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# Atomic energy levels

## Atomic energy levels

The electron of an atom can be located at various energy levels around the nucleus with varying probabilities. These regions are called orbitals.

When an electron absorbs an amount of energy corresponding to the energy difference between two levels, it becomes excited and moves into an orbit associated with a higher energy level.

An atom with an excited electron is also said to be excited.

The concept of energy levels for orbiting electrons in an atom has some parallels with the concept of kinetic energy of an orbiting satellite in gravitational physics. If the kinetic energy is too high, the electron will leave the atom altogether.

However, in an atom, the levels do not correspond to orbits or paths but rather to regions around the nucleus where the electrons have a probability to be located in.

An electron transits from a lower energy level $E_{1}$ to a higher energy level $E_{2}$ after absorbing a photon (left). The same electron transiting from $E_{2}$ to $E_{1}$ emits a photon (right).

## Emission spectra

When an electron in an atom moves from a higher-energy level to a lower energy level, energy is released in the form of photons.

The photons emitted by excited atoms form an emission spectrum, which appears as coloured parallel lines on a dark background.

These coloured bars, called spectral lines, are arranged according to the frequencies of the emitted photons.

An emission spectrum can be made up of spectral lines of any frequency.

However, some energy transitions produce photons whose frequencies are either too high or too low to be visible to the human eye (the visible spectrum comprises wavelengths of $400\text{ nm}$ to $750\text{ nm}$).

Examples of an emission spectrum (above) and an absorption spectrum (below)

## Absorption spectra

When an electron in an atom absorbs a photon, it moves from a lower energy level to a higher energy level. Only photons of wavelengths corresponding to the difference between energy levels can be absorbed by electrons.

White light consists of light of all frequencies from the visible spectrum (from $400\text{ nm}$ to $750\text{ nm}$).

An atom exposed to white light only absorbs photons of particular frequencies, leaving the rest to pass through unaffected.

If the white light, after passing through the atom, is separated into its components (e.g. by a prism) and displayed on a screen, dark lines appear in the continuous visible spectrum corresponding to the frequencies absorbed.

This gives rise to an absorption spectrum, which appears as dark lines on a coloured background.

These dark lines are arranged according to the frequencies of the absorbed photons.

Examples of an emission spectrum (above) and an absorption spectrum (below)

## Photon energy equation

An orbital electron which transits from a higher energy level $E_{2}$ to a lower energy level $E_{1}$ would emit a photon with an energy that is equivalent to the difference between the energy levels. This is given by: $$hf=E_{2}-E_{1}$$ $hf$ is the energy of the photon.

Note that the energy levels of an atom are considered, by convention, to be negative (e.g. $E_{1}=-6.3 \text{ eV}$ and $E_{2}=-3.2 \text{ eV}$).

The energy of an unbound electron at rest is set as zero and the electron is considered to lose energy as it becomes more tightly bound to the nucleus. This means the energy becomes more negative as an electron moves closer to the nucleus.

This is comparable to gravitational potential energy which is set to zero where the gravitational field strength is zero (i.e. at an infinite distance from the centre of a gravitational field).

An electron transits from a lower energy level $E_{1}$ to a higher energy level $E_{2}$ after absorbing a photon (left). The same electron transiting from $E_{2}$ to $E_{1}$ emits a photon (right).