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So, it immediately becomes clear that atoms are mainly composed... of emptiness. Rare head-on collisions should be understood this way: inside the atom there is a positively charged nucleus. Electrons are located near the nucleus. They are very light and therefore do not pose a serious obstacle to the alpha particle. The electrons slow down the alpha particle, but each individual electron collision cannot deflect the particle from its path.
Rutherford admitted that the interaction forces between the similarly charged atomic nucleus and the alpha particle are Coulomb forces. Further assuming that the mass of an atom is concentrated at its nucleus, he calculated the probability of particles being deflected by specified angle and obtained a brilliant agreement between theory and experiment.
This is how physicists test the models they come up with.
Does the model predict the results of the experiment? - Yes. ,
So does it reflect reality?
Well, why so harshly? The model explains a number of phenomena, which means it is good. And its clarification is a matter for the future...
The results of Rutherford's experiments left no doubt about the validity of the following statement: electrons under the influence Coulomb forces move near the nucleus.
Some theories also followed from the theory. quantitative estimates, which were confirmed later. Smallest sizes atomic nuclei turned out to be approximately 10""13 cm, while the dimensions of the atom were of the order of 10-8 cm. ^
By comparing the experimental results with calculations, it turned out to be possible to estimate the charges of colliding nuclei. These assessments played a large, if not the main, role in the interpretation periodic law structure of elements.
So, the model of the atom has been built. But it immediately arises next question. Why don't electrons (negatively charged particles) fall onto the nucleus (positively charged)? Why is an atom stable?
What is incomprehensible here, the reader will say. After all, planets do not fall on the Sun.. Strength electrical origin is, like the force of gravity, a centripetal force and provides Roundabout Circulation electrons near the nucleus.
But the fact of the matter is that the analogy between planetary system and carries only an atom superficial character. As we will find out later, from the point of view general laws electromagnetic field the atom must radiate electromagnetic waves. However, you may not know the theory of electromagnetism. Matter, i.e. atoms,
capable of emitting light and heat. If so, then the atom loses energy, which means the electron must fall onto the nucleus.
What is the way out? It is very “simple”: you need to come to terms with the facts and elevate these facts to the rank of a law of nature. This step was taken in 1913 by the great physicist of our century, Niels Bohr (1885-1962).
ENERGY QUANTIZATION
Like all first steps, this step was relatively timid. We will outline new law nature, which not only saved Rutherford’s atom, but also forced us to come to the conclusion that the mechanics of large bodies is inapplicable to particles of small mass.
Nature is structured in such a way that a number of mechanical quantities, such as angular momentum and energy, for any system of interacting particles cannot have continuous series values. On the contrary, the atom that we are talking about now, or the atomic nucleus, the structure of which we will talk about later, has its own sequence of energy levels, characteristic only of a given system. There is the lowest level (zero). The energy of the system cannot be less than this value. In the case of an atom, this means that there is a state in which the electron is at a certain minimum distance from the nucleus.
A change in the energy of an atom can only occur abruptly. If the jump occurred “up”, this means that the atom absorbed energy. If the jump occurred “down,” then the atom emitted energy.
We will see later how the emission spectra of various systems can be beautifully deciphered from these positions.
The formulated law is called the law of energy quantization. We can also say that energy has a quantum nature. ~
It should be noted that the law on quantization is completely general character. It applies not only to the atom, but to any object consisting of billions of atoms. But when dealing with big bodies, we can often “not notice” the quantization of energy.
The fact is that, roughly speaking, for an object consisting of a billion billion atoms, the number of energy levels increases by a billion billion times. The energy levels will be so close to each other that they will practically merge. Therefore, we will not notice the discreteness possible values energy. So the mechanics that we outlined in the first book practically do not change when we're talking about about large bodies.
