Revisiting the Bohr Radius

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Global Journal of Science Frontier Research: A Physics and Space Science Volume 18 Issue 5 Version 1.0 Year 2018 Type: Double Blind Peer Reviewed International Research Journal Publisher: Global Journals Online ISSN: 2249-4626 & Print ISSN: 0975-5896

Revisiting the Bohr Radius By Gene Gryziecki Abstract- This paper questions the veracity of the Bohr theory of the hydrogen atom and accordingly, the meaning of the Bohr radius and the description of the electron. It introduces the reader to a new tool first discovered over 70 years ago but which died with the scientist until it was, much later, decoded by others. Using the new tool to expand the well-known mass-energy equation, the reader is led by a series of equations to a rigorous description of the electron which permits an improved understanding of the Bohr radius, all in agreement with 2014 Codata values. Keywords: energy, electron, mass-energy, bohr radius, wavefunction. GJSFR-A Classification: FOR Code: 020399

RevisitingtheBohrRadius

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© 2018. Gene Gryziecki. This is a research/review paper, distributed under the terms of the Creative Commons Attribution- Noncommercial 3.0 Unported License http://creativecommons.org/licenses/by-nc/3.0/), permitting all non commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Revisiting the Bohr Radius

Gene Gryziecki

Abstract - This paper questions the veracity of the Bohr theory Recently, there has been some amazing of the hydrogen atom and accordingly, the meaning of the meticulous scientific research work that has put forth an Bohr radius and the description of the electron. It introduces improved description of the Bohr radius and electron. the reader to a new tool first discovered over 70 years ago but This paper is intended to provide an introduction to and which died with the scientist until it was, much later, decoded by others. Using the new tool to expand the well-known overview of some of this work. mass-energy equation, the reader is led by a series of 201 II. Methods equations to a rigorous description of the electron which r permits an improved understanding of the Bohr radius, all in ea Building upon the work of Wilhelm Reich (1897- Y agreement with 2014 Codata values. 1957) and his research of pendulums, it was possible to Keywords: energy, electron, mass-energy, bohr radius, decipher his formula for converting mass to length. 591 wavefunction. Reich’s work showed a relationship between the length

of the pendulum and the atomic or molecular mass of a I. Introduction particle [2]. Accordingly, every particle of matter has an

he Bohr theory of the hydrogen atom, theorized by associated functional equivalent gravitational V

Niels Bohr (1885-1962), includes a negatively wavelength. V charged electron that travels in a circular orbit This can be shown for the electron (the entirety ue ersion I

T s about a positively charged nucleus. In the atom’s lowest of this paper applies to the electron and all reference s energy (or ground) state, the distance between values have been taken from a single source, CODATA I the two particles is called the Bohr radius and is equal to 2014 [3]) as 0.529 x 10 -10 m. Since then, further investigation has XVIII discovered that sometimes the electron behaves like a −2 Length=λe= m e NA 10 in meters [2] (1) wave and sometimes like a particle [1]. It has been suggested that the electron exists as a cloud or cavity where the length λe is the wavelength of the

) about the nucleus and measurements are based upon gravitational mass of the electron, me is the electron A the probability of a point particle being at a certain mass (in grams), and NA is Avogadro’s number: ( location in the cloud.

3 23 −31 10 gm 6.022×10  −−2 6 (2) λ=e (9.109 × 10 kg)  (10)( m) = 5.486 × 10 m. Research Volume 1kg mole    2 2 Using this tremendous insight and the famous E = mec = ∫ = λec , (3) equation for calculating rest energy or mass-energy, Frontier where energy E equals the product of mass m times the with c designating the speed of light and the symbol = ∫ 2 2 speed of light squared c , E = mc , one can determine = indicating an equivalence and the change of an electric equivalent to the mass-energy of an electron dimensions: Science in two dimensions rather than three, incorporating only of Space and Time instead of Mass, Space and Time. Accordingly, 2 E=× 9.109 10−31 kg 2.998×= 108 ms −− 1 8.187× 1014 Joules Journal ( )( ) (4) 2 =∫=( 5.486 × 10−−6 m)( 2.998× 108 ms1 ) = 4.930 × 1011 m3 s− 2 .

