First, Rutherford's atomic model is unstable. Electrons running around the nucleus will release electromagnetic radiation, causing electrons to fall into the nucleus instantly.
Secondly, Rutherford did not say how electrons are arranged outside the nucleus. Of course, at this time, people don't know the essence of the chemical properties of elements, let alone why the chemical properties of elements in the periodic table show periodic laws.
Let's start with the first question. Electrons fall into the nucleus, which is the result of classical mechanics and classical electromagnetism prediction. As long as you believe that classical physics is correct on the atomic scale, Rutherford's atoms are bound to collapse.
So how did Bohr consider this problem? He had to choose between classical physics and Rutherford's atomic model. Obviously, he believes that his teacher's model is correct.
Then Bohr must answer why the atom didn't collapse. Bohr believes that this only shows that some conclusions of classical physics are not applicable at the micro scale.
If atoms don't collapse, we can only assume that electrons can run in certain orbits, and electrons running in these orbits don't release radiation.
These orbits are called the steady-state orbits of electrons. That is to say, the orbit of electrons outside the nucleus does not run around the nucleus at any distance as in classical physics, but the electrons have a specific orbit and are not continuous.
For example, our solar system has only the sun and the earth, and the earth's orbit around the sun can be any size. The distance between the earth and the sun can be 80 million kilometers, 65.438+0 billion kilometers, 65.438+0.33 billion kilometers, any number you can think of.
But Bohr now says that the earth can only run in the orbits of 0/100 million kilometers, 200 million kilometers and 300 million kilometers away from the sun/kloc-,and it is impossible for the earth to exist in any orbit except these allowed orbits.
The same is true of electrons, which can only run in a specific orbit, and atoms are stable and will not collapse.
This is the first clue discovered by Bohr, assuming the existence of steady-state orbits, or that the orbits of electrons are discontinuous. But Bohr knows very well that there is a circular argument here, that is, why electrons have stable orbits, because they don't radiate energy in these orbits, and why they don't radiate energy in these orbits, because these orbits are stable orbits.
You see, this circular argument is obviously unconvincing, so Bohr needs to find a second clue to explain why the orbits of electrons are discontinuous, and what is the energy of electrons in these orbits? What is the radius of each stable orbit?
Bohr doesn't want to work in order to consider this problem. At the end of 19 12, he took a few months off and found a secluded country to think about this problem.
On Christmas Eve, he came across a key point in John Nicholson's paper, which was the second clue that Bohr needed to find.
Nicholson is no stranger to Bohr. This man was known when he was studying in Cambridge, and he didn't leave much impression on Bohr at that time. Nicholson proved such a thing in his own paper.
In classical physics, any object with mass has momentum when it moves. How to calculate momentum? Mass times speed, and an object moving in a circle also has momentum, but it is called angular momentum, which is equal to mass times radius and then linear velocity.
Classical physics has no restrictions on the magnitude of angular momentum, that is to say, angular momentum is also continuous, but Nicholson found that the angular momentum of electrons is not continuous.
Its angular momentum must be an integer multiple of H/2π, and H/2π is the quantum of angular momentum, which is the smallest unit of angular momentum, expressed by H, also called reduced Planck constant;
For example, the angular momentum of an electron can only be 1 times h, 2 times h, 3 times h, and so on until n times h.
This is Bohr's second clue. During this period, Bohr wrote to Rutherford many times and told him to give him the atomic paper as soon as possible. Rutherford wrote back: Don't put too much pressure on yourself. But Bohr knew that his colleagues were studying the atomic model now, so Bohr was very anxious.
Bohr now knows why an atom can only run in a specific orbit, because its angular momentum is quantized, so its orbit is quantized.
Bohr uses the letter n to represent the orbital quantum number of electrons, and n can only be a positive integer. In each orbit, electrons have their own specific orbital energy, called energy level, which is expressed by en.
Bohr took the hydrogen atom as an example and calculated the energy level and orbital radius of each electron of the hydrogen atom. For example, when n is equal to 1, the electron is at the lowest energy level, which is called the ground state, and the energy is-13.6 electron volts. Ev is a unit of energy, which represents the kinetic energy obtained by an electron passing through a potential difference of 1 volt.
This energy unit is very small, and it is specially used to represent the energy at the atomic level. In our daily life, we don't use electron volts, but joules. The reason is that the electron volt is too small to write.
For example, 1 electron volt is equal to 1 .602×10-19 joules, and each watt is equal to1joule per second. If the energy released by a 100 watt light bulb in life is expressed in electron volts, it can be written as: 6.24× 65438+. This is an astronomical figure, enough to see the size of electron volts.
Back to the topic, let's go on to say that the energy of the atomic ground state has been calculated. What about other energy levels? Other energy levels are also called excited States. Bohr found that the energy of other energy levels is equal to the energy of the ground state divided by the square of the orbital quantum number, that is, (e? /n？ ), for example, when n equals 2, the orbital energy of this energy level is equal to-13.6ev/4, and the result is -3.4ev.
Bohr also calculated that when the electron is in the ground state, the size of the hydrogen atom is 5.3 nanometers, and the orbital radius of other energy levels is the orbital radius of the ground state multiplied by the square of n. For example, the orbital radius of the ground state is r, so the orbital radius where n equals 2 is 4r, and so on, which is 9r, 16r.
So far, Bohr has established a quantized atomic model, but a correct theory needs to explain some phenomena that people can't explain before, otherwise the theory will be empty and useless.
So Bohr needs to find a third cable to finish his atomic paper. So where is the third cable? Bohr met a friend of his, Hans Hansen, at the University of Copenhagen. This friend also came back from studying abroad. His place of study is Gorgen University. As mentioned in the previous video, Germany is the frontier of spectroscopy research.