In the second book we found out that the transfer of energy from one body to another can occur in the form of work and in the form of heat. We are now in a position to explain the difference between these two forms of energy transfer. At mechanical impact(say when compressed) energy levels systems shift. This displacement is very insignificant and is detected only by subtle experiments and only if the pressures are high enough. As for thermal action, then it consists in converting the system from more low level energy to higher (heating) or from high to lower (cooling).
What holds an electron in an atom in the orbit of the atomic nucleus?
At first glance, especially if you look at the cartoon version of the atom that I described earlier with all its flaws, electrons orbiting around the nucleus look the same as planets orbiting the sun. And it seems that the principle of these processes is the same. But there's a catch.
Fig 1
What keeps the planets in orbit around the Sun? IN Newtonian gravity(Einstein’s is more complicated, but we don’t need it here) any pair of objects is attracted to each other by gravitational interaction, proportional to the product of their masses. Specifically, the Sun's gravity pulls the planets toward it (with a force inversely proportional to the square of the distance between them. That is, if the distance is halved, the force quadruples). The planets also attract the Sun, but it is so heavy that this has almost no effect on its movement.
Inertia, the tendency of objects to move in straight lines in the absence of other forces acting on them, works against gravitational attraction, and as a result, the planets move around the Sun. This can be seen in Fig. 1, which shows a circular orbit. Usually these orbits are elliptical - although in the case of planets they are almost circular, since that is how they formed solar system. For various small rocks (asteroids) and blocks of ice (comets) moving in orbit around the Sun, this is no longer the case.
Likewise, all pairs of electrically charged objects attract or repel each other, with a force also inversely proportional to the square of the distance between them. But unlike gravity, which always pulls objects together, electrical forces can either attract or repel. Objects that have the same, positive or negative charges, are repelled. And a negatively charged object attracts a positively charged object, and vice versa. Hence the romantic phrase “opposites attract.”
Therefore, the positively charged atomic nucleus at the center of the atom attracts lightweight electrons moving at the back of the atom towards itself, much like the Sun attracts the planets. Electrons also attract the nucleus, but the mass of the nuclei is so much greater that their attraction has almost no effect on the nucleus. Electrons also repel each other, which is one of the reasons they don't like to spend time close to each other. One could think of the electrons in an atom as moving in orbit around the nucleus in much the same way as planets move around the sun. And at first glance, this is exactly what they do, especially in the cartoon atom.
But here's the catch: it's actually a double trick, and each of the two tricks has the opposite effect of the other, causing them to cancel each other out!
Double catch: how atoms differ from planetary systems
Fig 2
The first catch: unlike planets, electrons moving in orbit around a nucleus must emit light (more precisely, electromagnetic waves, of which light is one example). And this radiation should cause the electrons to slow down and fall in a spiral towards the nucleus. In principle, in Einstein's theory there is a similar effect - planets can emit gravitational waves. But it is extremely small. Unlike the case with electrons. It turns out that the electrons in an atom must very quickly, in a small fraction of a second, fall in a spiral onto the nucleus!
And they would have done so if not for quantum mechanics. The potential disaster is depicted in Fig. 2.
The second catch: but our world works according to the principles of quantum mechanics! And it has its own amazing and counterintuitive principle of uncertainty. This principle, which describes the fact that electrons are waves just like particles, deserves its own article. But here's what we need to know about him for today's article. General consequence This principle is that it is impossible to know all the characteristics of an object at the same time. There are sets of characteristics for which measuring one of them makes the others uncertain. One case is the location and speed of particles such as electrons. If you know exactly where the electron is, you don't know where it's going, and vice versa. It is possible to reach a compromise and know with some accuracy where it is and know with some accuracy where it is going. In an atom, this is how everything works out.
Suppose an electron falls in a spiral onto a nucleus, as in Fig. 2. As it falls, we will know its location more and more accurately. Then the uncertainty principle tells us that its speed will become more and more uncertain. But if the electron stops at the nucleus, its speed will not be indefinite! That's why he can't stop. If he suddenly tries to fall down in a spiral, he will have to move faster and faster randomly. And this increase in speed will take the electron away from the nucleus!
