Technology

That's for normal activity and it's totally irrelevant. So these are some stats about ionizing radiation dosages:

• Average from all sources for an average person for 1 year: 4mSv
• Additional if living within 50 miles of a nuclear reactor for 1 year: 0.09 µSv
• Additional of living within 50 miles of a coal plant for 1 year: 0.3 µSv
• Living within 30 km of Chernobyl before evacuation (10 days): 3-150 mSv
• Maximum allowed dose for radiation workers over 1 year: 50mSv
• 10 minutes next to the Chernobyl reactor after the meltdown: 50Sv
• fatal lifetime dosage beyond our ability to treat: ~8Sv

So, yes, nuclear power plants and storage pools are designed to shield radiation and thus during normal operation release an insignificant amount of radiation so much so that even coal burning releases a heck of a lot more.

But both of those are extremely insignificant if you consider that living near a coal plant will only give you a tiny fraction of additional exposure as the amount of radiation you receive normally from natural sources.

The problem is that with nuclear fission waste, a tiny leak can cause fatal amounts of exposure in a very short time. If a storage pool cracks after the 100 years or so they're designed to last, or if a flood happens and overflows a storage pool, or a tornado picks up that storage water, or any number of other catastrophic events happen within the 10,000-1,000,000 years before that waste is safe, depending on the type, the people living nearby will likely not survive very long and that area will be contaminated for many times longer than human life has existed.

Fukushima was a good example and had to rely on the vast Pacific ocean to disperse the radiation. Chernobyl will be unsafe for 10s of thousands of years even if the coffin is maintained for all that time.