What are the chemical properties of uranium-233 that makes it a more efficient fuel than uranium 235? i'm trying to find what the best nuclear fuel would be. I've already tried finding this answer online but there's nothing that helps. i would like to find an answer please. btw, by efficient, i mean why can we extract more energy from it more easily than u-235
 A: It’s complicated question; the “best” nuclear fuel depends on lots of engineering details about the fuel cycle and the reactor design.
Uranium-235 occurs naturally, as a small fraction of uranium ores.  By contrast, U-233 has a “short” half-life of 160,000 years. All of the U-233 on Earth has been produced in reactors.  The process is neutron capture on thorium-232, followed by a cascade of two beta decays.
When discussing the likelihood of an interaction, physicists use the “cross section” associated with a process.  The cross-section works mathematically like an area.  A common unit for cross sections is $\rm 1\,barn = 10^{-28}\, m^2$. (Think, “how could those particles pass by without interacting? The cross section is as big as a barn!”) You can look up cross sections for various interactions.  For neutrons interacting with uranium, the cross-section for induced fission is about the same for -233 and -235 (530 b versus 580 b).  However, the probability of neutron capture to -234 or -236 is reduced in the lower-mass nucleus (45 b versus 99 b).  So in a given fuel assembly, you get more fissions per neutron from U-233 than an equivalent mass of U-235.  The Wikipedia article calls this the “capture-to-fission ratio.”
But if your scarce commodity is neutrons, you have the issue that U-233 doesn’t exist until you put neutrons on some thorium.
But, if you are concerned about the entire fuel cycle, you have the fact that thorium is more common than uranium in Earth’s crust (by a factor of four-ish), and that most uranium is the heavier, stabler U-238, whose fission cross-section is way down in the microbarns.  So while U-233 might be only a modest improvement over U-235 in an existing reactor, a process which generates U-233 can in principle transform material which isn’t nuclear fuel into material which is nuclear fuel.
A: One common measure of fuel "efficiency" is the ratio of neutrons produced by fission of the fuel to the number of neutrons absorbed by an atom of fuel.  This ratio is called "eta" ($\eta$) and is defined
$$ \eta = \frac{\nu \Sigma_f^{f}}{\Sigma_a^f}$$
The higher the value of $\eta$, the better. A more efficient fuel will create more neutrons per absorption. A plot of $\eta$ is shown below which shows the U233 is more efficient than U235 and Pu239 at most energies.  Pu239 is higher at high energies.
A 
Another advantage often cited for U233 is that it has a lower atomic number, therefore it takes more reactions to build up the higher actinides, like plutonium, neptunium, americium, etc.  This will reduce the radiotoxicity of the spent fuel.
However, as @rob mentioned, U233 does not occur in nature naturally.  The only way to create U233 is to breed it from thorium.  This is a lot more difficult than digging up uranium.