So the downward spiral trend will be counteracted by the upward trend. fast movement according to the uncertainty principle. Balance is found when the electron is located at a preferred distance from the nucleus, and this distance determines the size of the atoms!
Fig 3
If the electron is initially far from the nucleus, it will move towards it in a spiral, as shown in Fig. 2, and emit electromagnetic waves. But as a result, its distance from the nucleus will become small enough for the uncertainty principle to prohibit further approach. At this stage, when a balance has been found between radiation and uncertainty, the electron organizes a stable “orbit” around the nucleus (more precisely, an orbital - this term was chosen to emphasize that, unlike planets, the electron, due to quantum mechanics, does not have such orbits as planets have). The orbital radius determines the radius of the atom (Fig. 3).
Another feature – electrons belonging to fermions – forces electrons not to descend to the same radius, but to line up in orbitals of different radii.
How big are atoms? Approximation based on the uncertainty principle
In fact, we can roughly estimate the size of an atom using just calculations for electromagnetic interactions, electron mass and the uncertainty principle. For simplicity, we will perform calculations for the hydrogen atom, where the nucleus consists of one proton, around which one electron moves.
The uncertainty principle states:
$$display$$m_e (Δ v) (Δ x) ≥ ℏ$$display$$
where ℏ is Planck's constant h divided by 2 π. Note that he says that (Δ v) (Δ x) cannot be too small, which means that both definitenesses cannot be too small, although one of them can be very small if the other is very large.
When an atom settles into its preferred ground state, we can expect the ≥ sign to turn into a ~ sign, where A ~ B means that "A and B are not exactly equal, but not very different either." This is a very useful symbol for ratings!
For a hydrogen atom in the ground state, in which the position uncertainty Δx will be approximately equal to the atom radius R, and the velocity uncertainty Δv will be approximately equal to the typical speed V of the electron around the atom, we obtain:
How to find out R and V? There is a relationship between them and the force that holds the atom together. In non-quantum physics, an object of mass m, located in a circular orbit of radius r, and moving with speed v around a central object attracting it with a force F, will satisfy the equation
This is not directly applicable to an electron in an atom, but it works approximately. The force acting in an atom is electric force, with which a proton with charge +1 attracts an electron with charge -1, and as a result the equation takes the form
where k is the Coulomb constant, e is the unit of charge, c is the speed of light, ℏ is Planck’s constant h divided by 2 π, and α is the constant we defined fine structure, equal to . We combine the two previous equations for F, and the estimated relationship is as follows:
Now let's apply this to an atom, where v → V, r → R, and m → m e. Let's also multiply the upper equation by . This gives:
In the last step we used our uncertainty relation for the atom, . Now we can calculate the radius of the atom R:
And it turns out to be almost accurate! Such simple estimates will not give you exact answers, but they will provide a very good approximation!
What good readers there are! They not only love and respect natural history teachers, but also know how Bohr’s atomic model explains that electrons do not fall on nuclei.
Or are they falling?
The question “why don’t electrons fall onto nuclei” does not mention the fact that we are talking exclusively about a one-electron atom. Bohr's atomic model (and old quantum mechanics in general) says nothing about the stability of many-electron atoms and molecules. The fact that the “fall” does not occur in a one-electron atom does not guarantee the same for other systems. If you are experts in old quantum theory and undertook to help natural history teachers, then bring your reasoning to the end. For example, I need proof general position unknown.
