Molecules possess discrete energy levels called quantum states. Unlike atoms, which have simpler energy levels, molecules possess additional rotational and vibrational energy levels. Each energy level is separated by an energy gap, with the gaps between adjacent electronic, vibrational, and rotational levels varying significantly. The three types of energy levels in a diatomic molecule are shown in Figure 1.

In Ultraviolet–Visible (UV–Vis) spectroscopy, the absorption of electromagnetic radiation is used to probe the electronic structure of molecules. This technique provides insights into molecular electronic transitions, particularly the movement of electrons between different molecular orbitals. Radiation is absorbed if the energy of the electromagnetic radiation passing through the molecule is precisely equal to the energy difference between the excited and ground states. During this process,...

A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
According to Hooke's law, the vibrational frequency is directly proportional to the...

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...

Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as the nucleus...

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.