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

(Image credit: Rost-9D via Getty Images)

An atom: Compact, dense nucleus with electrons spread throughout must be the conceptualization that best describes it. This raises a question about why the electrons around the nucleus do not lose their speed and go the way of a free-wheeling flywheel without slowing down.

It was a hot topic during the early 20th century, and a quest for an answer to this question gave birth to quantum mechanics.

It was really only after millions of experiments that scientists began assembling a coherent image of the atom around the turn of the 20th century. They discovered that each atom has a dense, solid, positively charged nucleus surrounded by a swirl of tiny, negatively charged electrons. They proceeded further and constructed a more elaborate model keeping that larger picture in view.

The model for the early versions of this idea was the solar system, which is made up of a dense “core” (the sun) surrounded by a “cloud” of smaller particles (the planets). However, this methodology revealed two major problems.

The first is that the acceleration of a charged particle causes electromagnetic radiation. In addition, electrons should radiate since they are charged particles that accelerate as they orbit. This emission, the University of Tennessee at Knoxville informs us, (opens in new tab), would cause electrons to spiral quickly, lose energy, and collide with the nucleus. In the early 20th century, scientists calculated that such an internal spiral would happen in a picosecond, or a billionth of a second. This was not going to work because it was evident that atoms have a lifetime longer than a picosecond. The other, much trickier question had to do with the nature of the radiation itself. It has been known since long ago that atoms are emitting radiation but with a variety of frequencies. These differences, though, are considerable. Observations are in contradiction to the expectation that an orbiting electron in this model of the solar system would be emitting all wavelengths.

The Quantum Solution

The first who offered his solution to this problem was the famous Danish scientist Niels Bohr.

In 1913, he suggested a theory: electrons of an atom could not randomize their orbit. Later, according to the citation for the Nobel Prize, which they actually received, “they must be held in definite orbits at displacements of nuclear distances”. He also proposed the smallest distance a free electron could travel before losing its ability to leave the nucleus. Such thoughts did not suddenly come to him.

According to State University’s HyperPhysics reference page of Georgia, opens new tab) German physicist Max Planck proposed a theory that emission of radiation could be “quantized,” meaning an object could only absorb or emit radiation in discrete pieces and therefore didn’t have the value I was seeking. However, one of these units was constant and was called Planck’s constant. Earlier scientists assumed that these emissions are continuous, that is, that any frequency can cause the particles to be produced. The angular momentum units, or momentum of an object moving in a circle, are the same as those of the Planck’s constant. Bohr then went on to elaborate that the smallest conceivable orbit an electron may have would have an angular momentum equal to one of Planck’s constant using electrons orbiting a nucleus as his example.

The highest orbits could be three, two, or any other integer multiple of Planck’s constant; they could never have a value that was a fractional part of the constant, such as 1.3, 2.6, etc. So to really understand why the orbit of electrons must be so small and actually consist of several separate orbits, quantum mechanics needs to be fully developed. Electrons have wave and particle properties as does all other constituents of matter. An electron might be envisioned as a small planet circling the nucleus or as a wave around the nucleus.  There are special limiting conditions that apply to waves confined to a region.

They have to arise from standing waves that are bounded by space; they can’t have any wavelength.

They are similar to the limited number of wavelengths that will fit when the ends of a guitar string are pressed together producing different tones. It’s similar to how an electron wave has to fit around a nucleus, the first standing wave of an electron shows its orbit nearest to the nucleus. The representation would become more accurate as quantum mechanics developed, but the basic idea remained the same: an electron cannot move closer to the nucleus because quantum theory forbids it from occupying less space.

Adding the energies

However, there is another completely unconnected line of reasoning that does not involve quantum physics at all: look at all the energy involved. A nucleus attracts and holds an electron in its orbit because it has a strong electrical pull toward it. There’s always that attraction. But because the electron has kinetic energy too, it can fly.

Together, these two give the atom stability. The total energy of an electron is the sum of its potential and kinetic energy. This total energy is negative. It implies that to take away the electron from the atom, more needs to be provided to the electron in terms of energy. The case of planets around the sun is a parallel case: one would need additional energy for removing one.

Picture an electron “falling” toward a nucleus because it is attracted to the opposite electrical charge of the latter. But it will never reach the nucleus since the laws of quantum mechanics will prevent it. The orbital standstill leaves it stranded. But since the total energy of the system is negative-a sign that it is stable and bound to create an atom having a long half life-this is well within the domain of physics.

Reference

Leave a Comment