Let us think of a single electron floating in space. How do we even measure its kinetic and potential energy? Start by imagining a single proton, far away. Together, they can unite and form a hydrogen atom. As we measure their progress towards each other, in terms of energy, we will see in many ways what we see in classical physics
The electron, approaching the proton, will have kinetic energy and potential energy. When it is far away, it will have a relatively huge amount of potential energy, the same way objects raised high above the ground have huge amounts of potential energy. As it moves towards the proton, it loses some of that potential energy. Some of it is radiated away, as electromagnetic energy. Some of it is converted to kinetic energy. Kinetic energy keeps an electron hopping, and keeps it from staying in a nucleus and combining with a proton.
Here's where the deck is slightly stacked in favor of electrons not combining with protons. The kinetic energy, if the electron is in the nucleus, is infinity. The potential energy, if the electron is in the nucleus, is negative infinity. But if you want to figure out the kinetic energy at any point, it's twice the decline in potential energy. In other words, the kinetic energy has more heft, and the electron stays out of the nucleus. The final distance of the electron from the nucleus that represents the balance of those two energies and their two-to-one proportion.