NSC20 CRSI2017 Gauhati University Feb-2017 Preliminary information of the Abstract material; In lieu of FULL PAPER with Abstract submitted To The convener of NSC20 SYMPOSIUM http://www.ugc-inno-nehu.com/events-2017.html#E02 Prof. S. Aravamudhan Department of Chemistry North Eastern Hill University SHILLONG 793022 Meghalaya saravamudhan@hotmail.com Phone: 9862053872 URL: http://www.ugc-inno-nehu.com http://www.ugc-inno-nehu.com/19nsc-nbu.html 2/24/2019 7:55:19 PM

At the outset attend to the contents of the youtube video linked below http://ugc-inno-nehu.com/Charge_cloud_1.ppt One finds that integrals are evaluated between two charge clouds by dividing each charge cloud into infinitesimal charges, and calculating the electrostatic interaction between each of the small elemental charge of one cloud with every one of similar division of another charge cloud. . But within the same charge cloud the interaction between one small subdivided element with another small element in the same cloud is not calculated in any context Related to the statistical interpretation for the wave function in Quantum Mechanics Fig.1 2/24/2019 7:55:19 PM

As noted from Fig.1 and the excerpt, the statistical interpretation for probability density/charge cloud depiction means one and the same electron quickly moves (fast moving with atto second range speed) from place to place all over the volume in the region. While it is quick, it should be implicit that at no time the electron can be present at more than one position. Thus there is no possibility of any fraction of charge being present at two places. No consequences for calculating electrostatic interactions The Statistical description in this slide does not describe the particle motion in a regular wave form; only a statistical hopping is envisaged. When finally in the time independent description (of long exposure photographic image) only a cloud is discerned, this can be simulated either by a random discrete hopping in the fast time scale regime or a suitable discrete jumps along a wave form amenable to describe as a continuous function of time for the motion. electron displacements occur in the time scales of atto seconds 10-18 then for the human vision persistence time scales the electron might appear to be at all points. In the limit of long time exposure picture, image a cloud will appear to be present rather than discretely electron at diiferent points. e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e Electrons as Waves http://www.kentchemistry.com/links/AtomicStructure/wavesElectrons.htm 2/24/2019 7:55:19 PM

(Statistical Interpretation of Quantum Mechanics) Schrodinger’s wave mechnics Sinusoidal motion transverse to the circumference of the circular orbit. BOHR’s Model Linear motion along the circumference of the circular orbit e e While considering the electron particle movement, nothing much is mentioned at this juncture the speed of the electrical field originating from the charge on the electron INTO THE REALMS OF STATISTICAL PHENOMENA (Statistical Interpretation of Quantum Mechanics) In the next 3-4 slides animated illustrations try to depict the possibilities and the convenience for mathematical formulation. 2/24/2019 7:55:19 PM

e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e A CONTINUOUS MOTION OF A PARTICLE IS TO BE ENVISAGED AS A STATISTICAL PHENOMENON Digitize the continuous function Thus discrete are the points to which electron jumps on the circumference of a circle. e e e e e e e e e e e e e e e e e e e e e Continuous motion of 50 seconds per revolution. e e e e e e Digitized points e e Hopping motion on the sequnence of digitized points. e e e e e e e e e e e e e Following slides: Distribute the points about the circumference (either randomly or on a sinusoidal form ). e e e e e e e e e e e e e e e e e e e 2/24/2019 7:55:19 PM

e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e hopping in digitized waveform A CONTINUOUS MOTION OF A PARTICLE IS TO BE ENVISAGED AS A STATISTICAL PHENOMENON e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e 2/24/2019 7:55:19 PM

