That I know but an element that is comprised of atoms with God knows how many protons, neutrons, and electrons cannot exist for longer than a few trillionths of a second. It would be extremely unstable and radioactive. So how does it reach singularity if due to its short lifespan releases all its energy
Gravity is the cause of, and solution to, all of life's problems

The cause of instability in heavy nuclei is due to the fact that an extra neutron doesn't contribute that much more to the stability of the nucleus.
Imagine you're stacking boxes. You start with a single box. Naturally, that's as stable as stable can be. You add another box on top, slightly off centre - it's slightly unstable, but still pretty good. You add a third box, so you have a sort of inverted triangle of three stacked boxes, and voilà, your three boxes are more stable than the two. Keep doing this: each new box goes on the left and works its way right, then going up a level.
This is kinda what happens with nuclei. Each new box offsets the whole structure's stability somewhat, and when you get to high levels of boxes, a single box can destabilise it by quite a lot - unless it is itself acting as a counterweight and making the whole thing tentatively stable.
So, that's what happens normally, that's why excessively heavy nuclei spit out excess nucleons left right and centre. In reality, nucleons stick together because of the residual strong nuclear force (i.e., the force holding a proton's quarks together also causes quarks from different nucleons to pull together - hence why nucleons stay together).
So, usually, extra nucleons are repelled by various forces, and attracted by the residual strong nuclear force. Excess nucleons just aren't held on tightly enough, so get spit out, taking some nucleons with them - i.e., spontaneous alpha decay - or even splitting the nucleus in two - i.e., nuclear fission.
But what if there was a force much much greater than the residual strong force to hold them together? In the case of a black hole, gravity overcomes
any internal or external force that might try to push them apart. Two protons, despite being repelled by their similar charges, are forced into a fatal hug by gravity.
Can you calculate the atoms of such an element?
Do some number crunching for us

puhleeeezzzzzz
I don't know which element you mean

:o
Or how large would an atom have to be for the radius of the nucleus to equal its Schwarzschild radius? Would the size of the protons and neutrons be compressed by their gravity too?
Well, the Shwarzschild radius is proportional to the mass of the object, and atoms are so very light that their radius is so very small that you'd probably never squeeze a single atom into a black hole - according to some theories in quantum mechanics, there is a fundamental graininess to the universe, the plank scale, beyond which you can't get any smaller. It may just be that atoms are simply too light to become black holes.