Likely scenario if a nuclear missile is shot down by a missile defense system

Shooting down a nuclear missile with another missile cannot and will not result in a nuclear detonation.

The process required to cause a nuclear detonation are so exacting that the destruction of the missile would prevent those processes from happening as designed.

There are three possible scenarios here.

1. The warhead breaks up with the physics package remaining intact.

   In this case the core, the radioactive part that gets smashed together to create the chain reaction and nuclear detonation, remains intact and falls to earth. if it still remains intact on impact there is no radiation contamination. If it breaks apart on impact, there would be some radioactive contamination in the area immediately surrounding the impact point.

2. The physics packages breaks apart on destruction of the warhead.

   In this case the core is broken apart at altitude. Contamination would again be limited to the area immediately surrounding the impact points but there would be multiple impact points of the pieces of the core, covering a larger area.

3. The destruction triggers the high explosive shell of the nuclear device.

   In this case the High Explosives intended to trigger the nuclear detonate are exploded, But because of the destructive nature of the impact triggering the detonation rather than the perfectly timed detonation sequence… the implosion lens is not formed properly and the warhead just blows itself apart rather than creating a nuclear detonation. there may be some localized compression of parts of the core creating a criticality event, but not the supercritical state necessary for the nuclear explosion. The core would blow itself apart in a pre-detonation reaction. This would cause an increased radioactive contamination from the reaction process and would also be scattered over a much larger area because of the HE explosion. What you would get would in effect be a Conventional Dirty Bomb scattering radioactive material over a larger area.

   It would still be less that what would happen had the Nuke detonated as designed.