Many rockets use hydrogen- and oxygen-based propellants as fuel.
Why are hydrogen-fluorine fuels not used? It has a specific impulse of 390 seconds, higher than hydrogen-oxygen combustion (360 seconds).
LF2/LH2, or liquid difluoride liquid dihydrogen bipropellant (binary cryogenic fuel) has a specific impulse of 410 seconds (by weight) at sea level, which is more than e.g. LOX/LH2 (liquid oxygen liquid dihydrogen) with average specific impulse by weight of 391 seconds, also at sea level. As the oxidizer is in both cases on board and one of the binary cryogenic propellants, the difference in specific impulse (19 seconds) would remain the same in vacuum, too. I'm not sure where you got your numbers from, though.
So this seems pretty straightforward, LF2/LH2 has a roughly 4 to 5% greater specific impulse per weight. But, as mentioned by many in this thread before me, there's a lot more to liquid difluoride (LF2) than meets the eye with a presentation of a few simple statistics on its performance as a rocket propellant. Mainly, it's toxic, a strong irritant and, as the strongest oxidizer (i.e. the most electronegative element) we know of, will react with anything that's ready to lend it a spare electron. That's not good, because it makes it - in practical terms - too reactive:
Reactions with elemental fluorine are often sudden or explosive. Many substances that are generally regarded as unreactive—such as powdered steel, glass fragments, and asbestos fibers—are readily consumed by cold fluorine gas. Wood and even water burn with flames when subjected to a jet of fluorine, without the need for a spark.
Excerpt source: Wikipedia on Fluorine
Needless to say, this makes it extremely difficult and rather costly to produce (NASA was paying \$ 6.00 per kg, compared to LOX that cost \$ 0.04 per kg in 1959), store, and use as a propellant component of any system, rockets being no exception. Combining it with liquid hydrogen in lower atmosphere also brings oxygen and water vapor to the equation, producing hydrofluoric acid. While it's a weak acid, it's not really a desirable byproduct of reaction of fluoride and hydrogen, while reaction of LOX with LH2 produces H2O (water).
So, in short, LOX/LH2 is a lot cheaper, much safer, many times over easier to design (engines, storage tanks, e.t.c.) for, and because of all of these trades a preferred oxidiser for large space launchers. It does have a few drawbacks, but ones we've learned to design around, and has been used in many launches, with no need to evacuate a large radius around a launch site prior and during actually using LF2, of fear environmental catastrophe. Sacrificing 4-5% of performance is well worth lowering these risks, no question about it.
Edit to add: But, it should be mentioned, 4-5% is a theoretical best case difference between LF2/LH2 and LOX/LH2 specific impulse, and this difference would lower quite substantially, possibly even reverse in favor of LOX/LH2, when we account for design constraints and the added weight to stages and their engines when using LF2/LH2 instead. This is a bit argumentative, but should also be considered when interpreting theoretical best case data.
In addition to all the issues raised by TidalWave, you also need to consider the exhaust products.
The space shuttle main tank carried about 730 tons of hydrogen and oxygen. Burning that produces about 730 tons of water, the happy chemical we all love. Burning about 730 tons of hydrogen and fluorine produces about 730 tons of very hot hydrogen fluoride, which is highly toxic and extremely corrosive. It attacks glass, metals and pretty much everything else, most likely including rocket nozzles and launch pads. It causes horrific burns to human flesh. You do not want this.
Fluorine is very toxic and tends to oxidize more than just the fuel.
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