Notes to a video lecture on http://www.unizor.com
Photons and Matter
In previous lectures we discussed different forms of interaction between matter and electromagnetic oscillations.
In this lecture we will present some scientific foundation of these interactions.
Contemporary view on electromagnetic field oscillations is based on the fact that energy carried by these field oscillations is not infinitely divisible in however small pieces, but is delivered in chunks called quanta (this is a plural form, a singular form is quantum) or photons.
Quantitatively, these chunks of energy depend only on the frequency of oscillations f and are equal to h·f, where h=6.63·10−34J·s is Planck's constant.
Notice that the amount of energy in one photon depends only on the frequency of electromagnetic field oscillations, not on an amplitude of these oscillation. What does depend on an amplitude is the density of photons in space and time: the higher amplitude of oscillations at the source of radiation - the higher density of photons per unit of space during a unit of time.
Let's talk now about matter or, more precisely, about the structure of an atom.
The model of an atom, as we understand it today, consists of a nucleus and electrons orbiting around a nucleus on different orbits or, better said, in different shells around a nucleus. Electrons of any particular shell have the same energy. Every shell has its unique energy level shared by all electrons populating this shell. Shells can be viewed as concentric spheres characterized by their energy level.
The most important about these shells is that they can be only at discrete energy levels shared by electrons within it.
Since shells are at discrete energy levels, any exchange of energy between an atom and an electromagnetic field oscillations is possible only if photons of electromagnetic oscillations fit by their energy amount to a difference in energy level between different shells around a nucleus of this atom.
Consider an absorption of radiation by matter.
The absorption of a single photon means that some electron jumps from its shell with a lower energy level to a shell with the higher one.
This photon's energy is ΔE=h·f.
An atom can absorb energy in chunks only equal to a difference in energy levels between its shells.
An obvious consequence of this is that, if electromagnetic oscillations have such a frequency f that each photon's energy is equal to the energy difference between energy levels of two shells around a nucleus, atom can absorb this photon by some electron getting excited and jumping to a shell with a higher energy level.
If there is a mismatch between frequency of electromagnetic oscillations and difference between energy levels of shells around a nucleus, atom cannot absorb the photon. Most likely, an atom increases its own oscillations that results in heating.
A particular case of a mismatch between the energy of a photon and energy levels of the atom's electron shells is when a photon carries energy higher than the difference between the levels of energy of the atom's shells.
In this case excited electron cannot just jump to a higher energy shell, held there by a nucleus' attraction, but, instead, flies free. This happens in the photoemission. In this case excess of energy beyond maximum absorbable by an electron goes into kinetic energy of the electron that flies free.
Now consider an emitting light (that is, initiating electromagnetic oscillations) by previously excited electrons that return back to normal state by jumping from a higher energy shell to a lower one.
Since we deal with discrete amounts of energy between the shells, the frequency of emitted light will also have only discrete values.
Therefore, radiation emitted by any element, as a result of releasing previously absorbed energy, has certain number of possible discrete frequencies that depend on the properties of an element - the energy levels of electron shells of its atom.
Thus, for example, if there are 6 shells where electrons can potentially jump to, there are 5 different frequencies, when electron jumps from the 6th shell onto any of 5 others, releasing some photons of a corresponding frequency, plus there are 4 destination shells for an electron in the 5th shell, plus there are 3 shells to jump to from the 4th one, plus 2 shells to jump down the energy scale for an electron in the 3rd shell, plus 1 destination for an electron in the 2nd shell.
Altogether we have for this element k=5+4+3+2+1=15 different jumps with 15 corresponding frequencies of emitted radiation.
This simple result can be also obtained by using Combinatorics, as the number of combinations of 2 elements from a set of 6, which is
k=6!/(4!·2!)=6·5/2=15.
Consider, for example, an atom of hydrogen with one proton in its nucleus and one electron in some shell.
The normal state of this electron is called a ground state.
We can excite this electron by infusing it with energy of E1=10.2eV, which will cause it to raise to a first excited state.
When this electron with electric charge of −1.602·10−19C returns back to a ground state from the first excited state, it will emit a photon with the same energy that required to excite it - E1=10.2eV.
This amount of energy in a photon corresponds to its frequency
f1 = E1/h =
= 10.2·1.602·10−19/6.626·10−34
= 2.466·1015Hz
and wavelength
λ1 = c/f1
where c=3·108m/sec is the speed of light.
That gives
λ1 = 3·108/2.466·1015 =
= 1.216·10−7 ~= 122nm
Therefore, when an electron jumps from the first excited state to the ground one, it will release 10.2eV of energy, which corresponds to a photon with frequency f=2.466·1015Hz and wavelength 122 nanometers (ultraviolet part of a spectrum).
Any jumping of an electron from a shell with higher energy level to a lower one will emit certain radiation. Since each element has specific for this element energy levels, it also can emit only specific frequencies of radiation. By analyzing a spectrum of radiation we can determine what elements emitted this radiation.
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