# Energy Level Formula

## Energy Level Formula

In the middle of the 1920s, the atom’s structure was a hotly contested subject. There have been several atomic models developed, including the notion put forth by J.J. Thompson and Ernest Rutherford’s discovery of the nucleus. However, it was Neil Bohr who claimed that, like planets around the sun, electrons rotated around a positively charged nucleus. A presumption regarding the quantization of atoms was made in the Bohr model of the hydrogen atom, according to which electrons orbited the nucleus in predetermined orbits or shells with definite radii. It was impossible for electrons to reside between any shells other than those having a radius given by a specific equation. The equation mathematically states the permitted atomic radius value. Students need to learn the Energy Level Formula used to get the energy of the electron at the nth energy level.

## Energy Level

Bound, or spatially confined, quantum mechanical systems or particles can only take on discrete energy values known as energy levels. Classical particles, on the other hand, can take in any quantity of energy. The phrase can also refer to the energy levels of nuclei or to the vibrational or rotational energy levels in molecules. The term most frequently describes the energy levels of electrons bound by the electric field of the nucleus in atoms, ions, or molecules. A system is said to have a quantized energy spectrum if it has so many different energy levels.

### Energy Level Formula

The Bohr model of the hydrogen atom needs to be taken into account when using the rotational Energy Level Formula. In the Bohr model of the hydrogen atom, an assumption was made regarding atom quantization. This hypothesis states that electrons move in predetermined orbits or shells with specific radii as they orbit the nucleus. The only permitted shells were those whose radius was specified by the equation. Additionally, there could not possibly be any electrons in the space between the shells.

### Electron Energy Level Formula

Bohr used the electrons in circular, quantized orbits as his starting point to determine the energy of an electron in the nth level of the hydrogen atom. An electron is stimulated to a higher energy level when it takes in energy in the form of photons. The excited electron is less stable after jumping to the higher energy level, also known as the excited state, and would therefore quickly emit a photon to return to a lower and more stable energy level. For a particular transition, the energy emitted is equal to the energy difference between the two energy levels. The Energy Level Formula can be used to compute the energy.

### Solved Examples

Solved examples for the Energy Level Formula are provided by Extramarks.

### Summary

Bohr’s hydrogen model is based on the nonclassical idea that electrons orbit the nucleus in specific shells or orbits. Using Bohr’s model, the energies for an electron in the shell were calculated. Bohr described the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels. The photon energy is expressed in electron volts (eV).