What determines the size of an atom?

Why don’t atoms collapse due to the the attractive force between protons and electrons? What determines their size and stability? In this video, we explore the fundamental principles of quantum mechanics that explain these phenomena. In the first part of the video, we take a heuristic approach using Heisenberg’s uncertainty principle to understand why atoms are stable and estimate the size of the hydrogen atom. In the second part, we use the ground-state wave function of the Hydrogen atom to derive the radial probability density and calculate the most probable radial distance. We then show that the expected value of radial separation is larger than the most probable value. Finally, we calculate the expectation value of the ground state energy. References: Introduction to Quantum Mechanics - A.C. Phillips An Introduction to Quantum Physics - D. Griffiths The Feynman Lectures - Volume 1 - Feynman, Leighton, Sands The uncertainties in radial position and radial momentum of an electron in the non-relativistic hydrogen-like atom - Cheng-Deng Kuo An Introduction to Quantum Theory - Jeff Greensite Of Atoms, Mountains, and Stars: A Study in Qualitative Physics - Victor Weisskopf The hydrogen atom in the momentum representation; a critique of the variables comprising the momentum representation - Lombardi and Ogilvie You can help support this channel via the Physics Explained Patreon account: https://www.patreon.com/physicsexplained You can follow me on instagram: https://www.instagram.com/physics_explained_ig You can follow me on Twitter: https://twitter.com/PhysicsExplain1