In Bohr's atomic model, there is a quantum number called orbital quantum number, also called principal quantum number, which is represented by the letter n, so why is the orbit of electrons discontinuous? Bohr said that the angular momentum of electrons moving around the nucleus is quantized and can only be an integer multiple of the reduced Planck constant H.
So the first energy level of an electron is called the ground state, and the second, third and fourth energy levels are called the excited state. After electrons absorb enough energy, they will jump to the excited state in a ghostly way. As for which excited state it is, it depends on how much energy the electron absorbs.
When an electron is in an excited state, it will spontaneously jump back to a lower energy level, releasing the energy difference between the two energy levels in the form of electromagnetic waves.
Based on the above assumptions, Bohr's atomic model explains the emission spectrum of hydrogen atoms and explains why Balmer formula is effective. For balmer formula, you can watch the video of the tenth episode.
In the emission spectrum of hydrogen atom, there are a series of emission lines in visible light band, called Balmer system, which are located in red light, green light, blue light and purple light respectively. These four lines are released when electrons jump from the third, fourth, fifth and sixth excited states to the second excited state respectively.
However, it was later found that the Balmer system of hydrogen atom spectrum is not a simple four-wire system. If a more accurate spectrometer is used to split the spectrum of hydrogen atoms, it will not work. If you look at the Balmer system of hydrogen atom with a magnifying glass, you will find that each spectral line is actually not one, but two, with a small crack in the middle.
I didn't find it before because the wavelength difference between these two lines is very small, and the two lines are very close. At first glance, I thought it was one. This discovery is called the fine structure of hydrogen atom spectrum.
Bohr's atomic model can't explain this problem. Soon, Sommerfeld of Munich University wrote a letter to Bohr, and the contents of the letter solved this problem perfectly. Sommerfeld added a quantum number to Bohr's atomic model: angular quantum number, which can be called orbital shape quantum number and is easier to understand.
At that time, 48-year-old Arnold sommerfeld had passed the golden age of a theoretical physicist, but the physics department of the University of Munich he led was about to become the research center of quantum mechanics, because he was about to welcome two students, one was Pauli and the other was Heisenberg. The other two research centers of quantum mechanics are the Physics Department of the University of G? ttingen led by Bonn and the Bohr Institute to be established soon. These three places are called the golden triangle of quantum mechanics.
Sommerfeld studied mathematics at first, then turned to theoretical physics. He came from the same place as the great mathematicians Hilbert and Minkowski, where there was a strong mathematical atmosphere and he was a mathematician.
You can see how awesome Sommerfeld is from the attitude of two people towards him. The first one is Einstein, who generally doesn't value anyone easily and doesn't take the initiative to compliment anyone. At school, Minkowski was so angry that Einstein was a "lazy dog".
However, Einstein said in his letter to Sommerfeld that if I were in Munich, I would definitely come to you to study math and physics. At this time it was 1908, and Einstein was still working in the patent office. You see, whether it is true or not, Einstein never said such a thing to others.
The second person is Paulie. Pauli, who made great efforts to find air, basically found all the people who could find air. People gave him a nickname: God's whip. But whenever I see Sommerfeld, no matter what the occasion, Pauli will immediately get stiff, which is a respect for Sommerfeld. This may be the charm of personality.
Back to the topic, sommerfeld got a key message from the fine structure of hydrogen atom spectrum. The line is split, indicating that two electrons with different energy levels jumped to a lower energy level, but the crack is not big, indicating that the energy difference between the two electrons is not big, very small.
In Bohr's atomic model, electrons revolve around the nucleus in a circular orbit. Sommerfeld thought, can electrons revolve around the nucleus in an oval shape?
He immediately calculated that if the electron rotates around the nucleus in an elliptical orbit, his speed will be different from that of the electron in a circular orbit. If the relativistic effect of electron motion is considered, the electrons in the elliptical orbit will gain higher mass because of higher speed, so there will be a slight energy difference between the two orbits.
This energy difference just corresponds to the energy difference of two spectral lines. If electrons jump to circular orbit and elliptical orbit, the wavelength of electromagnetic radiation released is slightly different due to different energy levels.
