Radioactive Rarity on Mars
There is some question about how rare radioactive elements are on Mars, and to what extent this will effect the usefulness of nuclear power on the planet. The most important radioactive elements are Uranium / Thorium / Potassium (U/Th/K).
Mars formed out of the same planetary nebula as Earth, so it should have broadly the same proportion of elements as Earth. Mars was closer to the 'ice line' so we would expect Mars to initially have a higher proportion of volatile elements (low melting point elements, water, and gases). (The ice line the point where ices are stable in space and do not evaporate from the sun's warming - currently the ice line in our solar system is 2/3 of the way thru the asteroid belt, moving outwards from the Sun.)
Mars has since lost many of these volatiles to space, due to its lower gravity, and because of solar wind sputtering. (See Atmospheric Loss for more details.) Therefore we would expect Mars to have similar amounts of radioactive elements as Earth.
Mars has had a long history of vulcanism and hydrology, both of which have helped to create ores on Earth. Thus on the surface, there is every reason to expect radioactive ores on Mars.
Note that on Earth thorium is about 3 times rarer than lead, and uranium 238 is about ten times rarer than lead. (U235 is ~1400 times rarer tho.) Even if these elements were twice as rare on Mars as on Earth, (which I think is unlikely as there is no reason that the such elements should be discriminated against during planetary formation), there would still be vast amounts of these metals on Mars.
However, two sets of data suggest that Mars has significantly lower amounts of U/Th/K than Earth. The first is the Shergottite meteorites (meteors of surface material of Mars which has been knocked off of Mars by asteroid impacts and have later fallen to Earth), and the Mars Odyssey orbiter which can detect the elemental composition in the top meter of Mars crust. Both of these have shown that Mars seems to have about 6 times less radioactives in the 'soil' than the Earth does.
Several studies have suggested that the Shergottite meteorites are not typical Martian rocks, but the Odyssey data is harder to explain. See...
- Analysis suggests that radioactive elements must be more common on Mars than shown in Martian meteorites (shergottite meteorites) which have fallen to Earth. 
- Evidence that the bulk of the Martian crust is richer in radioactive materials than the shergottite meteorites. 
- Yet another study saying that the shergottite meteorites are not representative of Mars. 
Mars has a smaller / less defined core
Earth has an iron core which is mostly iron, nickel and other siderophile (iron-loving) minerals and elements. In other words, the elements that dissolve easily in molten iron have been pulled out of the rocks in the crust and mantle and concentrated in the core of the Earth. These elements include: Mn, Co, Ni, Mo, Ru, Rh, Pd, W, Re, Os, Ir, Pt, and Au. These are the elements in the centre of the transition elements in the periodic table, and include the platinum group metals such as osmium, iridium, platinum, and gold. Cobalt, nickel, and tungsten (wolfram), are also valuable metals which are depleted on the Earth's crust for this reason.
Mars seems to have not developed a well defined iron core, but rather the core and the mantle are better mixed together. (The Martian core is larger than expected and less dense, so it is not 'pure' liquid iron, but has sulphur, oxygen and other elements mixed in with it.) This suggests that Martian mantle material would be richer in the iron-loving minerals, and therefore the lithophile (rock-loving) minerals would be proportionally rarer. Volcanic eruptions will bring mantle material to the surface. U/Th/K, are all rock-loving minerals so this might help to explain their relative rarity. In other words, gold, platinum, cobalt, nickel, and tungsten are likely to be slightly richer on Mars, and the radioactive elements are likely to be slightly rarer in the Martian crust.
Mars has less granite
Granite on Earth is generated with water rich rock (from subducting oceanic plates) and volcanic eruptions. Granite is common on Earth, and much rarer on Mars (tho some granite has been found). The U/Th/K ores are most common in granites, so this suggests that it would be harder to find rich radioactive ores on Mars than on Earth.
Basalt group minerals are common on Mars, but radioactive ores are not normally found in them. This suggests that Martian U/Th/K ores would be more geographically constrained.
Movement by water
Uranium oxide is easily dissolved in water, (vast amounts exist dissolved in Earth's oceans), and if Mars had geologic periods with a hydrological cycle, (likely), Uranium could be moved from upland areas to the northern ocean basin and be then buried. Thorium oxide is less easily dissolved, but if flowing water ran for a very long time, it also would be moved to the northern ocean basin. Potassium (K), is easily moved by water.
This suggests that much of the surface U/Th/K is buried in the northern hemisphere. However, deep ore bodies which were not subjected to flowing water, would still remain, and they would not be detected by Odyssey.
Impact Concentrated Ores On Mars
The Sudbury Nickel mine in Ontario Canada was created when a small asteroid hit the Earth. It (and local rocks) melted. The dense metals sank to the bottom of the melt and froze, producing rich metal ores. 
Since Mars is closer to the asteroid belt, this process could produce such hard rock ores more often than on Earth. (The Hellas Basin, in particular is likely to have rich ores deep underground.)
U/Th/K are silicon loving elements, and so are less likely to be concentrated by such processes, but any differentiated melting and solidifying of minerals can concentrate elements. In other words, such a process is not likely to make ore bodies of metallic uranium, but could concentrate the U/Th/K above the local average is some parts of the melt.
Would Lower Radioactives Cripple Martian Nuclear Power
Even if Mars (for some reason) had significantly less U/Th/K than the Earth, it would not preclude nuclear power on that planet.
- Early exploration bases and colonies could have the nuclear materials refined, enriched, and shipped to Mars. (Note that nuclear core before the control rods are removed to allow it to go critical, is not highly radioactive.) A one time shipment of a reactor would provide years or decades of reliable power for less mass than solar cells with a similar power output. See Cost of energy on Mars for more details. (If geothermal power sites are found, the cost might be close if you include the advantages of liquid water from geothermal.)
