New hydrogen atom model and radiation absorption mechanism


 Only Coulomb force is considered in Bohr model. It is found that electron in ground state hydrogen atom is also affected by Lorentz force of the same magnitude. Under the combined action of Coulomb force and Lorentz force, the radius of hydrogen atom is twice that of Bohr, and the rotation frequency of electron is half that of Bohr. The "half frequency" problem of Bohr's theory is solved, and the quantization result of the energy level of hydrogen atom is obtained by using the standing wave condition of quantum mechanics. The mechanism and details of photon absorption by hydrogen atom are analyzed and explained, and the physical meaning of Planck constant is explained.


Introduction
As early as the 1850s, people found four lines of hydrogen in the visible spectrum of sunlight: Hα, Hβ, Hγ and Hδ. In 1884, Balmer, a middle school teacher in Switzerland, proposed a simple formula for calculating the wavelengths of these spectral lines [1] (1) 4 where n is any positive integer greater than 2, and Ba=3645.6×10 -10 m.
In 1890, Johannes Robert Rydberg of Sweden independently put forward a more general formula for the spectrum of hydrogen atom [2] (2) ) 1 1 ( R where ṽ is the wave number of the spectral line (cm -1 ), n1 and n2 are positive integers, and n1 < n2; Ry is the Rydberg constant, and the determined value in 1987 is Ry = 109737.31573(3) cm -1 [1] . If n1 = 2, and let n2 = n, the formula (2) can be simplified as Balmer formula (1); If n1 = 1, and let n2 = n, we obtain the Lyman series formula.

Rydberg frequency and Rydberg radius for hydrogen atom
With the speed of light c，let cṽ = ν and cRy = fR, formula (2) can be rewritten as Look at both sides of equation (3). The left, the ν is the frequency of the radiation photon. The right, the fR should be a fundamental frequency of the atomic vibration, and here, we call it the Rydberg frequency. fR = cRy =2.998×10 8 m/s × 1.0974×10 7 m -1 =3.290×10 15 s -1 . (4) According to modern knowledge, the electron in the ground state hydrogen atom moves in a circular orbit, and the ratio of its speed to the speed of light is a constant, which is the fine structure constant α [3] 。 υ=cα = 2.998×10 8 m/s × 1/137.0 =2.188×10 6 m/s (5) If f R is a fundamental frequency，a radius corresponding the ground state orbit of hydrogen atom, rR, can be calculated Here, we call rR the Rydberg radius. In formula (2), 2 R n f is a frequency corresponding the orbital resonance of hydrogen atom at the nth level.
The rR value obtained here is obviously different from the orbital radius of the ground state hydrogen atom in the current textbooks. In fact, it is only inconsistent with the Bohr radius in Bohr model named after a Danish physicist, Niels Bohr. This issue will continue to be discussed in section 3, and resolved in section 4. In this paper the solution for this problem will be a great breakthrough for the current theory, and also become the theoretical basis for discussing the mechanism of atomic absorption radiation.

Bohr model and Bohr radius
In 1913 Bohr assumed that electrons in atoms move in some stable orbits, different orbits belong to different energy levels, and that electrons moving in these stable orbits neither absorb nor radiate photons; Electrons absorb or radiate photons only when they jump between different levels. He first dealt with the hydrogen atom，and the lowest energy orbit is called the ground state [4] .
When an object moves in a circle with velocity (υ), if the radius is r, the centripetal force (FX) it receives is where m is the electron mass when it is in hydrogen atom. According to Newton's third law, Bohr thinks that the Coulomb force FC between electron and proton provides centripetal force to balance the circular motion.
where e is the charge of proton or electron, ε0 is the dielectric constant in vacuum. At that time, Bohr thought that in an equilibrium system of hydrogen atom , FC = FX, and by combining formula (7) and formula (8), the following formula is got For the hydrogen atom in the ground state, all the physical quantities in formula (9) are constants.
According to either the quantization condition supposed by Bohr or formula (5) The rB value is only a little larger than the covalent radius of hydrogen, so the calculated value of Bohr has been considered reasonable. Bohr also derived the expression of Rydberg constant by known physical constants [4] c h Obviously, Bohr's success began with "general mechanics". However, he also encountered a lifelong trouble. The main problem is that rB is only half of the Rydberg radius rR calculated in (6) above. In other words, Bohr's calculation of the circular orbital frequency (fB) for the ground state of hydrogen atom is twice as large as the above Rydberg frequency (fR) by formula (4). The frequency fB calculated by Bohr must add a 1/2 factor to be consistent with the empirical Balmer formula [4,5] (13) 2 ) ( After introducing this "half frequency" factor, Bohr can deduce Balmer formula and Rydberg constant from classical mechanics theory. Therefore, Bohr has great confidence in his classical theory.
He insisted that quantum mechanics should be a theory as little as possible divorced from classical mechanics [6] . According to the missing radiation mechanism in quantum theory, Bohr tried to restore the relationship between radiation and electron motion in quantum theory similar to classical radiation theory. However, Bohr did not succeed in his life. Not only did he not put forward new hypotheses about the mechanism of radiation, but after 1924 he began to avoid the original hypotheses [5] . He can only use the limiting case where n→∞, n-1→n, under high quantum number to weaken the "half frequency" difference, which is the correspondence principle he later advocated [7] .