That is to say, Sommerfeld quantized the orbital shape, which was represented by the letter L. In the past, Bohr's orbit was a circular orbit, and when principal quantum number n was 1, it was 2, it was 3, and so on, and only one circular orbit could hold electrons.
Now that the orbital shape is quantized, electrons have many choices. The value of l is an integer between 0 and n- 1. For example, when n= 1, l can only take one value, which is 0. At this time, the hydrogen atom has only one circular orbit.
When n=2, then l can take 0 and 1, and there are two possible quantum state orbits, so the spectral line splitting is solved.
N=3, l can take 0, 1, 2, n=4, l can take 0, 1, 2, 3, that is, principal quantum number n determines the value of angular quantum number L.
When l=0, the orbit is round, which is called Bohr orbit, and all orbits greater than 0 are different ellipses, which is called sommerfeld orbit, so the extra quantum state can explain the fine structure of the spectrum of hydrogen atoms.
But there is a magical constant in Sommerfeld's formula, called the fine structure constant α, which is the ratio of the linear velocity of electrons in the first Bohr orbit to the speed of light in vacuum. This is a dimensionless constant, that is, there is no unit. The value is about1137.
The formula is what you see in the picture, so you can get a general idea. Where e is the charge of the electron, ε (ε) is the vacuum dielectric constant, C is the speed of light, and H is the reduced Planck constant, that is, H/2π.
At first glance, the fine structure constant is a combination of some other physical constants, which seems to have no special significance, but with the development of quantum mechanics, it becomes more and more magical.
For example, the improved classical electrodynamics, called quantum electrodynamics, is used to describe the electromagnetic interaction between charged particles. It is found that any electromagnetic phenomena is related to this fine structure constant, which indicates the intensity of electromagnetic interaction.
Later, people developed quantum chromodynamics to describe the intensity in the nucleus, and also found a similar fine structure constant, which determines the intensity of strong interaction.
Later, people unified the weak force and electromagnetic force, and of course, the weak-current interaction also has fine structural constants. So now it is suspected that gravity is also related to the fine structure constant, which represents the strength of gravity.
More strangely, after analyzing the spectra of distant quasars, astronomers found that the fine structure constant 65.438+0.2 billion years ago was smaller than the current value, which indicates that the fine structure constant may not be a constant, but is increasing slowly, with a very small change rate of one in 30 trillion per year. Because the fine structure constant represents the strength of the basic force, if this constant changes, the force acting on everything will also change.
You may think that there are some constants in the fine structure constant formula. Why the fine structure constant becomes larger can only show that some of them are not frequent, but a variable.
Looking around, people suspect that c, that is, the speed of light, may be the reason for the change of fine structure constant. At present, these are all speculations. C is not a constant, then Einstein will cry.
It's a little far-fetched Back to the topic, continue to talk about sommerfeld's atomic model.
Now Sommerfeld has added an orbital quantum number, also called angular quantum number, to Bohr's atomic model. Besides principal quantum number n, there is a quantum number L now, but this is not enough, because the modified atomic model still cannot solve the following two problems.
One is Zeeman effect and the other is Stark effect. Zeeman effect says that if you add a strong magnetic field to an atom, you will find that the original single spectral line will split into three lines, and when you remove the magnetic field, it will return to normal. Adding an electric field has the same effect, that is, stech effect.
After Sommerfeld solved the fine structure of spectral lines, he was familiar with this problem. Since the spectral line can be split, it means that there is still a quantum number that has not been discovered.
Consider first, what will the electromagnetic field interact with? Charged particles, when electrons revolve around the nucleus, will produce magnetic moments, which will interact with the electromagnetic field and deflect the orbital direction of electrons.
In the past, the electron's orbit was flat, but now the electron's orbit may have an angle with this plane, so the electron has more energy states to choose from. So how many inclined orbits can electrons choose?
Judging from the number of split spectral lines, there is no infinite orbit for electrons to choose from, otherwise the spectral lines will be split into countless ones, which shows that the spatial orientation of orbits is also quantized.
