Ill give you a slightly long answer. I am going to assume that when you say nuclear atoms, you mean radioactive material that can be used in a nuclear power plant.

First you should know that radioactivity is all around you and occurs naturally and is called background radiation. It makes up ~80% of the radiation you will probably see in your life. Bananas and table salt substitute are all slightly radioactive for instance. Just not enough to make a power plant work. I am not entirely sure, but I believe when they are mining Uranium for instance they do not even need to wear much protective gear. After they have purified it into rods and make it ready for a nuclear power plant, then they have to be more careful.

Each nuclear power plant produces about a soda can in size of high level radioactive waste to provide one person electrical usage for 70 years. This high level radioactive material is contained in thick, welded shut, steel barrel contains at various sites that are constantly being checked for leaks. My understanding is that they fill the container with gases which further protect anyone walking around outside. Typically these barrels are further placed in thick concrete rooms to provide further radiation protection. The main problem with nuclear power plant waste is that you have to store that soda can for thousand and thousands of years.

They currently want to place all of this high level radioactive material in a mountain in Nevada. Almost everyone likes this idea (including me), except for those who actually live in Nevada. Well, we will have to wait and see what happens.

Nuclear power plants also produce low-level radioactive waste, that takes up around a 1000 times as much volume. This is stuff like water, air filters, pipes, and mops that can trap some radioactive material. This material is almost always just buried 20 feet under the ground and allowed to decay until it is no longer radioactive.

I hope this answers you question.