Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (2023)

Journal of Modern PhysicsVol.05No.18(2014), Article ID:52202,10 pages
10.4236/jmp.2014.518199

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems

Stanisław Olszewski

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Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland

Email: olsz@ichf.edu.pl

Copyright © 2014 by author and Scientific Research Publishing Inc.

This work is licensed under the Creative Commons Attribution International License (CC BY).

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Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (1)Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (2)

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (3)

Received 16 October 2014; revised 12 November 2014; accepted 5 December 2014

ABSTRACT

The mechanical angular momentum and magnetic moment of the electron and proton spin have been calculated semiclassically with the aid of the uncertainty principle for energy and time. The spin effects of both kinds of the elementary particles can be expressed in terms of similar formulae. The quantization of the spin motion has been done on the basis of the old quantum theory. It gives a quantum number n = 1/2 as the index of the spin state acceptable for both the electron and proton particle. In effect of the spin existence the electron motion in the hydrogen atom can be represented as a drift motion accomplished in a combined electric and magnetic field. More than 18,000 spin oscillations accompany one drift circulation performed along the lowest orbit of the Bohr atom. The semiclassical theory developed in the paper has been applied to calculate the doublet separation of the experimentally well-examined D line entering the spectrum of the sodium atom. This separation is found to be much similar to that obtained according to the relativistic old quantum theory.

Keywords:

Spin Effect and Its Semiclassical Quantization, Electron and Proton Elementary Particles, Electron Drift in the Hydrogen Atom, Separation of the Doublet Spectral Lines

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (4)

1. Introduction

In physics we look usually for general rules which govern the properties of a physical object, or a set of such objects. For example the Bohr atomic model gives a rather perfect description of several quantum parameters characterizing the hydrogen atom, but not the spin effects. The main items obtained from the Bohr description have been confirmed both on the experimental way, as well as on the quantum-mechanical footing which is considered to be a more flexible formalism than the old quantum theory. Simultaneously, however, quantum mechanics seemed to be enough complicated to give no transparent idea on the spin effects of the charged particles entering the atom. In consequence a treatment of the spin effects of the electron and proton was evi- dently absent in such simple model as the semiclassical Bohr approach to the hydrogen atom; see e.g. [1] . The aim of the present paper is to bridge this gap.

A general warning on the treatment of spin is that it should not be seeked as a result of the circulation effect of a particle about its own axis (see e.g. [2] ), and this view is shared also in the present approach. But instead of the motion about an axis which crosses the particle body, a charged particle may perform its spontaneous circulation in the magnetic field about an axis located outside the particle mass. The sense of such behaviour is―as we shall see―that in effect of the particle interaction with the magnetic field created by the particle motion, the particle energy becomes much lowered below the zero value of energy which can be assumed to be associated with the particle at rest.

In defining the position of the axis of the particle circulation in the magnetic field, the uncertainty relation for energy and time can be of use [3] - [5] . Beyond of time Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (5) and energyElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (6), the principle contains also a reference to the particle mass Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (7) and the speed of lightElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (8):

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (9). (1)

Evidently the rule (1) derived for electrons in [3] - [6] does apply to the particles which obey the Fermi statistics. But, for example, instead of electrons of the mass Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (10) considered in [3] - [6] , we can have also the gas of the proton particles of the mass Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (11) distributed in the field of a negative background which makes the gas electrically neutral. A reasoning of [3] - [6] repeated in the case of an ensemble of the proton particles gives the result

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (12). (2)

This makes (2) different from (1) solely by a replacement of Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (13) in (1) by Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (14) in (2). Certainly Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (15) and Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (16) in (2) refer to the proton particle.

A consequence of the principle in (1) and (2) is a rule that two Fermi particles of the same kind cannot approach together to an arbitrarily small distance but they should be separated at least by the interval which―in view of (1)―is equal to [6]

(Video) Electrons DO NOT Spin

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (17)(3)

for electrons, but becomes equal to

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (18)(4)

for the protons case; see e.g. [7] for the proton mass, spin angular momentum and spin magnetic moment.

The minimal distances (3) and (4) between particles represent respectively the Compton length of the electron and proton particle, on condition that the rationalized Planck constant Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (19) is replaced by the original Planck constantElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (20). The kind of the formulae given in (3) and (4) has been derived before in [8] - [10] ; see also [11] .

