Why do electrons not fall into the nucleus?

Summary

The picture of electrons "orbiting" the nucleus like planets around the sun remains an enduring one, not only in popular images of the atom but also in the minds of many of us who know better. The proposal, first made in 1913, that the centrifugal force of the revolving electron just exactly balances the attractive force of the nucleus (in analogy with the centrifugal force of the moon in its orbit exactly counteracting the pull of the Earth's gravity) is a nice picture, but is simply untenable. Figure \(\PageIndex{1}\): Most popular science pictures of the atom show electrons moving around a nucleus like planets around the sun. These pictures are quite simply wrong. They come from an old idea about the structure of the atom and have lasted, partly from habit, and partly because the modern view of the arrangement of electrons in the atom is too difficult to draw simple pictures of. One origin for this hypothesis that suggests this perspective is plausible is the similarity of the gravity and Coulombic interactions. The expression for the force of gravity between two masses (Newton's Law of gravity) is \[F_{gravity} \propto \dfrac{m_1m_2}{r^2}\label{1}\] with \(m_1\) and \(m_2\) representing the mass of object 1 and 2, respectively and \(r\) representing the distance between the objects centers The expression for the Coulomb force between two charged species is \[F_{Coulomb} \propto \dfrac{q_1q_2}{r^2}\label{2}\] with \(q_1\) and \(q_2\) representing the charge of object 1 and 2, respectively and \(r\) representing the distance between the objects centers However, an electron, unlike a planet or a satellite, is electrically charged, and it has been known since the mid-19th century that an electric charge that undergoes acceleration (changes velocity and direction) will emit electromagnetic radiation, losing energy in the process. A revolving electron would transform the atom into a miniature radio station, the energy output of which would be at the cost of the potent...