Buoyant force is proportional to the mass of the fluid displaced minus the mass of the volume doing the displacing. Thus the best choices of lifting gas are nothing(vacuum), hydrogen, and then helium in that order. The first is not yet technologically feasible as the reinforcement needed to stop the balloon from imploding cancels out any weight savings, the second is rarely used due to its flammability, leaving only helium and occasionally hot air as the most commonly used lifting gases. However a thought occurred to me recently, wouldn't helium-3 be a better lifting gas than normal (almost entirely He-4) helium?
A gas's density is proportional to the mass per particle composing it. Helium-4 has 4 atomic masses per atom while helium-3 has 3, meaning it should have 75% the density. This still isn't as good as hydrogen (2 atomic masses per molecule of H2, composed of two atoms of protium massing about 1 Da each) but it would be a about halfway between hydrogen and normal helium and better than pure deuterium and about as good as hydrogen deuteride or a 50/50 mix of H2 and D2. It would be extremely expensive since helium-3 makes up only 2 ppm of normal helium, meaning that you would probably have to synthesize it through D-D fusion or decaying tritium or harvest it from the Moon or from one of the gas giants but ignoring economic limitations it seems to be superior to normal helium. Is there anything wrong with this chain of reasoning?
