# Element Separation

If nature is not creating ores by chemical separation over megayears, it is costly to do so technologically. Some chatter about using particle beams and electromagnetic separation - how much does this cost?

Separating 0.72% of U235 from 99.28% U238 at Oak Ridge in 1944 and 1945 was incredibly expensive per kilogram of product - indeed, the calutrons were mostly used to separate gas-diffusion-enriched material. But let's be generous and assume that the entire 1000 kilograms of U235 produced started with 140,000 kilograms of mixed metal.

Uranium metal weighs 238 grams per mole, so a kilogram of uranium is 2.53e24 atoms. The atoms must be singly ionized into an electric current; the electric charge is 1.6021e-19 coulombs, so a 1 kilogram stream of uranium is 405,000 colombs. 140,000 kilograms is 57 billion gigacolombs.

A calutron accelerated the ions to 30 keV - so the total energy to separate 1000 kilograms of U235 was 3e4 V times 5.7e10 C or 1.7e15 Joules; 1.7e12 joules per kilogram of product, or about half a million kilowatt hours of electricity, about 500 GW-hr for the whole process. Oak Ridge separation operations had a 270 MW power plant, so the separation required 1750 hours of power using the numbers above - the figure was actually closer to 10,000 hours, because of inefficiencies and downtime. Oak Ridge cost eight billion 2014 dollars, adjusted for inflation, so a kilogram cost $8M 2014 dollars.

Gaseous diffusion is a much more cost-effective way to produce U235, laser resonance separation is better, and integral fast reactor breeder technology is even better, since it uses the U238 and burns up the long-lived actinides.

Electromagnetic separation is a laboratory measurement process - not an industrial one. It makes no sense for removing ppm elements from ore bodies - we have chemistry (and sometimes electrochemistry) for that.