An Overview of Energy Level Definition

The energy level can be defined as the stable or constant energy state achieved by a system consisting of particles like atoms, electrons, etc. These states are highly important, especially in the quantum states of the particles. Energy levels are also referred to as energy states. The concept of energy level was used for the first time in 1902. The energy level is a more flexible terminology referring to the space surrounding an atom where there are possibilities of discovering electrons. Each of these locations has specific quantum energy associated with it. The energy level formula can be used for calculating the energy associated with each level.

Energy Level Formula

It was assumed that the electrons revolve around the nucleus in fixed orbits, similar to how the planets move around the Sun. Later, it was found that the electrons did not exist in all possible orbits around the nucleus. Neils Bohr developed a solution for this with his atom model. In this model, the electrons revolve around the nucleus in particular orbits where they are stable.

Electrons exist in particular orbits where they have stability. The shells (energy levels) that meet the radius parameter as per the Bohr model have electrons occupying the levels. According to the Bohr theory, the minimum possible energy for a hydrogen atom at its ground level is 13.6 eV. Based on this, for an electron at the level of the hydrogen atom, the energy possessed by the electron is given by this equation:

E(n)= – 1/n² * 13.6 eV

This is called the energy level formula.

Other forms of energy level formula

The above formula is used to find the energy of an electron at a particular level, which is denoted by n. In the case of a transition, where the electron moves from one level to another, this energy level formula is inapplicable.

An electron might absorb energy from some source, leading to a disturbance in its stability in the current energy level. The electron moves to an excited state. Since it possesses higher energy, the electrons are unstable and tend to emit a photon to return to the lower and stable energy level. The energy of the emitted photon is the difference in energies between the excited and the stable energy states. This difference in energy can be indicated asΔE = hμ.

If n1 is the lower energy level and n2 is the higher energy level, the equation becomes

ΔE = hμ = -(1/n2² – 1/n1²) 13.6 eV

Taking negative signs inside,

ΔE = hμ = (1/n1² – 1/n2²) 13.6 eV

This form of energy level formula is used in case of transitions between two energy levels to find the energy of the emitted photon.

Calculating the energy level of an electron

The energy of an electron in any shell of a hydrogen atom can be calculated using the energy level formula. For an electron in the 4th level, energy can be calculated as shown below:

The formula for calculating the energy level of an electron:

E(n)= – 1/n² * 13.6 eV

Given n = 4,

E(4)= – 1/4²* 13.6 eV

        = – 1/16 * 13.6 eV

= -0.85 eV

Calculating the energy level of an electron in atoms other than hydrogen

None of the above forms of the energy level formula can be used for atoms other than hydrogen. Z, indicating the atomic number of the considered atom, is used while calculating the energy level of an electron. Then, the energy level formula becomes

E(n)= – Z²/n² * 13.6 eV

where Z is the atomic number of the atom.

All the energy level formula forms can be applied only to monatomic atoms or ions like hydrogen, He⁺, Li²⁺, etc.

Conclusion

The concept of energy levels has great importance. It refers to the area around the nucleus where electrons are found commonly. The first energy level is the nearest to the nucleus, accommodating two electrons. Moving further, each level has a specific number of electrons occupying them. Valence electrons occupy the farthest levels. Elements with the same number of valence electrons occupy the same group in the periodic table. All of these show the importance of energy levels. The energy level formula helps to calculate the energy level of an electron. The energy level formula for hydrogen atoms helps in understanding the overall behaviour of hydrogen-like atoms and their energies at each level.

The energy level formula also helps in analysing the spectral behaviours of atoms. Different spectral lines or series can be drawn on how the transitions from one energy level to another occur. The advanced concepts of valence and conduction electrons, as well as the Fermi energy, are derived from the energy level concept.