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How does the uncertainty principle help explain the size of an atom?

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Bohr model diagram of a hydrogen atom showing a green nucleus labeled H, a single electron orbit, and text with atomic mass 1.008 and electron configuration 1. — atom The Bohr model describes the structure of atoms, in this case hydrogen.

The Heisenberg uncertainty principle is fundamental to understanding the size of an atom. It states that there is a limit to the precision with which a particle's position and momentum can be simultaneously known; the product of these uncertainties is proportional to Planck’s constant.12

If an electron were confined to a space smaller than the typical atomic scale (approximately $10^{- 10}$ meters), the uncertainty principle dictates that the uncertainty in its momentum—and consequently its velocity—would become extremely large. Specifically, forcing an electron into a smaller volume increases its kinetic energy significantly due to this required uncertainty in momentum.12

In an atom, the electron is bound by the electrostatic potential of the nucleus. The atom's size is essentially a balance: the electron is attracted to the nucleus, but the uncertainty principle prevents it from collapsing into a point, as doing so would require an impossibly high kinetic energy. Thus, the atom maintains a stable, finite size defined by the probability distribution of the electron, often visualized as a "cloud" or "fuzz ball" rather than a precise orbit.3124