Global For electromagnetic energy where the wave electron Compton wavelength can be used to determine velocity is restricted to the speed of light the well-known the Compton frequency as shown below: c ν= ce (5) λce 2.998×1081ms− ν= = × 20− 1 ce −12 1.236 10 s . 2.426× 10 m Author: e-mail: [email protected]

When energy is quantized, it can be calculated Compton frequency, then the result is the mass-energy

by the product of Planck’s constant h and frequency. If of the electron. Modern science shows this calculation the frequency happens to be the quantum electron as E=ν= h 6.626×10−34 Js 1.236× 1020 s−−1 = 8.187 × 1014 Joules, ce ( )( ) (6) 2 matching the E = mec calculation above in equation (4).

It is now apparent that an equivalent Planck’s constant h in meter and second dimensionality can be

determined by rearranging the above equation as

E 4.930×1011m 3 s−2 = = = × −−9 31 (7) h 20− 1 3.990 10 m s . 201 νce 1.236 × 10 s r

ea Our limited understanding of charge has James Maxwell’s (1831-79) theory that charge could be Y confused the issue more than necessary. Going back to dimensionally understood to be [4] 601 0.5 1.5 -1 q = M L T (M = mass, L = length, T = time), (8)

agrees with the dimensions for charge in the equations (15) and (17), this linear momentum charge Electrostatic System Units (ESU) [5], and also as function is inherent to the mass-energy of the electron V proposed in the work of Harold Aspden (1927-2011) [6]. and every particle of Matter. Charge is a special type of V If the mass to length conversion is applied to this linear momentum that is electric. The equivalences of

ue ersion I dimensionality of charge it can be seen that charge is charge in three different dimensionalities s s equivalent to a function of linear momentum: (ESUs, Coulombs, and meters squared per seconds) I are 0.5 1.5 -1 2 -1

XVIII q = M L T = ∫ = L T = p e, (9) where pe symbolizes charge as an electric linear momentum vector function. As shown below in

−10 −−19 2 1

) (10) q= 4.830x10 ESU=∫= e= 1.611× 10 C =∫= pe = 13.970m s [7]

A ( in addition to Joules, per equation (4) above, the represented by “e,” multiplied by voltage, found to be electron mass-energy can also be expressed as charge, equal to 510,998.946 electron volts (eV): h 2 (11) E =me c =( e)( 511kV) = h νce =∫=( pe )( νce ). pe At first glance, this equation may appear trivial where fmax is the maximum frequency, V is the voltage

Frontier Research Volume but upon further inspection, it becomes apparent that the applied to the tube, e is charge, and K is equal to the (h / pe) ratio obeys the Duane-Hunt Law and is actually a kinetic energy of the accelerated electron. Notice that if wavelength. Their law states that the maximum the terms are rearranged to solve for energy and if the

Science frequency of X-rays emitted from a tube, resulting from maximum frequency happens to be the quantum electrons, accelerated via an applied voltage, striking a electron Compton frequency ( fmax = νce ), then the of metal anode, is proportional to the applied voltage and kinetic energy would have the same magnitude as the is quantized by Planck’s quantum of action h per the mass-energy of the electron:

Journal equation: Ve K e fmax = = = V, (12) Global hh h h = = = = = ν =∫= ν (13) K hfmax Ve E( e)() 511kV hce ( pe ) ( ce ). pe In the meter and second system of units, the as λ x, may be determined for the electric equivalent of term (h / pe) has the dimensionality of meters, which is the electron mass-energy as a wavelength. This Duane-Hunt wavelength, referred to h 3.990×10−9m31 s− λ= = = × −10 (14) x 21− 2.856 10 m. pe 13.970m s ©20181 Global Journals Revisiting the Bohr Radius

Expanding the electron mass-energy equation to include linear momentum results in

=2 = =ν=∫=λ2 = =ν (15) Emcpche Ae ce e cpWh, e x ce where pAe is the photoinertial linear momentum mec, pe called “the voltage equivalent electric wave speed of the is the electric linear momentum, and Wx is the electric electron mass-energy ” [8] and is the product of the wavefunction corresponding to the intrinsic voltage Duane-Hunt wavelength λ x and the quantum electron (511kV) of the electron mass-energy. The function Wx is Compton frequency νce: =∫= =λ ν = × −−10 × 20 1 511kV Wx x ce (2.856 10 m)( 1.236 10 s ) (16) = 3.529 × 1010 ms−1 . Confirming that 201

