Energy Level Formula

Definition of Energy Levels

Thus, discrete energy levels of an atom are those particular fixed energies that an electron of the atom can possess. In simple words, according to quantum mechanics, electrons revolving in an atom around its nucleus stay in certain specific, quantized energy states. To be sure, electrons cannot exist between such states but only on fixed levels.

Formula of Energy Level for Hydrogen Atom

The Bohr model is the simplest model that describes the energy levels of the hydrogen atom. The description is effective in describing what one intuitively understands about the quantized nature of the electron energy level. Shown below is a detailed explanation of the formula and how it should be applied:

Introduction to Bohr Model

The Bohr model of an atom, proposed by Niels Bohr back in 1913, had been among the very first theories ever developed and truly capable of explaining the discrete levels of energy that exist within an atom. Considering a hydrogen atom with only one electron, the Bohr model is very capable of clearly spelling out a formula for calculating electrons' energy in various orbits.

Energy Level Formula for Hydrogen Atom

The energy En of an electron in the n-th energy level is given by:

 

where,

• En: The energy of the electron in the n-th level.

• 13.6 eV: The ionization energy of hydrogen, that is the energy that will remove the electron from the ground state (n = 1) to infinity.

• n: The principal quantum number (1, 2, 3, .).

The energy is absorbed by an electron in the form of photons, which get excited to a higher energy level. Immediately after jumping to the higher energy level, further known as the excited state, the excited electron turns less stable and hence quickly emit a photon to come back to a lower and more stable energy level. The energy emitted is equal to the difference in energies between any two energy levels involved in a particular transition. Energy can be calculated by the expression

The expression defining the energy of levels of a hydrogen atom is

where E0 is 13.6 eV and n is 1,2,3……and so on

Energy Level Formula for Multi-Electron Atoms

Energy levels for atoms containing more than one electron, such as helium or carbon, are more complex and involve the interactions of electrons with each other as well as the nucleus. These energy levels are approximated using quantum mechanical models and are generally described by:

where:

• Z is the atomic number, i.e., the number of protons.

• n is the principal quantum number.

• l is the azimuthal quantum number. It gives the shape of the orbital.r Hydrogen Atom