Of course, Hans also mastered a lot of spectroscopy knowledge. He asked Bohr, can your atomic model explain the emission spectrum of atoms? He suggested that Bohr know the Balmer formula of hydrogen atom spectrum. We have talked about the emission spectrum of atoms in detail in the previous video, so I won't go into details here.
However, when it comes to balmer's formula, we have to rewind the time to 1850. This year, physicist Anders measured the emission spectrum of hydrogen atom in detail. In the visible light range, the hydrogen atom has four spectral lines, which are located in the red, green, blue and violet regions, and the corresponding wavelengths are 656.438+00, 486.072 and 386.072 respectively.
People at that time were curious. How do you think the spectral line of this atom came from? Why is it discrete, not continuous? These two questions are difficult to answer, and Bohr will solve them today.
However, people at that time made great breakthroughs. Now that the wavelengths of four spectral lines of hydrogen atoms in visible light have been measured, what is the relationship between these wavelengths? Can it be expressed by mathematical formula?
This is about to mention a math teacher in a Swedish middle school. His name is John balmer. He often complains to his friends that he is bored every day and there are no math problems bothering him. His friend told balmer, why don't you find out the relationship between the wavelengths of the spectrum of hydrogen atoms, that is, the relationship between the above four numbers.
This old man is really awesome. No wonder he is bored all day. 1June, 884, balmer really expressed these four spectral lines with a formula. This formula looks like this.
Where m and n are positive integers, and b is a constant with a value of 364.56 nm. When we make n equal to 2, m takes 3, 4, 5 and 6 respectively, and the calculated wavelength is exactly the above four numbers, which is really amazing. These four spectral lines are now also called Balmer system of hydrogen atom spectrum.
Old Balmer thought, can this n be other numbers? For example, n equals 3, and m takes 4, 5, 6, 7. What does the calculated wavelength represent?
It has been proved that Balmer's formula predicts the emission spectra of hydrogen atoms in the infrared region. These spectral lines were discovered by Paschen in 1908 and named Paschen system.
What about n = 1? M takes turns to take values. What is it? This is the emission spectrum of hydrogen atom in ultraviolet region, which is now called Lyman system.
I have to say that mathematics is really amazing. No wonder some people say that mathematics is a natural language. Balmer formula successfully predicted the emission spectrum of hydrogen atoms, but no one knows why this formula is so useful. No one knows the physical meaning behind this.
Bohr saw this formula and immediately knew what was going on. This is the transition of electrons between different energy levels. When n is equal to 1, this is the ground state, and m is equal to 2, 3, 4, 5, 6, all of which are excited States. When the electrons in each excited state transition to the ground state, the energy difference between the two energy levels will be released in the form of electromagnetic waves. The wavelength can be directly calculated by Planck-Einstein formula.
At this point, Bohr completed the transformation of Rutherford atom and quantized the atomic model. He quantized the angular momentum of electrons and added a quantum number to the atomic model, which can be called orbital quantum number. It is now called the principal quantum number and is represented by n.
19 13 In March, Bohr gave Rutherford the first part of the paper. You may feel strange. At this time, Bohr was completely independent. Why should he give it to Rutherford first instead of publishing it directly?
There is a simple reason. Although Bohr is independent, he is still very young. If a respected person can write a message to the paper, he can improve his influence and make the paper published quickly.
Secondly and most importantly, Bohr really respects his teacher. Although Rutherford's hesitation once led Bohr to miss a discovery, Rutherford's evaluation of him is still very important in Bohr's heart.
After reading the paper, Rutherford really put forward a lot of critical opinions, such as Bohr's theory that electron jumps from one orbit to another, just like the flash skill in the glory of the king, which makes Rutherford feel that he has hit a ghost and is unacceptable.
Also, if the electron is now in the third excited state and can jump like the second orbit and the ground state, how can the electron choose which orbit to jump to?
If you jump to the second excited state, why do electrons choose the second excited state directly instead of the ground state? If the electrons jump directly to the ground state, why not choose to go to the second excited state first?
In Rutherford's view, electrons seem to have free will. To put it bluntly, they violated the law of causality. You see, people's world outlook began to crack from Bohr, but Rutherford didn't think much about it and didn't embarrass Bohr, because Bohr couldn't get the answer either.
19 16 years, Einstein also found that the electronic transition violates the law of causality, and it is necessary to explain its transition time and energy level with probability. Einstein introduced probability into quantum theory for the first time. He also wrote to Bonn that he could not accept the explanation of probability he found. Now it seems that Einstein is quite interesting. He promoted the development of quantum theory himself, but in the end he couldn't accept it. The following video will mention this again.
Rutherford couldn't accept the above two points, but he didn't like Bohr to write too long and asked for a shorter length. Bohr is dead to the end this time. He won't change his paper or even a symbol.
May be the last time Bohr suffered a loss, this time long memory, Rutherford kept writing letters, but also went to Manchester to find Rutherford, living in the teacher's house, Rutherford was exhausted by Bohr this time, and finally made concessions and agreed to publish Bohr's paper.
19 13 in July, September and 10, Bohr's three papers were published verbatim in the Journal of Philosophy, which is known as the "trilogy".
In the next 10 year, Bohr explained the periodic table with his atomic model, which is the second problem I mentioned at the beginning.
10 years, juvenile Pauli, Heisenberg and Dirac are all growing. What they have heard most in their study career is Bohr's atomic theory's explanation of atomic spectrum and periodic table of elements, and they all regard Bohr as their idol.
However, Bohr's atomic model was not recognized immediately after it was published. He needs two more experiments to verify it. This is the content of our next video.
Since then, we have really set foot on the quantum world, and you will find many incredible phenomena.