E=λ= c2 pW r e ex ea 11 3 −−2 2 1 10− 1 (17) Y 4.930×=10 m s( 13.970m s)( 3.529 × 10 ms ) 611 = 4.930× 1011 m 3 s− 2 , and expanding the electron mass-energy expression to include Wx and its constituents results in

=22 = = ν =∫=λ = =λ Emcpch cpWWW V e Ae ce e e x e k x (18) V =λe W. k( λν x ce ) ue ersion I

s Note that the quantum electron Compton electron mass-energy Wx. Also, notice from equation s

2 I frequency νce of the electromagnetic equivalent of the (18) above that c = Wk Wx. The product of these two electron mass energy h ce is shared with the actual k x ν wavefunctions W and W represents a superimposition, XVIII electric structure of that mass-energy λeWk (λxνce) [9]. where the two separate wavefunctions are For equation (18) to hold true, another wave superimposed perpendicular to one another. Since c speed function, namely Wk, needs to be included in the and Wx are known, it’s then a simple matter of

rearranging the terms to solve for Wk: product of the equivalent gravitational wavelength λe ) and the voltage equivalent electric wave speed of the A ( 81− 2 c2 (2.998× 10 ms ) (19) W = = = 2.547× 1061 ms− . k 10− 1 Wx 3.529× 10 ms Research Volume “ The wave speed Wk is a ctually the magnetic Rearranging the above terms permits the wave speed intrinsic to charge” and in the equation confirmation of the value of Wk. An interesting sidebar to below, “intrinsic to the elementary charge of the the main purpose of this paper is an insight into the

Frontier electron” as well as intrinsic to the electron meaning of the charge to mass ratio. It can be seen mass-energy [10]: below that this ratio results in a wave speed that is exactly equal to Wk, the magnetic wave speed intrinsic Science pe = λe Wk. (20) to charge: of p 13.970m21s− = e = = × 61− (21) Wk −6 2.547 10 ms . Journal λ×e 5.486 10 m

Returning to the Electrostatic System Units of 0.5 1.5−− 1 2 1 q= M L T =∫= LT= p , (9) charge as mentioned above in equation (9) and e Global repeated here for reference, then, if both sides are squared

q2= MLT 32− =∫=LLT32−−= LT42 = p 2 , (22) e and solving for M results in

q2 pp22L42T− = =∫=ee = = = M 32−−32 32−L, (23) LT LT E LT

which agrees with the previous conversion of superimposition of charges, the quantum electric linear 2 dimensionality from mass to length and identifies momentum squared pe , divided by the electron

another wavelength λh that is equal to the mass-energy:

21− 2 p 2 (13.970m s ) (24) =∫=λ = e = = × −10 m h 11 3− 2 3.958 10 m. E 4.930× 10 m s

Since the Duane-Hunt wavelength λ x is the the wavelength λh must be part of the magnetic wavelength of the electron’s intrinsic electric voltage wavefunction intrinsic to charge Wk . This allows the wave speed Wx and λ e is the electron’s equivalent determination of the magnetic wavefunction frequency gravitational wavelength, then by process of elimination as 201

r × 61− ea Wk 2.547 10 ms 15 −1 (25)

Y ν= = = × k −10 6.433 10 s . λ×h 3.958 10 m 621 III. Results A nd Discussion This is the final piece of the puzzle and permits the expansion of the expression for the equivalent electric electron mass-energy into its basic components: V

V E= mc22 =∫=λc = pW =λ WW =λλνλν( )() ue ersion I e e exekxehkxce s

s −−6 10 15 − 1

I =××× ( 5.486 10 m) ( 3.958 10 m)( 6.433 10 s ) (26) −− − XVIII 10 20 1 11 3 2 x( 2.856× 10 m)( 1.236 ×=× 10 s) 4.930 10 m s .

It might have been surmised that the As such the radii of the wavelengths are calculated in wavefunctions Wk and Wx are not electromagnetic since the normal manner: ) the Wx wave speed exceeds the speed of light. This is

A λ ( correct. They are not electromagnetic but electric and r,= (27) 2π travel as ambipolar longitudinal spinning helical waves.

