Final answer:
Gamma rays have the greatest penetrating power into matter, while alpha particles have the least penetrating power. To protect against gamma rays, thick shielding made of dense materials like lead is required.
Step-by-step explanation:
Gamma rays would have the greatest penetrating power into matter. Gamma rays are a form of electromagnetic radiation that have no mass or charge, allowing them to pass through matter with tremendous penetration power. They require several inches of dense material, such as lead, to shield them.
To protect yourself against gamma rays, you would need to use thick shielding made of dense materials like lead or concrete. This can block the gamma rays and prevent them from penetrating your body.
For protection against alpha particles, which have the least penetrating power, a thick sheet of paper or layer of clothes would be sufficient. Beta particles, which have slightly more penetrating power than alpha particles, can be blocked by a thin sheet of aluminum.