- If Fusion power is made to work, Mars has 5 times more deuterium than Earth, per water molecule. Thus this fusion fuel is cheaper on Mars than on Earth.
- Even looking only at fission reactors, one good ore body anywhere on the planet could provide fuel for hundreds or thousands of reactors.
- The cost of fission fuel is insignificant compared to the other costs of current nuclear power on Earth. Permitting, environmental reviews, public hearings, court challenges, building giant bespoke reactors, and the cost of capital dominate the cost of current nuclear power. (In Superfuel, Richard Martin points out that a nuclear power plant spends less on fuel than on plant security. They have no interest in finding CHEAPER fuel, the current fuel is trivially cheap compared to other expenses.) If those other elements were eliminated or reduced, then a ten fold increase in fuel costs would still result in nuclear power being cheaper on Mars than on Earth. . Note that natural uranium (U238) must be processed to increase the proportion of U235 and then formed into fuel rods (expensive). However reactors can be built which use metallic thorium (which has only one natural isotope), which makes Th fuel MUCH less expensive.
- Current nuclear power (light water pressurized reactors) were designed 70 years ago, and are WILDLY inefficient. (One example, they 'burn' only 0.5% of their fuel.) Far better, 4th generation reactors have been designed, and many are currently being tested. Presumably, Mars would not use 70 year old technology. (See LFTR for one such reactor. Note that some versions of LFTR could burn current nuclear wastes.)
- One kg of thorium has enough energy to power a town for a year. (See the books referred to below, and also...) If our Martian exploration colony had a LFTR shipped to it, 1 kg of cargo mass, would power the base for decades. It is entirely reasonable for even a fairly large Martian town to last for a long time with occasional shipments of a 1 to 5 kg of nuclear fuel from Earth every two years.
- If gold is more common in Mars' crust than Earth, (certainly possible), Mars could profitably trade gold for thorium (which is dirt cheap on Earth). Robert Zubrin pointed out in "The Case for Mars", that with _current_ space technology, we could export items as valuable as gold (or more so) between planets at a profit.
- Earth citizens might ship nuclear wastes to Mars to get rid of them. These can be used as fuel in several designs of 4th generation reactors since 99.5% of the fuel (U235) still remains 'un-burnt'.
- Thorium and uranium are always found with Rare Earth Element (REE) ores. If REE are mined on Mars for their magnetic and electronic industrial uses, enough U/Th would be produced to allow for nuclear power. (This would be for a well developed Martian economy, starting colonies would import REE from Earth, if needed.) This paper discusses a less expensive way to capture thorium from REE wastes.
Mining the dirt
Basically, tiny amounts of radioactive materials, can produce massive amounts of power. Four examples:
- In the thorium page, there is a long discussion of mining thorium ores, and burning them in a LFTR. The conclusion is that VERY poor ores could be burnt at a profit.
- Conway granite has 56 +/- 6 ppm thorium. New Hampshire is estimated to have 3,000,000 tonnes of this at shallow depth. Each 12 cubic meters of rock contains 1 kg of 'readily leachable' thorium worth ~$1.5M if efficiently burnt. See the thorium page for more details for that $1.5 M value.
- Even common granite (13 ppm) contains the potential nuclear energy equivalent to 50 times the rock's mass in coal.
- A cubic meter of ordinary Earth dirt contains enough thorium to provide the energy of 18 barrels of oil, so we could concentrate that thorium out of ordinary dirt and still make an energy profit. Note, that by using dirt, we don't have to spend the energy to crush the rock!
There is no incentive to use such poor quality 'fuel' when much better ores are widely available, but it is clear that even poor ores could be mined for an energy profit.
"Thorium: Energy Cheaper than Coal", By Robert Hargraves, ISBN: 9-781478-161295
"Superfuel", By Richard Martin, ISBN 978-0-230-11647-4. // This is a introductory book for the layman with nice history of molten salt reactors. The above reference is more scholarly.
"Molten Salt Reactors & Thorium Energy", Edited by Thomas J. Dolan, ISBN 978-0-08-101126-3 // Intended to be a review of all research projects working on molten salt Th reactors.
- ↑ https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1945-5100.2003.tb00017.x
- ↑ https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2005JE002645
- ↑ https://www.science.org/doi/abs/10.1126/science.1165871
- ↑ https://www.nature.com/articles/d41586-021-00696-7
- ↑ https://arstechnica.com/science/2015/07/curiosity-finds-continent-building-rocks-on-mars/
- ↑ https://www.sciencedirect.com/science/article/pii/S2666759221000792
- ↑ https://www.britannica.com/technology/nuclear-power/Economics
- ↑ https://en.wikipedia.org/wiki/Energy_density
- ↑ https://www.epa.gov/radiation/technologically-enhanced-naturally-occurring-radioactive-materials-tenorm
- ↑ https://www.youtube.com/watch?v=lxwF93wnRQo
- ↑ https://pubs.acs.org/doi/10.1021/jacs.8b07610
- ↑ https://www.epa.gov/radiation/tenorm-copper-mining-and-production-wastes
- ↑ https://aip.scitation.org/doi/pdf/10.1063/1.4972913
- ↑ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC221093/
- ↑ https://web.archive.org/web/20080811001036/http://www.energybulletin.net/node/13630
- ↑ https://energyfromthorium.com/cubic-meter/
- ↑ https://en.wikipedia.org/wiki/Occurrence_of_thorium#cite_note-27