About the Atom Vector Model II Dan Petru Danescu,

Transcription

1 About the Atom Vector Model II Dan Petru Danescu, Abstract The new version of the paper "About Atom Vector Model" (2011) brings some additions and also reinterprets the electric field lines in accordance with CP symmetry. These lines are related to quantization of angular momentum. Furthermore, it analyzes a possible connection between the proposed model and magnetism of cosmic origin. Keywords: vector model of the atom, atom vector model, quantized angular momentum, vector model of angular momentum, interplanetary magnetic field lines. Contents 1. Introduction. 2. Angular momentum and symmetry to the nucleus. 3. LS coupling and symmetry to the nucleus. 4. Bohr s model and symmetry to the nucleus. 5. From Bohr s model to the de Broglie Sommerfeld Schrodinger models 6. New atom vector model in cosmological context. 7. References 1

2 1. Introduction Vector model of the atom was developed around 1920 to explain the experimental results of spectroscopy. A. Sommerfeld [1], [2] and A. Lande [3] had an important contribution in this field. In quantum physics, vector model of the atom is a model of the atom in terms of angular momentum, considered as an extension of Rutherford - Bohr-Sommerfeld model. Primarily, the vector model of the atom refers to the total angular momentum which is a result of the vector sum of the orbital angular momentum (L) and spin angular momentum (S). Following, by examples, we propose to reexamine these interpretations considering the symmetry vector to the nucleus and the connection which must occur between the angular momentum and the orbital momentum (or electron cloud). Such considerations open up a new approach to atomic model of Rutherford -Bohr-Sommerfeld. Compared to the first version of "About Vector Atom Model" (2011), the approach of this subject is much broader and more systematic. The interpretation of electric field lines related to the quantization has been revised to correct the errors. In almost all cases the drawings were maintained in the initial form, as they are very conclusive and without the need of further explanations. 2

3 2. Angular momentum and symmetry to the nucleus Current vector interpretations do not reflect the symmetry of vector angular momentum to the nucleus. This fact can be easily found by referring to atomic physics manuals and specific works [4], [5], [6], [7], [8], [9]. This deficiency of vector interpretations makes it impossible to link the angular momentum to the electron cloud (or orbital). The interpretations presented here do not contradict the existing vector model but complete it, as it will be shown further on in this paper. Fig.1 and Fig.1a depicts two versions of the spin angular momentum (S). Next, Fig.2 and Fig.2a presents two versions of the orbital angular momentum of the atom. The link between the electron cloud (or orbital) and the angular momentum is shown in Fig.3 and Fig.3a. 3

4 Fig.1 4

5 Fig.1a 5

6 Fig.2 6

7 Fig.2a 7

8 Fig.3 Spin angular momentum and symmetry to the nucleus (Example for m s = 1/2) 8

9 Fig.3a 9

10 3. LS coupling and symmetry to the nucleus LS coupling and symmetry to the nucleus is shown through an example in Fig. 4 and Fig.4a (a simplified drawing). Fig.5 shows splitting levels referring to the external magnetic field. 10

11 Fig.4 11

12 Fig.4a LS coupling: correct representation (Case ml= 1, ms=1/2) Classic Modified 12

13 Fig.5 13

14 4. Bohr s model and symmetry to the nucleus. We can understand quantification of Bohr's atomic model starting from the symmetry of the orbital angular momentum to the nucleus (Fig. 2 and Fig. 2a) and interpretation of the electric field lines that occur during electromagnetic interaction (Fig.6). Here, we indicate that the electric field lines in the classical model lose their original meaning, which is in agreement with CP symmetry. Bohr's atomic model sketch with different circular orbits, for n = 1, 2, 3, from where quantification can be determined is shown in Fig.7. Rydberg's constant is resolved in Fig.8. In Fig.9, the classic symbol of the atom can be presented in a more suggestive way by revealing the connection with the space-time continuum (like in Feynman diagrams). The outline of the electron in the ground state, considering the Fig.1 and developed by us in [10], [11], [12] is shown in Fig.10. Connection with the electromagnetic wave from where results in an interpretation of the constant h/4 is exposed in Fig.11. Here we observe that h/4 is a relativistic invariant because it does not depend on the wavelength. 14

15 Fig.6 Electric field lines and CP symmetry Note: This deformation of electric field lines do not retain their original properties 15

16 Fig.7 Interpretation of quantization in the Bohr s theory 16

17 Fig.8 Interpretation of the Rydberg s constant 17

18 Fig.9 Atomic symbol 18

19 Fig.10 19

20 Fig.11 20

21 5. From Bohr s model to the de Broglie Sommerfeld Schrodinger models De Broglie's hypothesis of matter waves is illustrated in Fig.12. The transition from the Bohr's model to the de Broglie and Sommerfeld's model is shown for n = 3 in Fig.13. Here, Table 1 on semiclassical interpretation of orbital angular momentum function of quantum numbers was taken into consideration. Figure 14 presents the vector model of the atom and quantization (the general case). Bohr-Sommerfeld model, exemplified for n = 3, is shown in Fig.15. The connection between Sommerfeld s theory and the quantum modern theory, for n = 2, is revealed in Fig.16 (it is actually an explanation of elements from Fig. 3). LS coupling and quantization for m s = 1/2 and m l = 1 is shown in Fig