In Section 2 we apply (3) and (4) to define the positions of the axes of a spontaneous particle circulation giving, respectively, the electron and the proton spin. Before these motions take place we assume that the particle energy of the electron Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (21) and proton Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (22) is at zero:

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (23). (5)

2. Spinning Process of the Electron and Proton

A general law of physics is that any particle tends to assume a possibly lowest level of energy. In case of a charged particle this can be attained in effect of the particle circulation about some axis along which the particle motion induces the presence of the magnetic field. This situation implies that the kinetic energy of the orbital motion is associated with a particle. The axis of the motion can be located outside the extension area of the particle mass. As a distance of the axis from the particle location (Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (24)for the electron and Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (25) for proton) let us assume that (3) and (4) hold respectively in the electron and proton case.

The magnetic field Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (26) causes the velocity Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (27) along a circle normal toElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (28), and the balance of the forces requires that

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (29)(6)

where Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (30) orElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (31), Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (32)orElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (33), and Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (34) orElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (35). In effect the force in (6) represents an equilibrium between the force of the field and the mechanical force due to the acceleration of a particle toward the track center (see e.g. [12] ). We postulate that

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (36)(7)

in the case of the electron particle, and

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (37)(8)

in the proton case.

The mechanical angular momenta of electron and proton become respectively

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (38)(9)

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (39). (10)

For the sake of simplicity the same size of charge Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (40) for the electron and proton is assumed.

The Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (41) and Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (42) in (9) and (10) are the electron and proton circulation frequencies equal to

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (43)(11)

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (44). (12)

The Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (45) and Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (46) are the strengths of the magnetic field suitable for the electron and proton case. For both kinds of particles we assume that the strength of Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (47) is so large that electron or proton gyrate in the magnetic field with a speed close toElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (48). This requirement for the particle velocity is dictated by examination of the particle acceleration expressed in terms of the electric field Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (49) and magnetic field Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (50) [13] . In this case

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (51). (13)

Evidently the acceleration (13) vanishes when the particle velocity becomes a constantElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (52). Thus we have

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (53)(14)

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (54)(15)

and

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (55). (16)

With the aid of (3) and (4) we obtain from (14), (15) and (16):

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (56)(17)

and

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (57)(18)

on condition the absolute values of Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (58) are taken into account. The orbital radii Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (59) and Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (60) [see (7) and (8)] substituted together with the velocities of (16) into the formulae (9) and (10) for the angular momentum give respectively

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (61)(19)

for the electron and

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (62)(20)

for the proton particle. In effect we have

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (63). (21)

Evidently the formulae obtained in (19)-(21) do not depend on the particle mass. But a mass dependent parameter becomes the magnetic moment Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (64) of a particle. For the electron case we obtain:

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (65)(22)

(Video) Hydrogen atom wavefunctions

(which is the Bohr magneton) and for proton

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (66)(23)

called also the theoretical nuclear magneton applied in considering the nuclear particles [7] . The ratio between (23) and (22) is defined by

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (67)(24)

which is not very far from the ratio obtained from the experimental data for the magnetic moment of electron and proton [7] . In many cases the experiments performed on the nuclear magnetic momenta Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (68) give the ratio Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (69) not much different from Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (70) where Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (71) is the nuclear mass.

The energy of a spinning particle in the magnetic field is respectively represented by

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (72)(25)

for an electron, and by

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (73)(26)

for a proton. Therefore the gain of energy in the magnetic field due to formation of the particle spin is large. This gain of energy is expensed to provide the kinetic energy to a spinning particle having its velocity close toElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (74).

3. Magnetic Flux of a Spinning Particle, Conservation of Energy and Quantization of the Spin Motion

A parameter concerning spin which has its established experimental counterpart is the magnetic flux. Let us choose for an elementary planar area of that flux the circle

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (75)(27)

for electrons, and the circle

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (76)(28)

for protons. From (27), (28), as well as for the magnetic field strength taken respectively from (17) and (19), we obtain

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (77)(29)

and

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (78)(30)

respectively in the electron and proton case. An evident result is that

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (79). (31)

Therefore the flux extended over the elementary areas in (27) and (28) does not depend on the particle kind represented by the particle mass. Moreover, the flux calculated in (29) and (30) is equal to a constant quantum term observed experimentally since a long time in superconductors [14] .

