# Quantized Energy and Photons

By Gabrielle Stefou

The electronic structure of an atom, specifically regarding electromagnetic radiation (light) and the electron’s wave-particle duality, can tell us a lot about the properties of the atom. Understanding how the electrons of a particular atom or element behave was, and still is, the basis of the periodic table – the fundamental building block of our chemistry education. So, on that note, here is a little bit about electronic structure, specifically with regard to quantum mechanics.

The Bohr Model

After Earnest Rutherford conducted the famous gold foil experiment and discovered a small positive nucleus, he was left not really knowing exactly what the electrons of the atom were doing, and so conveniently stated that they move around the nucleus just like planets orbit around the sun. However, Neils Bohr, who worked under Rutherford, knew that any charged particle in circular motion would give off electromagnetic radiation, and would thus lose some of its energy, making it gradually spiral into the nucleus. He also expected that if the electrons did move in space around the nucleus, the radiation that they emitted as they travelled around the nucleus would create a continuous spectrum.

When Bohr analyzed the spectrum of hydrogen, he saw that the emission of light didn’t occur in a continuum; instead, light was emitted in discrete “packets”. Because of this observation, he created a model of the atom that he thought would best describe this “quantization” of energy.

Quantization and Electron Behaviour

Electrons travel in “shells” around the nucleus, called energy levels or energy states. As the shell number increases – this corresponds to the principle quantum number (n=1, n=2, n=3) – the electron gets further and further from the nucleus. If the electron jumps from a lower energy level (ie. n=1) to a higher energy level (ie. n=2), then the electron must absorb energy to overcome the attraction that it has between itself and the oppositely charged nucleus. When an electron travels from a higher shell (ie. n=2) to a lower shell (ie. n=1), the electron will emit light, kind of like it is letting go of the extra energy it doesn’t need in the form of electromagnetic radiation (a photon). The energy of that photon that is emitted is the exact amount of energy that it takes for the electron to travel from its previous high energy level to its low energy level that it just jumped to. We know this to be true because the positon of the electron in the energy shell is quantized (there is no in-between energy shells), and so the energy that its emitted through photons will also be quantized because of this lack of an in-between.

The Electromagnetic Spectrum Related to Photon Emission

Now, we can take the information we know about the photon that was emitted (ie. its energy, frequency, or wavelength) to figure out what type of light it is. (Note that we were previously talking about light in terms of photons, which is a particle, and now we are talking about it in terms of it being a wave, showing light’s mysterious wave/particle duality). We know that the electromagnetic spectrum consists of radio waves, microwaves, infrared waves, visible light, UV light, X-Rays, and finally Gamma Rays, each with their own corresponding range of frequencies, wavelengths, and energies, so if we can calculate the energy/wavelength/frequency of the photon emitted, we can know what type of light it is!

We can also sort the electron behaviour/photon emission characteristics to categorize the light into 4 main spectral series: Lyman, Balmer, Paschen, and Brackett. Each series includes a particular energy state jump unique to it, as well as the type of light that each usually emits. So, by finding the energy of the photon, or by knowing what energy state jumps the electron has made to emit light, you can sort the photon activity into these series. In the following section I will further discuss the qualities of each spectral series.

Spectral Line Series

For the photon to be sorted into the Lyman series, the electron in the atom must have jumped from any higher energy shell to the first energy shell (n=1). The frequencies of the photon emitted in this jump lie in the Ultraviolet range of the electromagnetic spectrum.

To be sorted into the Balmer series, the electron in the atom must have jumped from any higher energy shell to the second energy shell (n=2). The frequencies of the photon emitted in this jump lie in the UV/Visible Light range of the electromagnetic spectrum.

To be sorted into the Paschen series, the electron in the atom must have jumped from any higher energy shell to the third energy shell (n=3). The frequencies of the photon emitted in this jump lie in the infrared range of the electromagnetic spectrum.

To be sorted into the Brackett series, the electron in the atom must have jumped from any higher energy shell to the fourth energy shell (n=4). The frequencies of the photon emitted in this jump lie also in the infrared range of the electromagnetic spectrum.

Absorption and Emission Spectra

When energy is absorbed by an electron it is shown by an almost continuous spectrum (a spectrum with many colours of the rainbow due to the more continuous variation of energy absorbed by the electron rather than emitted).  When energy is emitted by an electron it is shown by a line spectrum, which is like a continuous spectrum but instead of having a continuum of wavelengths being displayed, you have a few lines on it with mostly black space that represent the wavelengths where light is emitted. If you compared the absorption and emission spectrum of an atom one on top of the other, you would find that the black lines on the absorption spectrum align exactly with where the emission lines are on the emission spectrum. This makes sense because where light is being emitted it is not being absorbed, resulting in the black lines in the absorption spectrum, and where light is being absorbed it is not being emitted, resulting in the black space on the emission spectrum.

What is most interesting, and perhaps what is most important about line spectra, is that where the wavelengths are indicates where jumps are made. You can see that they take place at distinct areas and distinct moments. This indicates the quantization of the energy shells and electron positions. Because the emission lines on the emission spectrum occur so that the distance between each colourful line increases as you go from left to right, it almost mimics the position of the energy shells.

Summary

• Electrons travel in quantized energy states, and thus produce quantized energy in the form of photons.
• Electrons absorb energy from lower to higher energy state, and emit energy from higher to lower energy state.
• The energy, wavelength, and frequencies of the photons emitted by electrons can be quantified.
• The quantified energy can be used to determine the type of light on the electromagnetic spectrum, which can then be sorted into the main four spectral line series: Lyman (UV), Balmer (UV/Visible), Paschen (IR), and Brackett (IR).
• Electron behaviour can be illustrated using absorption and emission spectra to help visualize the quantization of electrons and their emitted energy.

In general, electrons are removed from the valence-shell s orbitals before they are removed from valence d orbitals when transition metals are ionized.

So, what that does mean is that if you remove electrons from vanadium (0), you will remove the 4s electrons before you remove the 3d electrons. So, you have the following electronic configurations:

V is [Ar] 4s2 3d3
V2+ is [Ar] 4s0 3d3
V3+ is [Ar] 4s0 3d2
V4+ is [Ar] 4s0 3d1
V5+ is [Ar] 4s0 3d0