22 Fig.12 Interpretation of de Broglie hypothesis (Matter wave) 22

23 Orbital angular momentum: a new interpretation Example for n=3 Fig.13 23

24 Table 1 Semiclassical orbital angular momentum 24

25 Fig.14 Vector model of the atom and quantization 25

26 Fig.15 Interpretation of Bohr-Sommerfeld theory Example for n=3, l=2, m l = 2, 1, 0 a) Interpretation of quantization b) Illustration correct of the vector model of orbital angular momentum 26

27 Fig.16 From Sommerfeld s theory to modern quantum theory Example for n=2, l=1, m l =1 27

28 Fig.17 LS coupling and quantization Example for m s =1/2, m l =1 28

29 6. New atom vector model in cosmological context (proposal) Some sketches from an unpublished work temporary titled "Magnetic Continuity" might suggest the link (coupling) between the proposed model and the external magnetic field vector. A first sketch makes a comparison of the magnetic field lines for a magnetic bar in 2D and 3D (should illustrate continuity, Fig.18). In Fig.19 we present the magnetic fields of celestial bodies from magnetic polarity viewpoint. Starting from these considerations we can visualize the interplanetary magnetic field illustrated by the example of connection Sun-Earth-Moon (Fig.20). Furthermore, we can then extrapolate these observations to the universe scale (Fig.21). Here we used a well-known model, where we adopted the description of the closed, cyclic universe [13], [14], [15]. Description of the electron-positron pair appearance of a quantum of energy (Fig.22) [12] is intended to contribute to the understanding of the "big bang" mechanism "big crunch". We note that large-scale astronomical observations revealed the existence of a fiber space (as a sheaf) that could be associated with magnetic field lines or with the notion of "cosmic string". As shown by P.M.S. Blackett [16], [17], there is a connection between magnetism and gravity. However, this topic is beyond the scope of this work. 29

30 Fig.18 Continuity of magnetic field a) b) a) Classical design of magnetic field lines of bar magnet in 2D (local continuity) b) New design of magnetic field lines of bar magnet in 3D (cosmic continuity) 30

31 Fig.19 Geometry of the magnetic field of celestial bodies a) Zeropolar structure (The absence of general magnetic field), (example Moon) b) Bipolar structure (example Earth) c) Quadrupolar structure (example Sun) 31

32 Fig.20 32

33 Fig.21 Geometry of the universe a) Space-time diagram of the universe according to the density of matter b) Closed universe represented in 3D 33

34 Fig.22 Pair production 34

35 7. References [1] A. Sommerfeld, Zur Quantentheorie der Spektrallinien, Annalen der Physik, 51, 1 (1916). [2] A. Sommerfeld, Atombau und Spektrallinien, Friedrich Vieweg und Sohn, Braunschweig (1919). [3] Selected Scientific Papers of Alfred Lande edited by Barut and van der Merwe, Reidel (1988). [4] Handbook of Theoretical Atomic Physics, Publisher: Springer (2012). [5] Handbook of Atomic, Molecular and Optical Physics, Springer (2006). [6] Klaus Hentschel, Vector Model (In Compendium of Quantum Physics, pp ), Springer (2009). [7] TA Littefield, N. Thorley, The Vector Model of the Atom (In Atomic and Nuclear Physics, pp ), Springer (1979) [8] Max Born, Atomic Physics (8 th edition), Blackie & Son Ltd. (1969). [9] E.V. Spolsky, Physique atomique, tome II, Ed. Mir, Moscou (1978). [10] D.P.Danescu, Atom Vector Model, G.S.Journal (August 15, 2011). [11] D.P.Danescu, From the Bohr Theory to Modern Atomic Quantum Theory and the Double Helix of Magnetic Field G.S. Journal (August 13, 2010). [12] D.P.Danescu, Electron Structure and Inversion, revised version, May 29, 2012, Internet (First version: Gazeta Matematica no.3 (1978) ), [13] S. Hawking, Scurta istorie a timpului, Ed. Humanitas, Bucuresti (2008). [14]. N. Ionescu-Pallas, Relativitate generala si cosmologie, Ed. Stiintifica si Enciclopedica, Bucuresti (1980). 35

36 [15] NASA, Fundations of Big Bang Cosmology, Internet. [16] P.M.S. Blackett, The Magnetic Field of Masive Rotating Bodies, Nature 159, pp (1947). [17] A. Eid, M.M. Babatin, Magnetic Field of Celestial Objects, Adv. Studies Theor. Phys,, vol.8, pp (2014). 36