Why does an electron not lose energy

Big Bang HTL 4, textbook

The modern atomic model 13 Thermodynamics and modern physics (IV. Jg., 8th Sem.) 123 So you see: From a classical point of view, the particles would in any case “stick” to one another and be outwardly neutral. But what happens in reality when an electron meets a proton? A hydrogen atom is created! So you see why it was impossible to find a conclusive atomic model at the beginning of the 20th century. From a classical point of view, atoms should not even exist! But what prevents the atom from collapsing? The uncertainty relation! The uncertainty principle leads to a very spectacular conclusion: the smaller the space in which a quantum is locked, the greater its energy, the so-called localization energy (F6). The closer the electron is drawn to the proton, the less its spatial uncertainty and the greater its localization energy. This adds up to the potential energy given by the attraction between the particles. The electron-proton system now adjusts itself in such a way that the sum of energy becomes a minimum (Fig. 13.6). Info: Localization energy A stable state is established in which the energy sum is a minimum. However, this in turn results in a very specific positional blurring of the electron. This positional uncertainty corresponds to the radius of the atom (Fig. 13.7). In quantum mechanics, the concept of orbit loses its validity. So the electron is more or less about the Why does the term orbit lose its meaning in quantum mechanics? Read up in chap. 12.5! An electron meets a proton in empty space. Because they are oppositely charged, they attract each other. The proton has a mass around 2000 times that of the electron. What happens at this meeting? What happens to the kinetic energy of a quantum that is locked in a confined space? Think with the help of the uncertainty relation! F4 F5 F6 Fig. 13.6: Energy of an electron in the field of a proton: The potential energy created by the electrical attraction and the localization energy, which is a consequence of the uncertainty relation, add up. to find the entire area of ​​the spatial blur. To put it bluntly, it is everywhere and at the same time nowhere. The area where the electron is located is also called the orbital. a b Fig. 13.7: a) According to the classical view, only the potential energy exists and the electron “falls” into the potential well, so towards the proton. b) From a quantum mechanical point of view, there is also the localization energy, which increases with the approach. The electron stabilizes with a positional uncertainty ∆ x, which corresponds to the atomic radius. It is paradoxical and at the same time fascinating: that which gives all things mass (the atomic nucleus) has almost no volume. What gives things volume (the electron shell) has almost no mass. And about localization energy. The uncertainty relation shows that as the spatial uncertainty decreases, the impulse uncertainty must increase. If one “locks up” a particle, then its momentum p inevitably increases, because this cannot of course be smaller than the momentum uncertainty: p ≥ ∆ p ≥ h ___ 4 π∆ x Classically, the momentum of a particle is p = mv and the kinetic energy E = (mv 2) / 2. If you insert into the energy equation for v = p / m and link the whole thing with the uncertainty relation, you get: E kin = mv 2 ___ 2 = p 2 ___ 2 m ≥ (∆ p) 2 ____ 2 m ≥ ( h ___ 4 π∆ x) 2 _______ 2 m ≥ h 2 _________ 32m π 2 (∆ x) 2 Two things can be derived from this: 1) The kinetic energy of an electron in the atomic shell cannot be zero. 2) The closer you lock the electron, the greater the kinetic energy and vice versa. The following applies: E kin ~ 1 ____ (∆ x) 2 Important: This kinetic energy does not come about through any movement, but solely through the restriction of the occupied area. That is - admittedly - difficult to understand! Because this energy arises through the restriction of the place, ie through the localization, it is called localization energy. i For testing purposes only - property of the publisher öbv

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