Energy level

Energy levels are specific, discrete values of energy that a particle can possess. In a quantum mechanical system, a particle that is bound or spatially confined cannot have just any amount of energy. Instead, it can only take on certain fixed amounts. This concept is known as quantization. While classical particles can possess any energy value, quantum particles are restricted to these specific steps. This principle is most commonly applied to the electrons within atoms, ions, or molecules. These electrons are held in place by the electric field of the nucleus. However, energy levels can also describe the energy of nuclei or the vibrational and rotational movements within molecules.

To understand how this works, we must look at the behavior of electrons in an atom. An electron shell, also called a principal energy level, represents the orbit of one or more electrons around a nucleus. These shells are organized by principal quantum numbers, starting with n = 1, 2, 3, and so on. They are also labeled with letters such as K, L, M, and N. The shell closest to the nucleus is the 1 shell or K shell. The next is the 2 shell or L shell, followed by the 3 shell or M shell. Each shell has a specific capacity for electrons. The first shell can hold two electrons, the second can hold eight, and the third can hold 18. The general mathematical formula for the maximum number of electrons in the nth shell is 2n squared.

Electrons move between these levels through a process involving photons. A photon is a tiny particle of electromagnetic radiation. For an electron to change its energy level, it must absorb or emit a photon. The energy of that photon must be exactly equal to the difference between the two energy levels. When an electron absorbs energy and moves to a higher level, it is in an excited state. If the atom or its electrons are at the lowest possible energy level, they are in the ground state. When an electron drops from a higher level back to a lower one, it emits a photon. Scientists use a technique called spectroscopy to measure these possible energy levels.

The concept of quantized energy levels emerged through significant scientific discoveries. In the early 1800s, Joseph von Fraunhofer and William Hyde Wollaston observed spectral lines in sunlight. These lines provided the first evidence of quantization in atoms. Later, in 1913, the Danish physicist Niels Bohr proposed the idea of energy levels in his Bohr theory of the atom. By 1926, modern quantum mechanical theory was advanced by Erwin Schrödinger and Werner Heisenberg. They explained these levels using the Schrödinger equation, showing that electrons behave like waves. In these stationary states, the electron's energy does not change over time.

In a single-electron system, such as a hydrogen-like ion, energy is determined by electrostatic interactions. The energy depends on the interaction between the negative electron and the positive nucleus. This energy is often expressed as a negative value because the potential energy is set to zero at an infinite distance from the nucleus. For multi-electron atoms, the situation becomes more complex due to electron-electron interactions. These interactions raise the energy levels of the electrons. One way to describe this is through the shielding effect. Inner electrons, which are bound tightly to the nucleus, partially cancel out its charge. This means outer electrons experience an effective nuclear charge rather than the full charge of the nucleus.

Energy levels also change when atoms interact to form molecules. Chemical bonds form because the resulting molecular state is more stable than the separate atoms. Stability in this context means the total energy level of the atoms in the molecule is lower than it was when they were apart. As atoms approach each other to form a covalent bond, their orbitals overlap. This creates bonding molecular orbitals, which have lower energy, and antibonding molecular orbitals, which have higher energy. For a bond to be stable, the electrons must occupy the lower energy bonding orbitals. These are often labeled with symbols like sigma or pi. There are also non-bonding orbitals, such as lone pairs, where the energy remains the same as in the original atom.

Beyond simple shells, energy levels can be further divided into finer structures. Fine structure splitting occurs due to relativistic kinetic energy corrections and spin-orbit coupling. This is an interaction between the electron's spin and the electric field of the nucleus. There is also a very small change called hyperfine structure. This is caused by the interaction between the spin of the electron and the spin of the nucleus. Additionally, external magnetic or electric fields can affect these levels. A magnetic field can cause the Zeeman effect, while an electric field can cause the Stark effect. These interactions shift the energy levels in measurable ways, allowing scientists to study the fundamental properties of matter.