Lorentz force in hydrogen atom
By this paper it is found that the "half frequency" problem perplexing Bohr's whole life is due to a fact that Bohr only considers the electrostatic Coulomb force (FC) between electron and proton in his theoretical derivation (Fig. 1A) . The electron in the hydrogen atom is moving, and there must be a magnetic field B in the atom. In addition to Coulomb force FC, electrons in atoms are bound to be affected by Lorentz force FL.
In Lorentz force can also provide centripetal force for electron in circular motion. The Coulomb force and the Lorentz force are two independent forces, and both they should exist in the hydrogen atom.
If the electron charge is q, the electron velocity is υ，the electric field is E and the magnetic field is B, then the force F on the electron can be given by the following Lorentz equation In formula (14)  The right-hand rule can determine that the magnetic field generated by protons is perpendicular to the paper plane and inward. According to the left-hand rule, the direction of Lorentz force (FL) on the electron points to the center along the radius.
We don't know the values of B in formula (14) and (15). However, we can directly analyze the existence and magnitude of FL from following three aspects.
First, as shown in Fig.-1B, it is unrealistic to require a uniform magnetic field B in the whole atom. However, it is possible that there is an equal magnetic field B along the orbit of the electron, which is synchronous with the motion of the electron.
Second, we can learn about electrons by photons. In isotropic space, the electromagnetic energy of photon is [8] (17) ) 2 In this derivation, we use the formula (20), that is, F C = F L in the ground state hydrogen atom. When the hydrogen atom is in the external electric or magnetic field, the forces felt by the electron, FC ≠ FL, which will split the energy levels and the spectral lines. The splitting in the applied electric field is called Stark effect, and the splitting in the applied magnetic field is called Zeeman effect [9] .
Here, we have completely solved and eliminated the "half frequency" problem encountered in Bohr's theory. On the other hand, it also proves that Bohr's idea of using classical mechanics to explain radiation mechanism is correct.

Force analysis for electron in photon field
Now we can boldly follow Bohr's original idea to discuss both the atomic radiation mechanism and details by the classical mechanics and the standing wave theory in quantum mechanics.
A photon can be regarded as a long wave train represented by Poynting vector [10] . According to the duration of the atomic emission τ0 ≈ 10 -10 seconds [11,12] , we can estimate that the length of a photon wave train of visible light is about 4~7 × 10 4 wavelengths. As shown in  Figure 2 shows that a photon will be absorbed by a ground state hydrogen atom, and the electron orbits counterclockwise. In the absorption collision, the four phases a, b, c and d in the photon period are roughly synchronized with the four phases a, b, c and d in the orbital period of the ground state hydrogen atom.

1) Nuclear electric field E N
When an electron moves in a circle around the nucleus, the nuclear electric field only provides centripetal force, and Coulomb force is perpendicular to the velocity of electron motion, and does not change the electron velocity.
When an electron moves elliptically around the nucleus, the Coulomb force produces a component in the direction of the electron velocity. When the electron goes far, it slows down the electron, and it accelerates when it approaches. The nuclear electric field is a conservative potential field, which does not change the average velocity of electrons.

