In this blog post, we’ll explore how quantum mechanics and atomic models—which describe the microscopic world invisible to the naked eye—have evolved, and how we understand atoms today.
An atom is the fundamental unit of matter. Of course, modern physics has revealed that particles smaller than atoms exist, but observing them directly is extremely difficult. So, what is an atom made of, and what does it look like? Many people visualize an atom as having a nucleus at the center with electrons orbiting around it. While it is true that the nucleus consists of protons and neutrons, electrons do not actually orbit the nucleus like planets. Anyone who has studied science a bit more has likely heard of the concept of the “orbital” model. The orbital model is the most modern atomic model explaining how electrons exist relative to the atomic nucleus, and it is briefly covered in middle and high school science classes. However, it is not easy to fully understand. This is because, although the atomic model is a concept that emerged alongside the development of quantum mechanics, school curricula often focus on the results rather than the complex theoretical background. Therefore, in this article, we will examine how atoms are described from the perspective of quantum mechanics.
Quantum mechanics is fundamentally the study of the microscopic world. Prior to the emergence of quantum mechanics, physics had developed based on the achievements of physicists such as Galileo Galilei, Isaac Newton, and James Clerk Maxwell. Newton established the laws of motion and the law of universal gravitation, while Maxwell formulated Maxwell’s equations to explain electromagnetic phenomena. Classical physics was accepted as a theory that explained everyday phenomena with great precision. For example, the trajectory of a thrown ball can be predicted quite accurately using Newton’s equations of motion.
However, as the scope of physics research gradually expanded into the microscopic world of atoms and electrons, phenomena began to be discovered that could not be explained by existing physics. A prime example of this is the double-slit experiment. Thomas Young demonstrated the wave nature of light through the double-slit experiment. Interference patterns that could not have appeared if light consisted solely of particles were observed, demonstrating that light possesses wave-like properties. Subsequently, Clinton J. Davisson conducted a similar experiment using an electron beam instead of light. At the time, electrons were naturally considered particles, but surprisingly, they too produced interference patterns like waves. These results demonstrated that electrons possess wave-like properties even though they are particles, and since this phenomenon could not be explained by classical physics alone, it became a crucial catalyst for the subsequent development of quantum mechanics.
The core of quantum mechanics lies in the uncertainty principle, the wave function, and the Schrödinger equation.
The uncertainty principle states that it is impossible to simultaneously measure a particle’s position and momentum with arbitrary precision. More precisely, there is a fundamental limit to how much the uncertainty in position and the uncertainty in momentum can be reduced together when measuring them. The key point here is that this limit does not arise from the limitations of measuring equipment but is an intrinsic property of nature itself.
For example, consider a baseball thrown by a pitcher. Today, high-performance radar guns can measure the ball’s speed with great precision, and high-speed cameras and image analysis technology allow us to determine its position with precision as well. In the macroscopic world, it is possible to measure both position and velocity simultaneously with a high degree of accuracy. However, the situation is different in the microscopic world.
When we “see” an object, it is a process in which light reflected from the object reaches our eyes or a camera, thereby conveying information. However, for very small particles—such as electrons—the very process of interacting with photons (the particles of light) can affect the particle’s state of motion. In other words, unlike the macroscopic world, where the act of measurement has almost no effect on the object, in the microscopic world, the act of observation itself can alter the particle’s state. For this reason, it is fundamentally impossible to perfectly measure a particle’s position and momentum simultaneously, and this is precisely Heisenberg’s Uncertainty Principle. This principle is still accepted today as one of the most important fundamental principles of quantum mechanics.
The wave function is a mathematical concept that describes the state of such a particle. The wave function itself represents the various possible states of a particle, and through it, we can calculate the probability of finding the particle at a specific location or in a specific state. Therefore, when a particle is observed, one of these possibilities is realized probabilistically.
The Schrödinger equation is the fundamental equation of quantum mechanics, playing a role similar to Newton’s equations of motion in classical mechanics. This equation can be used to determine a particle’s wave function, and most of the various interpretations and computational methods studied in quantum mechanics have been developed around this equation. Furthermore, in the macroscopic limit, the Schrödinger equation naturally leads to the results of classical mechanics; thus, quantum mechanics can be understood as a more general theory that encompasses classical Newtonian mechanics.
Now that we have briefly examined what quantum mechanics is, let’s use this foundation to explain atomic models, particularly the nature of electrons. The atomic nucleus consists of protons and neutrons; protons carry a positive charge, while neutrons are electrically neutral. Therefore, the nucleus as a whole carries a positive electric charge. On the other hand, since electrons carry a negative charge, an attractive electrical force acts between the atomic nucleus and the electrons. This electrical force was also a key reason why, before the orbital model emerged, Rutherford’s atomic model led scientists to believe that electrons orbited the nucleus.
However, in the actual microscopic world, electrons follow the Schrödinger equation rather than Newton’s equations of motion. Therefore, rather than moving along a fixed orbit like the Earth orbiting the Sun, an electron essentially possesses the properties of a wave function.
Let’s examine this in a bit more detail. Just as the Earth possesses potential energy due to gravity, an electron also possesses potential energy due to the electrical force with the atomic nucleus, and at the same time, it possesses kinetic energy. The sum of these two energies is mechanical energy, and this energy can be expressed through the Schrödinger equation. Solving this equation yields the electron’s wave function, and it is precisely this wave function that determines the electron’s orbital.
As explained earlier, the wave function contains information related to probability. Therefore, the electron’s wave function represents the probability that the electron will be found at a specific location; when visualized, it allows us to predict in which regions of space the electron is most likely to be found. The orbital model is precisely what represents this probability distribution.
Earlier, we examined how atoms are structured using quantum mechanics. To summarize, quantum mechanics is a theory developed to extend classical physics to the microscopic world, and it describes the state of an electron through its core concept, the wave function. Furthermore, an orbital is the spatial representation of the probability that an electron will be found at a specific location.
An orbital does not mean that an electron orbits the atomic nucleus along a fixed path. Rather, it is a probability distribution that indicates the regions of space where an electron is most likely to be found. Therefore, today’s atomic model understands electrons not as particles moving like planets, but as probability distributions of wave functions described by quantum mechanics.
Since its inception in the early 20th century, quantum mechanics has established itself as a core theory of modern physics. Various cutting-edge technologies—such as semiconductors, lasers, magnetic resonance imaging (MRI), and quantum computing—have also developed based on quantum mechanics, and its validity continues to be verified through numerous experiments. Of course, science can always advance further with new discoveries, but to date, quantum mechanics is widely accepted as the theory that most accurately describes the microscopic world.
Therefore, if someone were to ask in the future what an atom looks like, explaining that electrons exist as a probability distribution called an “orbital” would be a more accurate answer according to today’s scientific understanding than describing them as orbiting the atomic nucleus in fixed paths.
