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

The most accurate way to imagine an atom is as a dense, compact nucleus with electrons running around it. This image generates the following query: How come electrons do not slow down when they revolve around the nucleus?

This was a popular topic in the early 20th century and the search for an explanation led to the creation of quantum mechanics.

At the beginning of the 20th century, physicists were just beginning to form a coherent picture of the atom after millions of tests. They discovered that surrounding a swirl of small, negatively charged electrons was a dense, solid, positively charged nucleus in each atom. With that big picture in mind, they went ahead and built a more complete model.

Early versions of this concept were inspired by the solar system, which consists of a dense "core" (the sun) surrounded by a "cloud" of smaller particles (the planets). However, this model pointed out two major problems.

The first is that electromagnetic radiation is created when a charged particle accelerates. Additionally, because electrons are charged particles and accelerate during their orbits, they should emit radiation. The University of Tennessee at Knoxville (opens in new tab) claims that this emission would induce electrons to rapidly spiral, lose energy, and crash into the nucleus. Scientists estimated that such an internal spiral would occur in a picosecond, or a billionth of a second, in the early 20th century. It was obvious that atoms have a lifetime longer than a picosecond, so this wasn't going to work.

The other, more complex issue was the type of radiation. Although it is recognized that the frequencies at which atoms release radiation differ greatly, the fact that they do so is understood. If an orbiting electron followed this model of the solar system, it would emit a wide range of wavelengths, unlike observations.

The quantum solution

Renowned Danish scientist Niels Bohr was the first to propose a solution to this problem. He postulated in 1913 that the electrons of an atom could not randomly select any orbit. They had to be locked in orbits at extremely exact distances from the nucleus, according to the Nobel Prize citation for its subsequent award. Furthermore, he proposed a minimum distance that an electron can move before losing its ability to migrate out of the nucleus.

These ideas did not suddenly occur to him. German physicist Max Planck proposed that radiation emission can be "quantized," which would imply that an object could only absorb or emit radiation in discrete fragments and did not have the value I desired, according to State University's HyperPhysics reference page of Georgia (opens in a new tab). But among all these different units, there was one that was always there and was nicknamed Planck's constant. Scientists once thought that these emissions were constant, meaning the particles could be released at any frequency.

The momentum of an object moving in a circle, or angular momentum, has the same units as Planck's constant. Using electrons orbiting a nucleus as an example, Bohr went on to explain that the smallest possible orbit for an electron would have an angular momentum equal to a Planck constant. The highest orbits could be valued at twice the value of Planck's constant, three times the value, or any other integer multiple of it; They could never be fractionals of the constant, that is, not 1.3, 2.6, etc.

It is necessary to fully develop quantum mechanics to properly understand why electrons have such a short minimum orbit and well-defined upper orbits. Electrons behave like waves and particles, just like all the other constituents of matter. An electron can be seen as a wave surrounding the nucleus, or it can be seen as a small planet orbiting the nucleus.

Waves in a limited area are subject to special restrictions. They cannot have any wavelength; They have to be formed by standing waves that fit within space. Like when someone plays an instrument, if you press the ends of a guitar string, only certain wavelengths fit, producing different tones. The initial standing wave of an electron shows its orbit closest to the nucleus, much like an electron wave must fit around a nucleus.

As quantum mechanics advanced, the details of the representation would improve, but the basic notion remained the same: an electron cannot get closer to the nucleus because quantum theory prohibits it from taking up less space.

Adding the energies

However, there is an alternative perspective that is not quantum mechanics at all: just take into account all the energy involved. A nucleus attracts and pulls an electron into its orbit due to its electrical attraction toward it. This attraction is constant. However, the electron can fly because it also has kinetic energy.

These two work together to create a stable atom. The total energy of an electron, which is made up of its potential and kinetic energy, is actually negative. This implies that more energy must be applied to the atom in order to extract the electron. Similar circumstances apply to planets in orbit around the Sun: more energy would have to be brought into the system to eliminate one.

Think of an electron being attracted to its opposite electrical charge and "falling" toward a nucleus. But according to the laws of quantum mechanics, it will never reach the nucleus. It becomes stranded due to its orbital stagnation. However, physics allows for this scenario since the total energy of the system is negative, indicating that it is stable and bonded together to form an atom with a long half-life.


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