Uranium is not common. For coal to just, by chance, contain enough uranium to run a nuclear reactor is just not consistent with the logic that mining + refining uranium is hard.

It's worth recalling that a coal plant burns 1.1 pounds of coal per kilowatt hour. Considering that a nuclear plant may produce 5 tera watt hours per year this translates to 2.5 million tons of coal burned per year for equivalent coal generation capacity.

Uranium rich coals with concentrations above 200 mg/KG are used in resource extraction around the world. Our hypothetical plant burning this coal would release the equivalent of 500 tons of uranium. In practice it's estimated that Chinese coal plants emit 62 tons of uranium into the atmosphere per year, however this estimate critically depends on the quantity of uranium in the coal - one plant in china was estimated to emit 3 tons of uranium into the atmosphere.

https://www.mdpi.com/2075-163X/7/12/239/htm

Note that 3 tons out of 2.5 million is not concentrated enough to run a nuclear power plant - but is producing greater emissions than our plant.

> the core claim is that coal ash contains more uranium and other radioactive metals

No, the core claim is that coal ash contains more radioactivity. That is, there are more nuclear disintegration events per second per kg of mass in coal ash than in spent reactor fuel. And it is wrong by many orders of magnitude. The thorium and natural uranium in coal ash have fairly low levels of radioactivity, nothing like the levels of spent fuel rods.

Simple numeracy will tell you it is fact. But in case that's not accessible, ask yourself: what is a person's radiation exposure by standing upon a coal ash mound 1 year after it is deposited?

Now ask yourself: what is a person's radiation exposure if they were able to stand next to a spent nuclear fuel assembly 1 year after it is removed from the reactor?

You could literally live on top of a coal ash heap and never suffer any radiation consequences. You would have suffered a fatal does from the spent reactor fuel in about a minute.

I'll leave the citations to you, since most of the published works assume basic knowledge of how radioactivity works and I'm not certain are appropriate to your question. If you want to know about spent fuel, the Swedish report [1] is fairly good for lay persons. I'm not going to dig out any studies on ash ponds, but I'm sure there are some.

[1] https://www.osti.gov/etdeweb/servlets/purl/587853

As it happens, my degree is in physics. the majority of high radioactivity elements that you are describing decay within 5 years the remaining waste that sticks around for 30k+ years isn't nearly as radioactive. The rods burning off hot radioactive material are not intended to leave the plant and hence I didn't call them out in the waste products.

When it comes to low concentrations of radioactive heavy metals like those in spent fuel rods after 5 years the bigger danger tends to be heavy metal poisoning where they are dramatically more toxic than lead.

Look on page 22 of the cited doc. At 50 years, the dose rate is still 20,000 mSv/hour/tonne. Compare that to fly ash for us, please.

I have written about this a couple of times:

https://news.ycombinator.com/item?id=26216669

https://news.ycombinator.com/item?id=14466887

The Scientific American article cites actual published research but distorts it in the retelling.