The time derivative of the flux term is zero, so we have the fundamental relation of electrodynamics

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (80). (32)

Physically this means that a linear integral over Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (81) representing the electric field along a circular path of the electron is equal to zero, therefore the energy of the circular motion in the magnetic field of Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (82) is conserved.

Having the magnetic flux

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (83)(33)

the spin motion can be quantized according to a rule of the old quantum theory [12] [15] . It originates from a general rule given by Sommerfeld that momentum Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (84) integrated over a closed path Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (85) of the particle motion should be a multiple of the Planck constantElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (86):

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (87)(34)

here Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (88) is usually considered as an integer number. But according to [12] Equation (34) can be transformed into

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (89). (35)

By taking into account the first equation in (33) we obtain for (35) the relation

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (90)(36)

from which the spin quantum number becomes:

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (91). (37)

This is a well-known result confirmed experimentally by the measurements on the gyromagnetic ratio in ferromagnets [16] performed a time before the spin discovery [17] .

4. Drift Velocity of a Spinning Electron in the Electric Field of the Proton Nucleus

Till the present time no other field than Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (92) spontaneously created by a spinning particle has been considered. Now let us assume that the spinning electron meets the electrostatic field of the proton nucleus. A minimal dis- tance which can appear between the electron moving particle and the proton being at rest is defined in (3) be- cause (4) is too small to have a decisive influence. In this case

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (93)(38)

where Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (94) is the absolute value of the electric field acting on the electron. Another force acting on the electron is Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (95) where Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (96) is the magnetic field intensity of the electron spin; see (17). Assuming that Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (97) is normal toElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (98), the driving electron velocity obtained as a result of the joined action of both fields is [18]

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (99). (39)

But it is easy to check from (17) and (38) that

(Video) Spin

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (100)(40)

is the fine-atomic-structure constant [2] [19] , so

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (101). (41)

The result in (41) is precisely the electron velocity on the lowest orbit of the Bohr atom [1] . Therefore a combined action of the spin magnetic force of the electron and electrostatic force acting between electron and the proton nucleus, gives the speed of electron equal to that possessed on the lowest quantum state in the hy- drogen atom. The spin action of the proton on the electron spin moment present on the orbit has been neglected.

In effect the velocity along the lowest orbit of the Bohr’s hydrogen atom can be considered as a consequence of a drift motion being a result of superposition of many spinning rotations along very small orbits having their radii equal to (7) and travelled with a speed equal toElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (102). The time necessary to travel along the Bohr orbit having the well-known radius

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (103)(42)

is

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (104)(43)

whereas the travel time along the spin orbit calculated from (7) and (3) is equal to

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (105). (44)

In consequence the number of spinning circular motions which take place in course of the electron drift along the first Bohr orbit is equal to

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (106). (45)

This is a number independent of the massElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (107). A diagram presenting schematically the motion of a spinning electron along the lowest Bohr orbit in the hydrogen atom is given in Figure 1. The circular frequency of a spinning electron is

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (108). (46)

The mass Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (109) has to be replaced by Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (110) in case of a spinning proton frequency.

5. Semiclassical Approach to the Doublet Separation in the Sodium Atom

Experimentally the doublet separations in the spectra of atoms ascribed to the presence of the electron spin are

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (111)

Figure 1. A scheme representing the motion of a spinning electron along the shortest (lowest) circular Bohr orbit of the hydrogen atom. The orbit circle is represented by a dashed line, the separation distance between two circles enclosing the motion is twice the radius re given by the Formulae (3) and (7). For the number of the spin oscillations along the orbit see Formula (45).

well known since a long time; see e.g. [20] . The problem is with a theoretical approach to these values. In the author’s opinion no satisfactory agreement between experiment and theory has been reported in this domain. Our aim is to calculate a doublet separation for the sodium atom in the case of the electron transition between two levels being on the same atomic shell Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (112) but having different angular momenta:

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (113)(47)

[20] . The level energies are approached by the quantum-defect method. We follow first the idea developed by the old quantum theory, next the formalism of the present paper is applied.

The considered electron of the sodium atom is the valence electron moving outside the atomic core. The electron energy is given by the formula

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (114). (48)

Here Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (115) is the first Bohr orbit radius, Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (116)and Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (117) is an effective quantum number associated with the electron level Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (118) by the quantum-defect formula

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (119). (49)

We apply

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (120)(50)

for term Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (121)Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (122) and

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (123)(51)

for termElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (124)Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (125); see Table 7.2 in [20] .