In this way, the flat atomic model has become a spherical shell structure. So how many orbital directions can electrons choose?
Sommerfeld uses ml to express orbital quantum number, also called magnetic quantum number. Its value is related to angular quantum number L. ml can be an integer from -l to L. For example, when l=0, ml can be 0, and when L is equal to 1, ml can be-1, 0, 1, L.
It can be seen that the angular quantum number L and the magnetic quantum number ml are both related to the value of principal quantum number n. When n= 1, l=0 and ml=0, which is the quantum state of hydrogen atom electrons in the ground state. At this time, the electron orbit is circular, the orbit has no spatial orientation, and the atom is spherically symmetric.
When n=2, then l=0, 1, ml=- 1, 0, 1. At this time, the electron not only has an elliptical orbit, but also has two orbital directions, so the atom is dumbbell-shaped.
When n=3, then l=0, 1, 2, ml=-2,-1, 0, 1, 2, which are two elliptical orbits with four orbital directions, and the atomic shape presents a four-petal shape.
With the increase of magnetic quantum number, the optional energy states of electrons increase again, which can explain Zeeman effect of spectral splitting under magnetic field and Stark effect under electric field.
After Sommerfeld's improvement, there are three quantum numbers in the current quantization model, namely principal quantum number N, angular quantum number L and magnetic quantum number ml.
So the current atomic model is renamed Bohr-Sommerfeld atomic model. The success of the atomic model once again made Bohr famous. 19 16 in may, the university of Copenhagen directly established the position of professor of theoretical physics for bohr.
Bohr, who lived with Rutherford, will definitely not be satisfied with this. He also wants to be as versatile as his teacher. 19 17, Bohr suggested to the school whether it was possible to build a theoretical physics research institute. Combined with the management of academic efficiency, since the discipline of theoretical physics has been established, it is not unreasonable to build a research institute. Bohr wants to find a way by himself, which is a question of money and land.
This is a small matter for Bohr. As long as money can solve the problem, it is not a problem for Bohr. Shortly after the end of World War I, the institute began to build, located next to a park. 192 1 On March 3rd, the Bohr Institute was formally established.
Later, the institute attracted many young people to study. At that time, there was a saying that all roads lead to "Piaobutang Road 17", which is the address of Bohr Institute.
During the construction of Bohr Institute, Rutherford wrote back to Bohr, saying that there is a position of theoretical physics professor in Manchester now, and you are here to work with us. Obviously Bohr can't go at this time. Rutherford went to Cambridge, England 19 19 when Bohr didn't come, and took over the position of his teacher Thomson, so Rutherford became the fourth director of Cavendish Laboratory.
Bohr's atomic model now seems to have achieved a staged victory, but soon people discovered a new problem, called the abnormal Zeeman effect, which is the normal Zeeman effect, and now there is an abnormal Zeeman effect.
That is to say, under the weak magnetic field, the single spectral line of hydrogen atom will not split into three, but into four or five, which is abnormal, so it is called abnormal Zeeman effect.
The person who solved this problem is no longer these old guys, but a young man after 00. 1900. His name is Paulie. I'll talk about Pauli in detail later.
If you fully understand the Bohr-Sommerfeld atomic model, you will have a feeling that the quantized atomic model is actually a freak born after the combination of classical physics and quantum theory.
Bohr explained the atomic model on the basis of classical physics, for example, we still regard the electron as a small ball, which has the angular momentum of classical physics, the orbit and velocity of classical physics and so on.
However, the quantization of atomic models is incompatible with classical physics everywhere, so the current quantum theory has no soul, that is to say, there is no basic theory suitable for it.
If the quantization of electrons can be deduced step by step from a more basic axiom hypothesis, then this theory has a solid foundation.
For example, Bohr said that electrons have quantized orbits and energy levels, so what is its theoretical basis? This is the question we will answer in the next video.
Now our series has almost finished the old quantum theory, leaving De Broglie's wave-particle duality, Pauli's exclusion principle and quantum spin.
When the old quantum theory is finished, we will enter the stage of quantum mechanics.