastic or inelastic depends on conservation of kinetic energy. If kinetic energy is conserved, then the collision is elastic.

In the case of a decay, there's no collision, so the term elastic versus inelastic is a ill-defined. But the kinetic energy of the particle in its rest frame will go from 0 to some non-zero value for the decay particles.