2) Photon B field
In Figure 3, when the electron moves to the left and reaches point a, the field strength of photon B field is zero, and the electron is not forced. When the electron moves from a to b, the photon B field increases gradually, and the direction is perpendicular to the paper plane and inward. The direction Fig.3. In a process of absorption collision, the photon moves to the right, which is equivalent to the electron moving to the left at the same speed into the photon field. The direction of Coulomb force is the same with of Lorentz force, both the two forces are to move the electron far away from the atomic nucleus along directions of +y and -y, respectively, and the period of revolution enlarges with the increase of radius.
hydrogen atom z y z of the Lorentz force on the electron is always perpendicular to the direction of motion, that is, along the radius outward, and the component in the y direction gradually increases. When the electron reaches the b point, the Lorentz force of the photon field is the largest, and its direction is outward along +y. The electron is pulled away from the nucleus and the orbital radius reaches maximum first.

3) Photon E field
The Coulomb force exerted by photon E field on electrons can not only increase the radius of the orbit along the direction of +y and-y, but also change the velocity of electrons. In Fig.-4A and -4B， the "-" and "+" represent the negative and positive photon E fields respectively. The photon field moves to the right (+x direction) at the speed of light, which is equivalent to the electron moving to the left (-x direction) at the same speed. Compared with the speed of light, the speed of electrons around the nucleus can be ignored. In Fig.-4A, in the first half circle (a→b→c), the electron feels negative photon E field. It is equivalent to shielding a part of the nuclear charge, which produces repulsive force and motion resistance to the electron, which increases the radius of the orbit in the +y direction and decreases the speed of the electron movement.
In Fig.-4B, the electron passes through point c, and the symbol of photon E field reverses. In the second half circle (c→d→a), the electron still feels negative photon E field, and the orbital radius increases along the -y direction and the electron motion speed decreases. When it returns to point a again, the photon wave train and the orbital rotation of the electron will enter the next period.
Under the influence of the three fields (EN, B and E), when a period is completed, the radius of the orbit along the x direction is not changed, but the radius of the orbit along the y direction is obviously enlarged. However, the average radius only increased a little per period. For each additional period, the electron velocities at points a and c remain almost unchanged, while the electron velocities at points b and d decrease a little , but the average velocity decreases even less.

The orbital change of electron in photon field
In classical physics, forces and motions can be synthesized or decomposed by vector law. A circular motion and a directional motion can synthesize the elliptical motion. Similarly, an ellipse motion can be divided into a circular motion and a directional motion. Figure 5 is a schematic diagram of orbit change of the earth satellite. In Fig.-5A, if only a directional force F is applied to the satellite in the a-point of the circular orbit to change its orbit, the circular orbit will be changed into elliptical orbit, and the earth  will be in one of two focuses of the ellipse. In Fig.-5B, if two forces with same size are applied at point a and b of the circular orbit respectively, it will also become elliptical orbit, but the earth will be at the midpoint of the ellipse. The effect of photon field on electron is similar to that in Fig.-5B. That is to say, whether in circular orbit or elliptical orbit, the nucleus is always at the center of the orbit, not at a focal point of the elliptical orbit.
The effect of a photon on electron is a kind of lateral directional motion superimposed on the original orbit on the same plane. As shown in Fig. 6, the photon wave train moves to the right at the speed of light along the x direction, which is equal to the electron moving to the left at the same speed. In the course of interaction, the diameter of the orbit along the x direction remains unchanged. Therefore, the time period of the photon wave train can repeat on the orbit along the x direction, which makes the photon and electron basically keep synchronous in the main interaction period.
Although one wavelength of a photon wave train can only lengthen the electron's orbit a little along the y direction, when the photon wave train with tens of thousands or more wavelengths is absorbed by an electron, the circular orbit of the electron will be pulled into an ellipse. The force Fy exerted by photon field on electron along the y-axis consists of photon B field and photon E field.
The magnitude of Fy is mainly affected by the phase difference (Δφ) between electron and photon.
The Δφ can be calculated according to the following formula If Δφ is a quarter of a cycle, (π/2), Fy = 0. If a photon is fully synchronized with the electron, i.e, the phase difference is 0, Fy = Fmax.    The parameters of electron orbit change related to four main spectral lines in Lyman series and Balmer series respectively are listed in Table-1. Of course, the accuracy of the orbital parameters related to each spectral line in the table also depends on the accurate determination of the wave train length (or τ0) in the future. This calculation and analysis only show that the motion state of micro particles can also be calculated and treated by classical mechanics.