P.S. The Bohr model can fairly well describe the singlet and triplet states of simple diatomic molecules. We discovered this, however, only in 2005, but better late than never. The construction is quite frontal:
Works a little worse than the original GL theory about chemical bond. By construction, electrons are guaranteed not to fall on nuclei (hurray!), but the model itself is far in spirit from quantizing adiabatic invariants. I saw something similar done for the H2+ ion, but in a more sophisticated version. The idea was to quantize not the integrals themselves, but their sum:
They probably would have been doing this for twenty or thirty years if Schrödinger had not come up with his equation. Figure out how to do even this little thing with the old one quantum mechanics- not easy. Pearson - luminary quantum chemistry, member National Academy, Herschbach - besides Nobel laureate. There is much more in front of you difficult task. We need to create what Bohr failed to achieve: a working general theory multielectronic systems. After this, all that’s left is to prove general case stability of all electron orbits.
Good luck.
P.P.S. Since I have no desire to discuss the topic that the stability of many-particle Coulomb systems in the (new) quantum mechanics explained by the self-adjoint of the Hamiltonian, the phases of the Moon, etc., commentators are advised to read
By the way, why the Heisenberg uncertainty principle alone does not explain the stability of the atom (as claimed by the cream of the Internet issued by Google) is written on pp. 554-555 of this essay, part I.
The positive charge of the nucleus and the negative charge of the electron are in a state of balance, which is why the electron does not fall on the nucleus and does not fly away from it. And yet, under certain conditions, this balance must be disturbed, that is, the electron must literally collapse onto the nucleus, causing the untimely death of the atom. But even from the fact that planets, stars and people still exist, it is obvious that this happens only under very specific conditions. This state occurs when the charge of the nucleus (that is, the number of protons in it) is above 137 (recent calculations have raised this figure to 170), and then theoretically the electron should not just fall onto the nucleus, but generate there its counterparts from the antiworld - positrons, which then fly away into the surrounding space and do all sorts of things.
An artificial atomic nucleus consisting of five calcium dimers on graphene, in an electron cloud located at the collapse boundary (here and below, illustration by M. Crommie).
“Such atoms, as expected, would collapse, “taking” an electron from the vacuum, attracting it to the nucleus and gaining an excess charge,” explains Leonid Levitov from (USA), one of the authors new job dedicated to this topic.
It would seem to be an excellent assumption - in the sense that it is firmly irrefutable: we have not yet been able to find nuclei of atoms above 118 either in nature or create them artificially. For many years now, physicists have been hoping to take the stronghold, if not by starvation, then by cunning. Since such heavy elements cannot be obtained, they are trying to achieve a similar effect by colliding two nuclei (for example, uranium with atomic number 92) on particle organizers. “Such experiments have been carried out for decades,” Mr. Levitov comments on the situation. But, of course, there was no clear evidence of atomic collapse.
Therefore, the authors of the work in question proposed using a new trick to simulate such a collapse. In graphene - a monatomic-thick lattice of carbon atoms - electrons, due to the unusual topology of this material, behave like massless particles, although in fact they have mass. However, they move at speeds much lower than real massless particles. This means that states that are formally similar to the collapse of atoms with the participation of such electrons can be caused with the same amount of less nuclear charge.
Physicists used pairs of calcium atoms (dimers) on a graphene substrate as substitutes for atomic nuclei. Using as a scanning manipulator tunnel microscope, they received clear evidence of an event completely analogous to the collapse of atomic nuclei.
A normal electron around a normal nucleus (like the ones you and I are made of) and ultra-relativistic electrons around an unstable supercritical nucleus.
Once three such dimers were close enough to each other, the surrounding electron field showed a specific spectrum of resonances that exactly matched those predicted for atomic collapse a decade ago. The observed resonances were also preserved for artificial “atomic nuclei” of four and five dimers.
Although the idea of the experiment was to confirm long-standing quantum mechanical predictions about the collapse of atoms, its applications may be somewhat practical. Firstly, as it turns out, it is possible to study many of the properties of graphene, which is now being actively promoted as a material for electronics. Secondly, such sensitivity of artificial “atoms” on graphene allows us to hope for the use of such structures as detectors of chemicals and biomarkers.