Technically, it should be possible to filter out uranium. Thorium, too. Both are heavy enough, it should be possible to centrifuge them out of just about any mixture, unless the compounds they're in are too tightly bound with lighter molecules by intermolecular forces. Even then, I would expect them to find their way "down", even if they had to drag some of the nonradioactive portion with them.
The amount of energy you get out of the coal or the uranium is a function of not only the amount of energy in each, but their relative quantity, as well. If there's not enough uranium present to extract a significant portion, I'd have to wonder if there's really enough to put out as much energy as the coal's total output.
Taking it a little further, if there isn't enough to extract, is there really enough to pose a significant health risk? We're exposed to a certain amount of background radiation on a daily basis already. How much more does the uranium in coal add to this? Again, I'm tempted to doubt it's significant, if there's not enough to be extracted.
So, do we have reliable numbers on this?
The following two articles cite "a 1978 paper for Science, J. P. McBride at Oak Ridge National Laboratory (ORNL)"
http://www.ornl.gov/info/ornlreview/rev26-34/text/colmain.ht...
http://www.scientificamerican.com/article.cfm?id=coal-ash-is...
and Wikipedia says, during normal operation the effective radiation dose from a coal plant is 100 times that of a nuclear power plant, http://en.wikipedia.org/wiki/Fossil_fuel_power_station#Radio...
You could've worked in something about potassium content of bananas while you were at it.
NB., a fun experiment: explain a smoker that the cigarette contains proverbial half of the Mendeleyev table.
In any case, the theoretical content of fissible elements in coal may be significant, but it doesn't seem to be economical to extract it at this point. We have heaps of uranium ore, and nuclear fusion seems to be around the corner.
Less snarkily, is there actually good reason to believe that we're any closer to usable fusion?
Several governments bet big (well, perhaps medium) money on race to the Moon, to extract helium-3 [3] from water ice in there. A key component to commercial nuclear fusion -- and with only small-time other uses in medicine and stuff.
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Hence, the biggest non point I've ever seen in my life. Unless coal is actually radioactive to a noteworthy significantly-more-than-a-banana extent, which I probably would have heard of by now (not that I haven't been wrong before).
Here is an example of someone else making the same point:
http://www.ornl.gov/info/ornlreview/rev26-34/text/colmain.ht...
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[1] http://www.totallywicked-eliquid.com/products/electronic-cig...
Your body has trace amounts of uranium as well. What's everyone so worried about?! Obviously the substance is perfectly safe.
And no, that's not a joke; it's a convenient measure of low radiation levels. Bananas are more naturally radioactive due to high potassium contents.