Dependence of nuclear stability on mass number

[dt19]

we're doing some nuclear work at college at the mo, and i came across a few sources which stated that nuclei with an even mass number tend to be more stable than nuclei with an odd mass number. so far so good. when i looked up why this was, there was very little information on the internet but from what i could gather it is because neutrons tend to form pairs with other neutrons, and protons with protons, so the atom is more stable and thus requires a higher energy incident neutron to induce fission. (if any of this is wrong, please correct me!)
is it known why the nucleons tend to pair up? is it something to do with the strong nuclear force?

also, my physics teacher asked me this question (which he doesn't know the answer to) : when a neutron is absorbed by a U235 nucleus, U236 is formed. why does this nucleus immediately split, since as it has an even mass number and should therefore be more stable? I've come across a few mentions of the kinetic energy of the neutron being converted to internal energy of the nucleons, but i don't really understand.

help very much appreciated!

 

[Astronuc]

See this page on nuclear structure.

http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/shell.html

In general it is true that nuclide with even numbers are more stable, until one looks at the heavier actinides.

In the case of U236, formed when U-235 absorbs a neutron, the excited U-236 nucleus undergoes internal osciallations, and effectively two new and more stable nuclei form. That is why the energy release from fission is ~200 MeV. BTW, there is a change that U-236 will decay by gamma emission and not fission in approximately 18% of absorptions of thermal neutrons.

See also the page on binding energy
http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/nucbin.html#c2

and http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/fiscon.html#c1

http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/fisfrag.html