From Sheet-7 of the display sheets at the 20NSC/ download link at http://www.ugc-inno-nehu.com/events-2017.html#E02 http://ugc-inno-nehu.com/nsc20-gu/nsc20-gu-display-sheets-12.pdf 2/24/2019 7:55:19 PM

e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e A n image from a very long exposure photograph. A ll points get diffused and a cloud picture results. A n image from a moderately long exposure photograph. Electron appears to be present at all the points e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e 2/24/2019 7:55:19 PM

e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e 2/24/2019 7:55:19 PM

Speed of particle motions 2.9 x 106 m/sec 2.9 x 108 cm/sec Velocity of light =3 x 1010 cm/sec speed with which interaction fields travel. When electron circulates, there would be no electrostatic field at adjacent points due to field generated by the electron while at the starting point; due to the faster speed of field compared to velocity of particle Bohr radius= 5.24 x 10-9 cm Circumference = 2.0 x 3.145 x 5.24 x 10-9 cm = 32.9596 x 10-9 cm Dist 1-2 = 32.9596 x 10-9 cm/12 = 2.7466 x 10-9 cm Dist 1-7 = 10.48 x 10-9 cm = 1.048 x 10-8 cm Speed of particle motions Two orders of magnitude slower than the speed of the field 1 2 7 Distance shorter than circumferential length 2/24/2019 7:55:19 PM

Physics - Modern Physics (15 of 26) The Bohr Atom: Radius of the Atom https://www.youtube.com/watch?v=xL02C8Tq3eU Physics - Modern Physics (16 of 26) The Bohr Atom: Velocity of the Electron https://www.youtube.com/watch?v=K6TJxuyPTdc Physics - Modern Physics (17 of 26) The Bohr Atom: Velocity and Radius of the Electron https://www.youtube.com/watch?v=wlWPntCRDDc Physics - Modern Physics (18 of 26) The Bohr Atom: Energy of the Electron https://www.youtube.com/watch?v=gtJAnQ2m__Y Electrons as Waves http://www.kentchemistry.com/links/AtomicStructure/wavesElectrons.htm 2/24/2019 7:55:19 PM

Electron revolving in circular orbit Case of finite time actual Electron revolving in circular orbit Case of Instantaneity Electron with Mass ‘m’ and Charge ‘e’ electron electron The negatively charged electron causes electric field at other points and the strength of the filed is proportional to inverse square of the distance. The points closer to electron have higher field strength. And with increasing distance filed strength decreases. Field at points along the circumference Field at points along the straight line The electric field is present whenever the electron is present. However, at the time when the charge is placed at a point, how much time does the electric field (due to the electron at the point) take to appear at the various points in the neighborhood far and near? Or is it instantaneous?. The sizes of the circles indicate the field strength relatively Field Field 2/24/2019 7:55:19 PM

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At the points where the green arrows point out, the an electron encounters the electric field generated by itself at the starting point. This means in a single electron system like hydrogen atom there could be electron-electron repulsion besides the proton-electron interaction. There could be in principle a stability criterion for the system with electron revolving at a particular distance from nucleus which In turn can be resulting in angular momentum quantization criterion. There are some results in the internet sub directory that would be presented in the NSC20. http://www.ugc-inno-nehu.com/nsc20-gu/ At appropriate relative speeds of electron and the electric field the situation as indicated here can arise. This aspect is considered for possibilities of exploring further. 2/24/2019 7:55:19 PM

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Possible optimum for speed Field/ Speed Charge <137(?) Typical minimum displayed 2/24/2019 7:55:19 PM

The Hydrogen atom is the system which for its stability has mainly the interaction of a proton and electron; which is attractive electrostatic interaction. Only at the closer proximities of these two particles there are consequences other than the attractive interactions and the energy of the system increases which is inherently taken care of in the wave nature of electron and the necessity to consider electron as not simply a point mass or point charge as in the classical sense. Schroedinger’s wave mechanics seem to provide for this inherently, where as in Bohr’s Model the discreteness and the quantization of angular momentum has to be presumed. In the case of the single electron and a single proton system, still there is a possibility of a repulsion can be envisaged if the field emanating from a location of electron reaches (experienced at) another point later and not instantaneously. This probably requires that the field of the electron at a point is experienced only at a later instant, during this time delay the electron itself moves to the point to experience the field generated by its presence at a previous (earlier) location. It is this possibility that was probed and the values for minimization is as a function of radius of the hydrogen atom, which determines the Nuclear-Electron distance and the appropriate velocities for electron circulation and the travelling of electrostatic field generated (arising due to the presence of electron). 2/24/2019 7:55:19 PM