A difference of energy (48)

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (126)(52)

calculated respectively from (50) and (51) gives the length of the spectroscopic line equal to

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (127)(53)

which is not far from the experimental length

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (128)(54)

measured for the examined doublet [20] .

A proposal of calculating the doublet separation based on the relativistic old quantum theory applies the following formula for the change of energy connected with that separation [21] [22]

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (129). (55)

Here

(Video) Why Don't Protons Fly Apart in the Nucleus of Atoms? RESIDUAL Strong Force Explained

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (130)(56)

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (131). (57)

For the effective nuclear charge equal to that applied before in (52), i.e.

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (132)(58)

moreover

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (133)(58a)

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (134)(58b)

we obtain

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (135). (59)

A semiclassical approach of the present paper is based on the interaction energy of two magnetic dipoles. One of them is provided by the angular momentum of the electron circulating about the atomic core, another dipole is due to the electron spin. For the sake of simplicity we assume that the magnetic momenta of the orbital motion and the spin motion are either parallel, or antiparallel, in their mutual arrangement. For both cases the absolute value of the coupling energy is the same. On the level of type Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (136) the electron has its angular momentum equal toElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (137), on the level of type Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (138) let this momentum beElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (139). This leads to two orbital magnetic momenta on Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (140) and Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (141) equal respectively to

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (142)(60)

and

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (143). (61)

We assume that momenta (60) and (61) are located at the nucleus. The absolute value of the spin magnetic moment (located at the electron position) is the same in both cases being equal to the Bohr magneton Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (144) given in (22).

The electron in course of an excitation does not change its spin, but a separation distance between the magnetic momenta of the orbital motion and the spin momentum is changed. For state Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (145) we have

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (146)(62)

and for state Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (147)

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (148). (63)

Therefore in case of a parallel arrangement of the orbital momentum and spin momentum the energy change of the momenta interaction due to the electron excitation becomes:

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (149)(64)

(the dot products of the vector joining the spin and orbital momenta with these momenta can be neglected be- cause the vector is assumed to be normal to the momenta).

The results obtained in (59) and (64) differ solely by a factor

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (150). (65)

A substitution of the valuesElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (151), where Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (152) is obtained in (59), in place of Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (153) into a formula similar to (53) provides us with two wave lengths which differ by the interval equal to about

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (154)(66)

in Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (155) the wave length calculated in (53) has been taken into account. The result (66) is smaller by the factor of about

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (156)(67)

than the experimental doublet separation equal to 6 angstroms [20] . A substitution of Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (157) from (64) instead of (59) gives a similar separation to that obtained in (66); see (65).

6. A Look on the Dirac Theory and the Present Theory of the Electron Spin

A difference of both theoretical treatments of spin is evident. Dirac’s theory is essentially a relativistic quantum- mechanical approach to the electron motion; see e.g. [2] [19] [23] [24] . After the Hamiltonian of the problem is linearized, the four-dimensional matrices are applied as substitutions of the Hamiltonian operator. In the presence of an external electromagnetic field a simplification of the problem can be obtained by separating large and small components of the Dirac equation. In this way the spin-dependent interaction energy with the field can be calculated. The spin magnetic moment is coupled with the spin angular momentum by a constant term which is twice as large as in the classical electrodynamics. This implies that the spin quantum number should have the size of 1/2. Dirac’s electron particle considered in the field of the Coulomb potential gives rather complicated formulae for the electron wave functions which have no counterpart in the present semiclassical theory.

An advantage of the Dirac theory is that it gives an insight into antiparticles like positron, and presents an interval in the energy spectrum of particles and antiparticles of the size equal toElectron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (158). On the other side, no approach to the spin and magnetic moment of such particles like protons has been explicitly outlined by Dirac.

The theory of the present paper is much different than the Dirac approach. First the method is essentially of a semiclassical nature since no wave functions are considered. A basic reference to the quantum theory is the uncertainty principle applied to the changes of energy and time; see (1) and (2). The term

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (159)(68)

included in the formalism is obtained in effect of the derivation procedure of the principle; see [3] - [5] . A further analysis of the change Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (160) of a free-particle energy entering the principle gives a minimal distance for the geometrical separation between the particles; see [6] . This separation allowed us to make a proposal of the spin as a result of a spontaneous circulation of the electron, or proton, performed about an axis located outside the particle mass; see Section 2.

