[MUSIC] Dear colleagues, in this module, we will discuss the quantum mechanical description of atom. But before we start this description, we will discuss another important topic. It's wave particle duality. For a long time where it has been two different ideas about the nature of light. Newton thought what light is real, consist of small particles, so it's Corpuscular theory of light. In contrast, Huygens thought of light as a wave. Both corpuscular and wave theories of light could describe reflections and refraction of light. However, such properties as diffraction and interference could not be described by corpuscular theory. But could be easily described by wave theory of light. So in the ninth century, it was thought what wave theory of light has one in its right and corpuscular theory is wrong. But this happened with a discovery over 40 effects, which could be described by Corpuscular theory but could not be described by Wave theory. What is photoelectric effect, photoelectric effect is a emission of electrons when the light strikes. Where metal surface are coating to Wave theory with smaller wave energy over light. The smaller velocity over emitted electron. However, experiments showed different picture at some threshold of energy. It was no more photoeffect observed. So by loving energy, you had photoeffect, and then it stopped completely. This was contradictory to the Wave theory and this could be described only in terms of new ideas, which were introduced by Max Planck. In the 19th century, where electromagnetic field theory has won and everything was possible to describe in it except over one small thing. It's where emission of a black body in ultraviolet region. This was called ultraviolet catastrophe. What is a black body? The black body is a model. It's a body which absorbs the light of all wavelengths. As a model of a black body, we can imagine a big room with a small hole. The light goes inside, it reflects many times and it's trapped inside the room so it cannot escape. So it's absorbed by this black body. So the classical physics could not describe where radiation of black body, because when you heat with black body starts to radiate light. And Planck introduced a new concept. He said what energy it's transferred by some portions or quants of energy. So he introduced quantization of energy, E equal H it's a Planck constant time to frequency. Using clear ideas of Planck, Einstein could describe the 40 effect theoretically. So, by doing this, he proved with the light can be considered both as a particle and as a wave. So where is a particle wave duality of light? Another important concept of duality comes also from Einstein, which noted equivalence of mass and energy. He's famous formula E equal mc squared, where is E is energy, m for mass and c is where velocity of light shows what where energy is equivalent to the mass. And we can indeed observe where creation, and destruction of the matter. For example, if you have high energy photons, for example, gamma quants with energy above one mega electron volts. Which strikes some particle, aside to the particle and also at this event, two new particles can be born. These particles have electron and anti-electron, positron. And you can clearly see this in Wilson's camera, because where therefore this pair. Electron and positron deviate in opposite directions in where electromagnetic field. So this shows what the matter can be created using energy voltage it is also true. If electron strikes with positron, when they annihilate they distract each other. And they need to go gamma quants, we've total energy of about one mega electron volt. So the matter can be created and the matter can be destroyed with the duality of mass and energy. This positron, it's actually antimatter but it's widely used nowadays in medicine. For example, in positron emission tomography. Veggie is as follows. We can make some nucleus for example, fluorine 18, which is radioactive by striking with oxygen agent from neutrons. Where nuclear reaction is given on this slide. And when we put this radioactive fluorine into some chemical for example, in the sugar on some other stuff and we label this chemical. This chemical goes to their body and it absorbs in certain tumor cells and something like this. And so this fluorine 18 radioactive nucleus, it's half life is only 110 minutes. It distracts and when the positron emitted and the positron is antimatter. It's surrounded by other atoms which have electrons and so it travels very small distance and it finds the electron and it annihilate. And two gamma quants evolved and if you see in the computer tomography. You see the two spots which should gamma quants go to direction 180 degrees exactly. So by simultaneously fixating where two spots in the tomography, you know exactly where the signal comes from. So you locate your tumor, which is very useful for diagnosis in medicine. Another important concept when we go into describe micromere will describe the inner parts of atom is what our common analogies are not working anymore. Therefore, Werner Heisenberg formulated, so called uncertainty principle. It says, what you cannot know exactly the position and velocity or impulse of a particle. So if you know its position, you don't know it impulse and if you know the impulse you don't know the position. This is summarized in this equation with delta x pair, uncertainty over position and delta pair uncertainty over inputs. Actually, the uncertainty principal is also used, for example, for estimation over a lifetime of excited states of some atoms and molecules. Because it's known for its spectrum, it's reciprocal to mean lifetime overexcited state. It's essentially the same uncertainty principle, but written for another case. So in contrast to the classical physics where we exactly know the position and where velocity over particles in the small particles, we cannot do it anymore. We mention big trough about a description of where electron came from Louis De Broglie. Here is as follows the light is both particle and the wave. We know what the electron is a particle can electron be wave also? The De Broglie said, with each particle of mass m, which travels with velocity of v, can be put in accordance with some wave, with wavelength of lambda. And if electron is a wave when such properties of a wave of us interference and diffraction could be also observed for electrons. And indeed, the experiment showed already in 1927 with diffraction of electrons. Later the diffraction of protons heavier Particles was also observed. And therefore, it was established with electron as the light has also duality. It's both a particle and a wave. Nowadays we use these techniques with diffraction of electrons and diffraction of neutrons to study the structure for matter. Because the wavelength which corresponds to about one angstrom. We have electrons of within about 100 electron volts, also called thermal neutrons. And so diffraction of these electrons or thermal neutrons on where chemical bonds or in the crystal structures results in establishing the structure of matter. So first it's important to conclude with electron is both a particle and a wave. And so we can use of a wave or quantum theory to describe the behavior of a electron.