In the context of physics and chemistry, the concept of electronic energy being negative is often encountered when discussing the energy of electrons in atoms or molecules. The negativity of electronic energy arises from the mathematical formalism used to describe the behavior of these systems.
In quantum mechanics, which is the branch of physics that describes the behavior of particles at the atomic and subatomic level, energy is quantized, meaning it can only take on certain discrete values. The energy of an electron in an atom or molecule is described by its wave function, which is a mathematical function that characterizes the electron's behavior.
When solving the Schrödinger equation, which is the fundamental equation of quantum mechanics, for an electron in an atom or molecule, the resulting wave function yields a set of allowed energy levels, often referred to as energy eigenstates. These energy eigenstates are labeled by quantum numbers, such as principal quantum number, azimuthal quantum number, and magnetic quantum number.
The zero energy reference point, or the energy level at which all other energies are measured, is typically set to the energy of a free electron far away from any atomic or molecular influence. Since an electron bound to an atom or molecule has less energy than a free electron, its energy is lower, or negative relative to the reference point.
It's important to note that the negativity of electronic energy is a convention and doesn't imply that electrons possess "negative energy" in a physical sense. It simply signifies that the energy of an electron in a bound state is lower than the energy of a free electron. This convention allows for a convenient representation and comparison of energy levels within the quantum mechanical framework.