What is it about the density of a substance that makes it more resistant to allowing radioactivity to pass through it? Since most of the atom is empty space?

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No. The denser a material, the bigger its atoms, or more precisely the bigger the nuclei This is what is relevant to protect humans. I found a good explanation on this DOE site
Pat Rowe said:
Radioactive elements decay to other elements because their nuclei are not stable, and in the process give off particles or energy. Alpha particles are nuclei of helium atoms, and because they are relatively large, they do not easily go through light materials such as clothing or paper. They easily pick up electrons to become helium. Beta particles are electrons that come from the nucleus (this is a little complicated, since you probably know that only protons and neutrons should be in the nucleus--if you think of a neutron as a proton plus and electron, then the electron comes from there). Beta particles penetrate light materials, but not too far into denser materials like water. Gamma rays are a real problem, however. They are high-frequency electromagnetic radiation, pure energy which can penetrate most materials, including human bodies. Molecules and cells struck by gamma rays are damaged. Dense materials, such as lead shielding, stop gamma rays. People who are exposed to harmful radioactive materials may suffer radiation poisoning and death.
There are also good illustrations and explanations on http://www.awe.co.uk/main_site/scientific_and_technical/Factsheets/URR/ [Broken]

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yes

I realise dense materials stop or reduce radiation, I was just wondering why 70 grains of salt in the center of saint peters dome would stop much better than 1 grain of salt in the middle of saint peters dome. Atoms are seemingly considered mostly space. Is it a charge? It seems the chance of a particle hitting a nucleus instead of the rest of the atom woud be small. Thanks for your help.

It is very easy to protect oneself of alpha or beta rays. Only gamma rays are a problem. Gamma rays can only be stopped by the nucleus, the rest of the atom, i.e. the electrons, are unlikely to do anything. So you need to rely on the nucleus. The nuclei will have a more efficient stopping power if they are bigger. It is not due to the charge, because gamma rays, which are photons, do not carry charge (although the photons are the mediator of the EM interaction : photons won't be deviated by a charge. Photon cannot be deviated ot slowed down at all. They can only be absorbed.) I understand your idea : how on earth could this tiny nuclei have any effect at all ? It is so small !" This is true, if the nuclei would be even bigger, the absorption would be even greater. Indeed, gamma rays are very penetrating ! Way more than other form of radiations as said above.

The radiation yield $$y$$ remaining after a thickness $$t$$ is given by :
$$y(t)=y_0 e^{-t/t_0} \rightarrow_{t \rightarrow \infty}0$$
with $$t_0$$ a stopping length. There are so many nuclei in a thickness $$t_0$$ ! The photon will escape most of them, but eventually be more and more likely to meet one.

It is the contrary for neutron protection : in order to slow down the neutrons, you need a material that is able to absorb as much quantity of movement as possible, and this is more efficient with light nuclei. This is why we use water in nuclear plants to cool the neutrons down. However, neutron radiation is usually not a problem, the problem is more to create the neutrons. We also use carbon in order to absorb the neutrons.