Where do electrons get energy to rotate around the nucleus of an atom?

An atom is best thought of as a tight, dense nucleus surrounded by buzzing electrons. This picture immediately leads to the question: how do electrons keep spinning around the nucleus without ever slowing down?

This was a burning question at the beginning of the 20th century, and the search for an answer eventually led to the creation of quantum mechanics. (will open in a new tab) myself.

At the beginning of the 20th century, after countless experiments, physicists were just beginning to put together a complete picture of the atom. They realized that every atom has a dense, heavy, positively charged nucleus surrounded by a cloud of tiny negatively charged electrons. With this big picture in mind, their next step was to create a more detailed model.

Related: Strange ‘gravitational molecules’ could orbit black holes like electrons orbit atoms

In the earliest attempts at this model, scientists drew inspiration from the solar system, which has a dense “core” (the sun) surrounded by a “cloud” of smaller particles (the planets). But this model introduced two significant problems.

First, a charged particle that is accelerating emits electromagnetic radiation. And since electrons are charged particles, and they accelerate in their orbits, they must emit radiation. According to the University of Tennessee at Knoxville, this radiation will cause the electrons to lose energy and quickly coil up and collide with the nucleus. (will open in a new tab). In the early 1900s, physicists calculated that such an internal spiral would take less than one trillionth of a second, or picosecond. Since atoms obviously live longer than a picosecond, this won’t work.

The second, more subtle question was related to the nature of the radiation. Scientists know that atoms emit radiation, but they do so at very discrete, specific frequencies. An orbiting electron, if it followed this model of the solar system, would instead emit all kinds of wavelengths, contrary to observations.

quantum fix

The famous Danish physicist Niels Bohr was the first to propose a solution to this problem. In 1913, he suggested that the electrons in an atom could not have any orbit they wanted. Instead, they had to be locked into orbits at very specific distances from the nucleus, according to the Nobel Prize citation entry for his subsequent award. (will open in a new tab). In addition, he suggested that there is a minimum distance that an electron can travel, and that it cannot move closer to the nucleus.

He didn’t just pull these ideas out of a hat. Just over a decade ago, German physicist Max Planck suggested that the emission of radiation could be “quantized,” meaning that an object could only absorb or emit radiation in discrete chunks and not have any value it needed, according to the HyperPhysics handbook. page at Georgia State University (will open in a new tab). But the smallest size of these discrete pieces was a constant that became known as Planck’s constant. Before that, scientists thought that such radiations were continuous, that is, particles could be emitted at any frequency.

Planck’s constant has the same units as the angular momentum or momentum of an object moving in a circle. So Bohr applied this idea to electrons revolving around a nucleus, stating that the smallest possible orbit of an electron would be equal to the angular momentum of exactly one Planck constant. Higher orbits can be twice the value, or three times, or any other integer multiple of Planck’s constant, but never a fraction of it (that is, not 1.3 or 2.6, and so on).

Planck's constant is written out in a notebook.

Planck’s constant was written out. (Image credit: ragsac via Getty Images)

It would take the full development of quantum mechanics to understand why electrons have such a minimal orbit and well-defined higher orbits. Electrons, like all material particles, behave both as particles and as waves. While we can think of an electron as a tiny planet orbiting a nucleus, we can just as easily imagine it as a wave going around that nucleus.

Waves in a confined space must obey special rules. They cannot have any wavelength; they must be made of standing waves which are placed within the space. It’s like someone playing a musical instrument: for example, if you pin the ends of a guitar string, only certain wavelengths will fit, giving you distinct notes. Similarly, the electron wave around the nucleus must match, and the nearest orbit of the electron to the nucleus is given by that electron’s first standing wave.

Future developments in the field of quantum mechanics will continue to refine this picture, but the basic idea remains the same: the electron cannot approach the nucleus because its quantum mechanical nature does not allow it to take up less space.

Addition of energies

But there is a completely different way to explore the situation that doesn’t rely on quantum mechanics at all: just look at all the energies involved. An electron orbiting the nucleus is electrically attracted to the nucleus; he is always drawn closer. But the electron also has kinetic energy that works to send the electron flying.

For a stable atom, these two states are in equilibrium. In fact, the total energy of an electron in orbit, which is a combination of its kinetic and potential energies (will open in a new tab), negative. This means that you need to add energy to an atom if you want to remove an electron. The same is true for planets in orbit around the sun: to remove a planet from the solar system, you need to add energy to the system.

One way to see this situation is to imagine an electron “falling” into the nucleus, attracted by its opposite electric charge. But due to the rules of quantum mechanics, it can never reach the core. So it gets stuck, forever revolving in its orbit. But this scenario is allowed by physics because the total energy of the system is negative, which means that it is stable and bound together to form a long-lived atom.

Originally published on Live Science in January. 21 June 2011 and rewritten 22 June 2022

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