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The answer to this depends on the radioactivity and the wall.

Alpha particles are usually stopped by just about anything. A piece of paper will usually do. But as they get faster, they need more to stop them.

Beta radiation penetrates deeper. They are somewhat problematical, because the damage they do seems to happen mostly when they are at lower energies, transitioning to become ordinary electrons. They are stopped by a few millimeters of aluminum. Wood and plastic will also do.

Gamma rays and X-rays are best stopped by lead. Actually depleted uranium is better at stopping gamma rays, but it is not available. Several centimeters might be required.

Neutrons are not easily stopped by either light or heavy metals. What you want here is water. Since concrete is made with water in it, a couple feet of concrete is usually sufficient.

Of course, since radioactivity is everywhere, it really cannot be kept out. Carbon-14 is a common isotope, and is widely known from reports of carbon-14 tests. But there are radioactive isotopes of every element, and most elements in nature have such isotopes in nature. So the radioactivity will be there, but just in small amounts.

If the wall is made of such a material as granite, it produces its own radioactivity.

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