Another advantage of the present theory is that both Fermi particles―electron and proton―can be considered on an equal footing because of the fermion character of these particles; see (1) and (2) which differ solely in their mass symbol. This allowed us to obtain an insight into the spin and magnetic moment of protons together with similar electron properties. The theoretical results obtained for both kinds of the particles are confirmed by the experimental data to a large degree.

Moreover, the Dirac theory assumes that certain magnetic field should be present in order to obtain a spinning electron particle, but the size of such field is not defined. In the present approach the size and source of the magnetic field acting on the particles are the results of the theory.

7. Summary

A semiclassical model of two spinning charged particles (electron and proton) has been proposed on the basis of a quantum uncertainty principle for energy and time and the classical electromagnetic theory. The main reason of a spontaneous formation of a spinning particle is a strong lowering of the particle energy in the magnetic field associated with the existence of the spin circulation.

The mechanical angular momentum connected with the spin is found to be the same for electron and proton, and the mass difference between the particles becomes sound only for the magnetic spin moment. This very fact is confirmed by experiment (see e.g. [7] ) which provides us with the ratio of the magnetic moments similar to that obtained by the present theory.

It could be noted that the mechanical moment of a proton equal to that of a spinning electron seemed to surprise many physicists since a long time; see e.g. [25] . This kind of feeling is stimulated by the fact that the magnetic moment of proton is about Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems (161) times smaller than that of electron. The independence of the mechanical spin momenta of both particles on their mass can be explained by a reference to the fact that the particles obey the same (Fermi) statistics and have the same absolute value of the electric charge. Therefore the uncertainty principle for energy and time applied to electrons and protons is different just in the mass value; see (1) and (2). But the orbit radius of each of these spinning particles is inversely proportional to their mass. Since the angular momentum is by definition proportional to the mass, the both mass expressions cancel together in the angular momentum formula which becomes independent of the mass size.

When a spinning electron meets the electrostatic field of a proton, it can be demonstrated that the resulted drift velocity of the electron becomes equal to the velocity of that particle on the lowest quantum level of the Bohr model of the hydrogen atom.

The effect of the spectral doublet separation has been also examined for the atomic sodium taken as an example. A semiclassical calculation of the present paper gives almost the same result as it is provided by the relativistic old quantum theory.

(Video) 4.14 Adding spins

References

  1. Bohr, N. (1922) The Theory of Spectra and the Atomic Constitution. Cambridge University Press, Cambridge.
  2. Landau, L.D. and Lifshitz, E.M. (1972) Quantum Mechanics (in Russian). Izd. Nauka, Moscow.
  3. Olszewski, S. (2011) Journal of Modern Physics, 2, 1305. http://dx.doi.org/10.4236/jmp.2011.211161
  4. Olszewski, S. (2012) Journal of Modern Physics, 3, 217. http://dx.doi.org/10.4236/jmp.2012.33030
  5. Olszewski, S. (2012) Quantum Matter, 1, 127. http://dx.doi.org/10.1166/qm.2012.1010
  6. Olszewski, S. (2014) Journal of Modern Physics, 5, 1264. http://dx.doi.org/10.4236/jmp.2014.514127
  7. Tolansky, S. (1948) Hyperfine Structure in Line Spectra and Nuclear Spin. 2nd Edition, Methuen, London.
  8. Ruark, A.E. (1928) Proceedings of the National Academy of Sciences of the United States of America, 14, 322. http://dx.doi.org/10.1073/pnas.14.4.322
  9. Flint, H.E. (1928) Proceedings of the Royal Society A, London, 117, 630. http://dx.doi.org/10.1098/rspa.1928.0025
  10. Flint, H.E. and Richardson, O.W. (1928) Proceedings of the Royal Society A, London, 117, 637. http://dx.doi.org/10.1098/rspa.1928.0026
  11. Jammer, M. (1966) The Conceptual Development of Quantum Mechanics. McGraw-Hill, New York.
  12. Slater, J.C. (1967) Quantum Theory of Molecules and Solids. Vol. 3, McGraw-Hill, New York.
  13. Landau, L.D. and Lifshitz, E.M. (1969) Mechanics. Electrodynamics (in Russian). Izd. Nauka, Moscow.
  14. Kittel, C. (1987) Quantum Theory of Solids. 2nd Edition, Wiley, New York.
  15. Onsager, L. (1952) The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 43, 1006- 1008. http://dx.doi.org/10.1080/14786440908521019
  16. Beck, E. (1919) Annalen der Physik, 305, 109-148. http://dx.doi.org/10.1002/andp.19193651802
  17. Uhlenbeck, G.E. and Goudsmit, S.A. (1925) Die Naturwissenschaften, 13, 953-954. http://dx.doi.org/10.1007/BF01558878
  18. Matveev, A.N. (1964) Electrodynamics and the Theory of Relativity (in Russian). Izd. Wyzszaja Szkola, Moscow.
  19. Schiff, L.I. (1968) Quantum Mechanics. 3rd Edition, McGraw-Hill, New York.
  20. White, H.E. (1934) Introduction to Atomic Spectra. McGraw-Hill, New York.
  21. Millikan, R.A. and Bowen, I. (1924) Physical Review, 23, 1.
  22. Rubinowicz, A. (1933) Handbuch der Physik. In: Geiger, H. and Scheel, K., Eds., Vol. 24, Part 1, Springer, Berlin.
  23. Rose, M.E. (1961) Relativistic Electron Theory. Wiley, New York.
  24. Avery, J. (1976) Creation and Annihilation Operators. McGraw-Hill, New York.
  25. Kobos, A.M. (2013) Postĕpy Fizyki, 64, 86.

