Final answer:
The Schrödinger equation is likely the one being referred to as it explains the behavior of electrons in atoms and underpins modern chemistry. The Bohr model and the Nernst equation are also important but they do not offer a comprehensive explanation like the Schrödinger equation does.
Step-by-step explanation:
The name of the one equation that explains all the behavior of electrons in atoms, and therefore all of chemistry in theory, is not explicitly given in your reference materials. However, your references to quantum mechanics and the behavior of electrons in orbits suggest that the Schrödinger equation, which is central to quantum mechanics, might be the equation being referred to.
This equation is fundamental because it describes how the quantum state of a quantum system changes with time. It is used to predict the probability distribution of electrons in atoms, and thus provides a foundational understanding of chemical behavior, bond formation, and molecular structure.
The Bohr model of the atom and its equations provided a foundation to understanding single-electron systems, such as hydrogen. But the Bohr model was ultimately replaced by quantum mechanics for more complex atoms. While the Nernst equation is crucial in electrochemistry, especially for redox reactions and calculating the voltage of an electrochemical cell, it does not explain the behavior of electrons in atoms comprehensively. The Schrödinger equation, in contrast, applies to all electrons in atoms and is central to the field of quantum mechanics.