If ever a headline deserved to be changed from the original statement on HN, it's this one. Not only is it linkbait, it's also a lie.
Even the footnote introduced by the publisher admits the headline is, at best, misleading. Sure, it's true, in a trivial sense, that nuclear waste when stored in a manner that effectively shields it from emitting radiation into the surrounding environment emits less radiation into the surrounding environment than a relatively benign substance emitted indiscriminately into the surrounding environment. If the article were trying to claim that coal dust in itself was particularly harmful that might still be an interesting comparison. But as it is, for those of us that know that properly-functioning nuclear plants don't pump nuclear waste into the surrounding atmosphere but do create storage hazards, it's about as insulting to the intelligence as a headline claiming that shandy[1] is more likely to cause alcohol poisoning than absinthe[2]
I think the level of density/concentration is an issue hardly ever discussed. But at the end of the day concentration is the only thing that counts. If you can successfully lower the radioactive concentration below the natural radiation, things are actually pretty safe. If you store nuclear waste in a salt deposit, usually a lot of ground water gets into the deposit. (Asse II is an extreme case) It gets contaminated and the question is: is the water much more radioactive than the water elsewhere? If not, it is actually relatively safe to live in proximity and do farming. According to this article it might be even safer than doing farming near a coal plant.
Actually another thing hardly ever discussed outside of Physics courses is the difference between solid radioactive objects and radioactive gas. The latter is actually a much more dangerous than the former. Not only because solid objects are easier to handle. The lungs are much more sensitive to radioactivity. Moreover gas particles can land on food, thus also getting directly into the body. Once "harmless" radioactive particles are inside the body, they radiate from within...
In Southern Germany there are areas with a lot of mountains. There people often have the radioactive gas Radon in problematic concentrations in the cellars. It is emitted by stones and when breathed cancerous and one of the top reasons for lung cancer. (Besides smoking)
Radon is a serious issue everywhere, not just Germany, and not just near mountains. Testing and mitigating radon in homes is one of the easiest and least expensive ways to reduce cancer risks.
The EPA has a good guide on radon and homes [1]. Even if you do not have a radon detector, it's very inexpensive to get periodic tests done (you can do them at home with a test kit). IIRC they are around $15-20 retail, although some fire departments or cities may provide them for free.
The only way to be sure your home does not have a radon issue is to test it yourself.
When I last looked at it, and this was long ago, '80s I think, radon appeared to only be a serious danger to smokers; the original studies were of uranium miners, who of course smoked a lot back then.
Which, given that "X and smoking is very bad" is true for a host of things, suggests to me the focus on radon might be misplaced.
As for your general starting point, I sure wish more would use the toxicologist's maxim "The dose makes the poison" vs. the clearly bogus linear no-threshold model: https://en.wikipedia.org/wiki/Linear_no-threshold_model
Heck, even the banana equivalent dose (https://en.wikipedia.org/wiki/Banana_equivalent_dose) would be more fruitful, you might say ^_^. Most of that is from potassium-40 in it, and Edward Teller had a favorite statistic based on sleeping with two other people based on the dosage you'd get from that isotope in them.
And that also addresses to an extent your inhalation/injection concern. We live in a sea of radioactivity, from isotopes inside us to cosmic rays which also flip DRAM bits. Anyone petrified of radioactive threats should never be told about the consequences of normal altitude commercial jet flying, unless they're planning on making a career of it.
And if something only cause lung cancer is smokers, then it really sounds like they didn't control for smoking in the radon studies--which I believe is exactly what happened.
Yes, in practice (ignoring disasters), coal plants release more radioactivity into the environment than nuclear plants. But that doesn't change the fact that the original title of the article, and the article itself, are phrased in a wildly misleading way. It suggests that the coal ash is more radioactive than the actual nuclear waste itself, and that's totally not true.
It's abusing the English language with misleading hysteria of how "more radioactive" term is defined.
On net volume of radioactive material released on a yearly basis: coal wins, by far. But it's diffused over a much larger area, and not as large of an immediate threat.
On potential for concentrated localized release: nuclear wins.
I've worked in this industry for a consulting shop in the US. There's a world of difference between diffused emissions that never reach significant levels and concentrations of radioactive material that have to potential to cause grave regional problems (Fukushima).
This title is better but still makes the error of assuming the linked story relates to nuclear waste. It doesn't, but instead compares the environmental radioactivity surrounding both types of power plants.
Even the footnote introduced by the publisher admits the headline is, at best, misleading. Sure, it's true, in a trivial sense, that nuclear waste when stored in a manner that effectively shields it from emitting radiation into the surrounding environment emits less radiation into the surrounding environment than a relatively benign substance emitted indiscriminately into the surrounding environment. If the article were trying to claim that coal dust in itself was particularly harmful that might still be an interesting comparison. But as it is, for those of us that know that properly-functioning nuclear plants don't pump nuclear waste into the surrounding atmosphere but do create storage hazards, it's about as insulting to the intelligence as a headline claiming that shandy[1] is more likely to cause alcohol poisoning than absinthe[2]
[1]ingested [2]not ingested.