FAQs

What is the spin of electron in hydrogen atom? ›

Let's go back to ground state of hydrogen: it has one proton with spin and one electron with spin (orbital angular momentum is zero).

Do electrons and protons spin? ›

The proton, like the electron and neutron, has a spin of ħ/2, or “spin-1/2”. So do each of its three quarks.

What is the spin of hydrogen nucleus? ›

Hydrogen nuclei (protons) have magnetic properties, called nuclear spin. They behave like tiny rotating magnets, represented by vectors. The sum of all the tiny magnetic fields of each spin is called net magnetization or macroscopic magnetization. Normally, the direction of these vectors is randomly distributed.

What is spin in atomic structure? ›

spin, in physics, the amount of angular momentum associated with a subatomic particle or nucleus and measured in multiples of a unit called the Dirac h, or h-bar (ℏ), equal to the Planck constant divided by 2π. For electrons, neutrons, and protons, the multiple is 0.5; pions have zero spin.

What are the two types of electron spin? ›

The electron can spin in two directions:

The spin up and spin down directions correspond to the spinning in the “+z” or “–z” direction. These spins (spin up and spin down) are the particles that have spin “s” equal to 1/2, i.e. for electrons.

Are protons actually spinning? ›

Protons always have "spin." The direction and strength of a proton's spin determines its magnetic and electrical properties. Changes to the proton's spin also alter its structure.

Where does the proton get its spin? ›

According to this view, the observed spin of the proton arises simply from the intrinsic spins of the quarks. In the late 1980s, however, experimental evidence began to show that much of a proton's spin comes from so-called orbital motion of the quarks relative to each other, rather than from their individual spins.

Does electron actually spin? ›

In quantum theories, we speak of electrons as having a property called “spin.” The reason we use this term is that electrons possess an angular momentum and a magnetic moment, just as one would expect for a rotating charged body.

Are electrons always spinning? ›

We don't think that electrons are really "spinning" around, because as far as we know, electrons are infinitely small. There's not really anything to spin. Even so, electrons do behave like they're "spinning" in experiments. Technically, they have "angular momentum," the type of momentum possessed by rotating objects.

Why is it called electron spin? ›

Much to their surprise, however, the two physicists found that electrons themselves act as if they are spinning very rapidly, producing tiny magnetic fields independent of those from their orbital motions. Soon the terminology 'spin' was used to describe this apparent rotation of subatomic particles.

What is the spin of proton and neutron? ›

Every photon has spin 1; every proton, and every neutron, has spin 1/2. But the quarks and gluons inside a nucleon have spin, as well, and their spins and orbital angular momenta must add up to the total nucleon spin of 1/2.

Do electrons really spin around the nucleus? ›

Electrons revolve around the nucleus in fixed orbits or shells called energy levels. Electrons rotate around the nucleus in one or more energy levels.

What are the 4 types of spin? ›

The acronym SPIN refers to the four categories of questions reps should use to guide customer conversations: situation, problem, implication, and need-payoff.

