Why can't alpha particles penetrate deeply into solids? alpha particles have low mass. alpha particles have high mass. alpha particles have low velocity. alpha particles have high velocity.

Alpha particles have both high mass and low velocity, but it would be the former that determines why they can't penetrate. An alpha particle is made of two protons and two neutrons, which is quite a large mass for a particle. This large mass keeps it from penetrating too deeply into anything, since it will essentially "get stuck" when it comes too near to another atom.
So the answer, I believe, is B. Alpha particles have high mass.