Spectroscopy: UNIZOR.COM - Physics4Teens - Waves - Photons and Matter
Channel: Zor Shekhtman on UNIZOR Education
Date: 2022-12-17

UNIZOR.COM - Physics through a Looking Glass of Mathematician
Notes to a video lecture on http://www.unizor.com

Spectroscopy

In the previous lectures we have discussed in details the interaction between photons and atoms of hydrogen, mentioned the energy levels of hydrogen electrons En=13.6 /n²eV (electron-volts) and investigated the colors of light emitted by hydrogen electrons, when excited electrons jump from higher energy shell down to lower energy one, emitting light.

Not surprisingly, analogous situation is with any other element.
Any element has its electrons positioned at some distinct shells around a nucleus, with each shell having a specific for this element energy level. When extra energy is infused into electrons, they can jump to higher energy level shell and, later on, they relax into a lower level, emitting extra energy as electromagneting oscillations of specific frequency.

Since energy levels of shells are fixed and distinct for each element, the amount of energy released by an electron during the process of relaxation is also fixed and distinct, depending only on the difference in the level of energy between the shells, specific for each element.

As we know, the frequency f of electromagnetic oscillations emitted by an electron, when it jumps from a higher energy level shell to a lower energy level (the relaxation process), is directly proportional to the amount of energy E released by this electron during this process of relaxation
E = h·f
where h is Planck's constant.

Considering the energy levels of shells for different elements are, generally speaking, different, the light emitted by electrons jumping from a higher energy level to a lower one for different elements will, generally speaking, have different frequencies and, therefore, different color, if it falls into a visible spectrum.

Most likely, each element has some levels of energy that correspond to some visible light and, since they are, most likely, different for different elements, we can identify the elements by the light they emit, if their electrons relax to a lower energy level after being excited.

Spectroscopy is the field of science dealing with analyzing the spectrum of emitted light by different elements, identifying the composition of complex objects by the light emitted from them and making judgements towards the properties of these objects.

While spectroscopy, as a branch of science, deals with many aspects of interaction between electromagnetic oscillations and matter, we will only address the analyzing the emission of light when electrons are relaxing after being exposed to energy that exited them.

There are many elements, each having certain number of shells on different energy levels. That makes a job of identifying a particular element by a light emitted by it quite a complicated task.
By now the scientists have a pretty good picture about most of the elements as far as what kind of light frequency and wave length they can emit.

Just as an example, the iron can emit the light of wave lengths 516.891 nm, 495.761 nm, 466.814 nm, 438.355 nm, 430.790 nm, 382.044 nm, 358.121 nm and 302.108 nm (the last three are in ultraviolet part of a spectrum, not visible by a naked eye).

Oxygen emits light with wave lengths 898.765 nm, 822.696 nm, 759.370 nm, 686.719 nm and 627.661 nm (the first three are in infrared part of a spectrum, not visible by a naked eye).

Knowing all the potential energy differences between shells of some element allows to make a judgement not only about the presence of this particular element by the light it emits, but also about its temperature.

The hotter the element - the more wavelengths with greater energy (shorter wave length, higher frequency) will be in the light it emits. This is how the temperature of stars can be evaluated.

In the above example with iron there are 8 different wave lengths observable, but if the shorter ones dominate, it means the iron is heated to a greater temperature.
As we know, hot iron starts emitting red glow first, but, when its temperature is rising, the color shifts from red to white, which means that lights with shorter wave lengths are added.

There are many other important aspects of spectroscopy, but they are beyond the scope of this course.