What is spin and its types? ›

Spin is a conserved quantity carried by elementary particles, and thus by composite particles (hadrons) and atomic nuclei. Spin is one of two types of angular momentum in quantum mechanics, the other being orbital angular momentum.

What is a spin state in chemistry? ›

The "north pole" of this spin-generated magnetic field points a certain direction in space. The nuclear spin state is the orientation of the spin-generated magnetic field relative to an external magnetic field (B0). Think of the nucleus as a top, and the magnetic field orientation as the spin axis.

Can an electron have two spins? ›

An electron can spin clockwise or anticlockwise, in two opposite directions. There are two possible values of 's' that are equal and opposite. The probability of rotation in one direction is only one half.

What are spin 2 particles? ›

Spin-2 means that the spin is equal to 2 in the same sense in which spin-1 means that the spin is equal to 1 or spin-1/2 means that the spin is equal to 1/2.

How many different spin states are possible for an electron? ›

There are two allowed spin states, up and down. Since only two new energy levels are observed then there are two possible spin states for an electron.

What do you call the spinning of a proton? ›

Proton spin describes the direction a proton “turns” on its axis. The spin tune is the number of times during a rotation that a proton's axis shifts. The protons in the Relativistic Heavy Ion Collider (RHIC)'s beam all need to spin in the same direction.

Does photon have spin? ›

Electrons and quarks (particles of matter) can have a spin of –1/2 or +1/2; photons (particles of light) can have a spin of –1 or +1; and Higgs bosons must have a spin of 0. Though particle spins are tiny, they have an impact on our everyday world. The spin property of photons allows us to create 3D movies.

Does neutron have spin? ›

The neutron has spin 1/2 ħ, but it has no net charge. The existence of the neutron's magnetic moment was puzzling and defied a correct explanation until the quark model for particles was developed in the 1960s.

Why electron rotates about a proton? ›

Electron is rotate around the nucleus because nucleus have a heavy part and positive charge of the atom so nucleus is stationary and then electron is light part and negative charge with respect to nucleus and not more energy so electron move around the nucleus.

How many spin states does a proton have? ›

Each proton can have two possible spin states with MI=±12 , giving a total of four composite spin states.

Does proton spin around the nucleus? ›

Really they exist in a sort of cloud around the nucleus. But perhaps you are talking about the "spin" property of electrons, sometimes pictured as the particle spinning on its own axis. If this is what you are referring to then the answer is that protons (and neutrons) do spin.

Can electron have zero spin? ›

Because the p electrons are in different orbitals their spins are not necessarily paired, so the spin could be zero or it could be one.

Where do electrons spin around? ›

Electrons are found in different levels — or orbitals — surrounding the nucleus. The electrons can be found at any point in their orbital. The orbitals can be shaped as a sphere, as lobes — which kind of look like two squashes put together at the small ends — or in the shape of a doughnut around the nucleus.

Do all particles have spin? ›

All elementary particles have intrinsic spin associated with them, but understanding what that means in a physical common sense way is not just almost impossible, but thoroughly impossible.

Why do electrons not spin? ›

The goto answer to that question is that the electron is a pointlike particle and cannot spin. The electron is not pointlike though. It is described by a wavefunction. One can prepare the wavefunction to describe a very small electron, but not a point-like electron.

Which has maximum spin proton neutron and electron? ›

Proton is the one who spins and the real culprit behind Electromagnetism.

What are the differences between nuclear spin and electron spin? ›

Although exactly the same property, nuclear spin is traditionally denoted by the letter I, while electron spin is denoted by the letter S. Electron spin has only one value (S = ½, always), but nuclear spin values ranging from I = 0 to I = 8 in ½-unit increments can be found across the entire periodic table.

Can protons move? ›

Answers and Replies. protons do move and current is the flow of negatively charged particles electrons... :) not the positive charge.

Do all electrons spin in the same direction? ›

No. They can have different 'directions'. Note the wikipedia atomic orbitals article which says an atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom.

Where do electrons get their energy to spin? ›

When electrons gain or lose energy, they jump between shells as they are rotating around the nucleus. For example, as electrons gain energy from photons (small bundles of energy), they might move from the second to the third energy level shell.

What are the three types of spinning? ›

1 Three main types of spinning processes: melt spinning, dry solution spinning, and wet solution spinning [27].

How many types of spin are there? ›

There are four main categories of spin bowlers, which are as follows: Right Arm Leg Break. Right Arm Off Break. Left Arm Chinaman.

