Coulomb's law describes the electrostatic interaction between charged particles, stating that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. While Coulomb's law successfully explains the interaction between charged particles on a macroscopic scale, it is insufficient to describe the behavior of electrons in the planetary model of an atom.
The planetary model of the atom, also known as the Bohr model, suggests that electrons orbit the nucleus in well-defined circular or elliptical paths, much like planets orbiting the sun. However, this model violates the principles of classical electrodynamics, which are based on Maxwell's equations and Coulomb's law. According to classical electrodynamics, an accelerated charged particle (such as an electron in orbit) would continuously emit electromagnetic radiation and lose energy, eventually spiraling into the nucleus. This phenomenon is known as the "radiation problem."
In contrast, the Bohr model posits stable electron orbits without radiation. To address this discrepancy, the Bohr model introduced the concept of quantized energy levels, proposing that electrons can only occupy specific orbits with discrete energy values. Electrons can transition between these energy levels by absorbing or emitting discrete amounts of energy in the form of photons. However, this model was still incomplete and didn't fully explain the behavior of electrons in atoms.
To accurately describe atomic behavior, a more comprehensive theory was needed, leading to the development of quantum mechanics. Quantum mechanics, with its mathematical framework and wave-particle duality, provides a more accurate understanding of atomic and subatomic phenomena. It describes electrons as wave-like entities described by wavefunctions, which represent the probability distribution of finding an electron in a particular region around the nucleus. The Schrödinger equation, a fundamental equation in quantum mechanics, governs the behavior of these wavefunctions and provides a more accurate description of electron behavior in atoms than the classical laws of electrodynamics.
In summary, Coulomb's law alone cannot explain the behavior of electrons in the planetary model of an atom because it doesn't account for the quantized energy levels, wave-like nature of electrons, and the associated radiation problem. Quantum mechanics, on the other hand, provides a more comprehensive framework for understanding the atomic structure and behavior of electrons.