In the process of electron transition the change of orbital angular momentum and the physical meaning of Planck constant h
When the electron moves in the steady orbit, the angular momentum is conserved, the rotation frequency is constant, and it is in the standing wave state, so it neither radiates nor absorbs photons.
However, the angular momentum is not conserved in the process of photon-electron interaction.
When both the photon wave train and the rotation of electron common complete one cycle (T or 2 π)，the orbit is elongated a little along the y-axis, and during the period T, the angular momentum changes by a Planck energy quantity (ℋ). That is, When the electron transitions from level n1 to n2 during τ0, the period number of interaction for the electron with the photon wave train is During τ0 the change of the total orbital angular momentum after the electron transition leads to the change of orbital energy level The change of angular momentum per unit time is also the change of energy, ΔEn1→n2 , and the expression (41) is also the radiation energy in the process of electron transition In the current textbooks, the energy expression of photons related to electron transition is Comparing the formula (43) with (42), we get It can be seen that ℋ is about 10 10

By standing wave principle to quantize the energy levels of hydrogen atom
According to the standing wave principle of quantum mechanics, waves from different sources (or directions) will be superimposed on each other and converge at the boundary of the standing wave potential box. The hydrogen atom can be regarded as a three-dimensional standing wave potential box. In the ground state, the diameter can be regarded as the length of the potential box. As shown in figure-7, when the hydrogen atom absorbs photon, the width of the potential box in the direction of photon motion (x-axis) remains unchanged. The photon is a transverse wave and only elongates the potential box along the y-axis. Standing wave condition requires that the stretching of potential box must be quantized. If the length of the potential box is 2r, the radius along the +y or -y direction can only be increased by an integral multiple of 2r. In other words, the short half axis of the new orbit remains unchanged, but the long half axis can only be r, 3r, 5r, 7r, 9r, ......, (2n-1)r.
The average radius of the nth stable orbit is ( ) r y r 3r 5r 7r 9r (2n-1)r The ratio of the f to the speed of light (c) is the Rydberg constant. From the energy point of view, when the electron transitions from the high energy level n2 to the low energy level n1, it will radiate photon.
The energy of the photon is The photon frequency in equation (50) is just equal to the difference between the orbital frequencies of the two energy levels (51) 2 1 n n f f − =  Equations (50), (51) are consistent with equations (3).

Width of spectral line
The linewidth of spectral line (Δλ) refers to the difference between two adjacent wavelengths in a photon wave train. There are the following relations between the linewidth (Δλ) and the length of photon wave train (L) and wavelength (λ) [10,13] . It can be seen that the frequency of the photon ν is the average of f1 and f2, but the wavelength λ is not the average of Λ1 and Λ2, and 2Λ1=Λ2 or Λ1=2Λ2. This is determined by the quantization condition of standing wave. Therefore, for a laser of the same wavelength, it is known from equation (52) that there will be a very small linewidth Δλ, and especially big λ/Δλ. That is to say, it has a very large wave train length L and a very large action time τ0。 (62) 0    =  The λ/Δλ represents the wave number of the whole wave train and its reciprocal (Δλ/λ) determines the accuracy of photon wavelength measurement. For example, in the 1850s, the Swedish spectrologist Angstrom measured the wavelengths of four visible spectra of hydrogen atoms, which reached 5~6 significant digits [1] . It shows that the wave train length of these spectral lines is at least 10 5 waves. The narrower the line width is, the longer the wave train is, and the higher the accuracy of the measured wavelength is, because there is always about one wavelength difference between the Λ1 and Λ2.

Conclusion and perspectives
Hydrogen atom is the simplest atomic system and the main research object of quantum mechanics. More than a century has passed, the Bohr model and Bohr radius have a wide influence and their incorrect impact is pervasive to University and middle school textbooks, so many generally believed that Bohr's theory uses the knowledge of classical physics and is difficult to be incorporated into quantum mechanics; Quantum mechanics uses too much mathematical language and lacks understanding of physical knowledge. In this paper, we break through this conventional thinking and use as few mathematical language as possible. Based on classical physics knowledge, we establish the direct relationship between radiation and electron motion with the help of standing wave quantization condition. This is a career that Bohr pursued in his life but did not complete. The motion state of micro particles can also be described by the combination of classical mechanics and quantum mechanics. Further research can also prove that the uncertainty principle may be a kind of interference effect of measuring instruments on the motion state of micro particles. The details of photons emitted by hydrogen atom will be discussed later due to paper space limitation.