What is the other name of spinning? ›

Words Related to Spinning

In this page you can discover 37 synonyms, antonyms, idiomatic expressions, and related words for spinning, like: spining, whirling, spin, twirling, reeling, gyrating, revolving, trundling, swirling, spiralling and rotating.

What are the different spin states? ›

These states are commonly denoted as ∣ +½ 〉and ∣ -½ 〉often referred to as "spin-up or "parallel" and spin-down or "anti-parallel" respectively.

How many spin states does hydrogen have? ›

Molecular hydrogen occurs in two isomeric forms, one with its two proton nuclear spins aligned parallel (orthohydrogen), the other with its two proton spins aligned antiparallel (parahydrogen). These two forms are often referred to as spin isomers or as nuclear spin isomers.

Does h2 have spin? ›

Molecular hydrogen (H2) is made of two hydrogen atoms, each of which has a nuclear spin of one-half. The spins of these two atoms can be pointing either in the same direction, forming ortho-hydrogen (oH2), or the opposite direction to each other, forming para-hydrogen (pH2).

What is the spin quantum number of hydrogen? ›

The spin quantum number has only two possible values of +1/2 or -1/2. If a beam of hydrogen atoms in their ground state (n = 1, ℓ = 0, m = 0) or 1s is sent through a region with a spatially varying magnetic field, then the beam splits into two beams.

What is the spin of a neutron? ›

Spin. The neutron is a spin 1/2 particle, that is, it is a fermion with intrinsic angular momentum equal to 1/2 ħ, where ħ is the reduced Planck constant. For many years after the discovery of the neutron, its exact spin was ambiguous.

How do you find the spin of an electron? ›

The spin quantum number is represented as ms m s , and for electrons, the electron spin is ms=+−1/2 m s = + − 1 / 2 . An electron that has a spin of +1/2 + 1 / 2 is called a spin up electron, and an electron that has a spin of −1/2 − 1 / 2 is called a spin down electron.

Can atoms have spin? ›

Atomic nuclei have nuclear spin which may be either half-integer or integer, so that the nuclei may be either fermions or bosons.

Is H2 a cathode or anode? ›

Hydrogen gas is liberated at the cathode as it is the negative terminal so it gets attracted towards the cathode and the oxygen been the negative ion gets attracted towards the positive electrode anode.

What is the difference between H2 and H2? ›

H2 is molecular hydrogen.it is a molecule of hydrogen that consists of two hydrogen atoms bonded together by one single bond. 2H denotes two moles of elemental hydrogen.it should be noted that elemental hydrogen is not bonded to anything.

What is the quantum state of hydrogen atom? ›

The ground state of hydrogen is designated as the 1s state, where “1” indicates the energy level (n=1) and “s” indicates the orbital angular momentum state (l=0).

What quantum number is electron spin? ›

Electron Spin or Spin Quantum Number is the fourth quantum number for electrons in atoms and molecules. Denoted as ms, the electron spin is constituted by either upward (ms=+1/2) or downward (ms=−1/2) arrows.

Do protons and neutrons spin? ›

Every photon has spin 1; every proton, and every neutron, has spin 1/2. But the quarks and gluons inside a nucleon have spin, as well, and their spins and orbital angular momenta must add up to the total nucleon spin of 1/2.

Is electron spin actually spin? ›

Introduction. In quantum theories, we speak of electrons as having a property called “spin.” The reason we use this term is that electrons possess an angular momentum and a magnetic moment, just as one would expect for a rotating charged body.

Do photons have spin? ›

Photons carry linear momentum and spin angular momentum when circularly or elliptically polarized. During light-matter interaction, transfer of linear momentum leads to optical forces, whereas transfer of angular momentum induces optical torque.

Videos

1. The spin of the proton
(SpinningParticle)
2. L36.1 Spin1/2 : The spin angular momentum of electron in hydrogen atom
(SAYPhysics)
3. L36.3 Spin1/2 : The spin angular momentum of electron in hydrogen atom
(SAYPhysics)
4. L36.2 Spin1/2 : The spin angular momentum of electron in hydrogen atom
(SAYPhysics)
5. General chemistry 3.2 Hydrogen like atoms
(Physical Chemistry ABC)
6. Ep-7 Multi-electron atoms
(H C Verma course)
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