−10 λ 3.958× 10 m r =h = = 6.30×10−11 m, (28) h 2π 6.283

Frontier Research Volume −10 λ 2.856× 10 m −11 r = x = = 4.456×10 m, (29) x 2π 6.283

Science resulting in

of 22 E= mec =∫=λ ec = pWexekxehkxce =λ WW =λ( 2 π r ν)() 2 π r ν . (30)

Journal The structure of the electron, broken down this Each complete circular revolution of the corkscrew has a

way into its basic constituents, presents itself as a flux of wavelength equal to λ x. Acco rdingly, there are λ e / λx Global electric energy shaped as a torus due to the 19,206 rings of wavelength that make up the λx superimposed and trapped wavefunctions Wk and W x. entire total corkscrew length λe. For visualization purposes, one may think of a toy Slinky When the geometric mean of the two

with its ends connected. The total corkscrew wavelength wavefunction radii is calculated, the result is the Bohr λ e is circularized with its ends connected and the radius which compares favorably with the CODATA 10 corkscrew center riding on a circle of wavelength λh. 2014 value of 0.529 x 10- m:

0.5 0.5 =×−−11 ×=×11 −10 (31) (rhx r ) (6.30 10 m)( 4.456 10 m) 0.535 10 m.

IV. Concl usion 3. Fundamental Physical Constants from http://physics.nist.gov.constants , complete listing This is a much more satisfactory and rigorous CODATA 2014. description of the electron and explanation of the Bohr 4. Maxwell JC (1891) “A Treatise on Electricity and radius. Rather than not knowing if the electron is a Magnetism”, Vol.2, republished in 1954 by Dover particle, wave, cloud, cavity, or “a point particle in a Publications Inc., New York, p. 153, referred to in cloud of probable locations”, it is best understood as a Correa PN & Correa AN (1998, 2010) “The Physical “precise toroidal volumetric flux structure” of energy Nature of Electric Charge, Massbound and resulting from two ambipolar longitudinal waves being Massfree”, Volume III of the Aetherometric Theory of superimposed upon and trapped with each other “that Synchronicity (AToS), Akronos Publishing, Concord, occupies the location of the entire ‘cloud’ [11].” Canada, ABRI monograph AS3-III.2, p. 18. The above will serve as an introduction to and

5. Correa PN & Correa AN (1998, 2010) “The Physical 201 simple overview of the amazing work that has been Nature of Electric Charge, Massbound and r accomplished by deciphering and applying Reich’s Massfree”, Volume III of the Aetherometric Theory of ea Y mass to length conversion technique to fundamentals. Synchronicity (AToS), Akronos Publishing, Concord, These tools have been used to further understand and Canada, ABRI monograph AS3-III.2, p. 5. 631 expand upon Louis de Broglie’s (1892-1987) theory of 6. Aspden, H (1977) “Space, Energy and Creation”, matter/particle waves, the complexities of the Lecture delivered to Physics Department at Cardiff electroscope, the thermal anomaly of Faraday cages (as University in Wales, referred to in Correa PN & identified by Reich) (12), and the output of Tesla coils (in

Correa AN (1998, 2001) “The Volt and the Electron- V agreement with Nikola Tesla’s (1856-1943) comments

Volt: An Aetherometric Perspective on Longitudinal V that the coils output energy that is not electromagnetic Electric Mass free Waves”, Akronos Publishing, ue ersion I even though he was unable to provide proof). They also s Concord, Canada, ABRI monograph S2-12, p. 8. s permit the ground-breaking discovery and analysis of 7. Correa PN & Correa AN (1998, 2010) “The Physical I energy that is MASS-FREE! For those interested in this Nature of Electric Charge, Massbound and earth-shaking science, in-depth learning is required and Massfree”, p. 23 equation 213. XVIII can only be accomplished by reading the monographs, 8. Ibid., p. 34. books and other publications. 9. Correa PN & Correa AN (1998, 2001) “The Volt and Some proof of concept machines based on this the Electron-Volt: An Aetherometric Perspective on

research have been built demonstrating utility and the ) Longitudinal Electric Massfree Waves”, Akronos A

correctness of the theories, some of which may be ( Publishing, Concord, Canada, ABRI monograph S2- commercialized. Descriptions of the technologies and 12, p. 10. supporting machines can be found at 10. Correa PN & Correa AN (1998, 2010) “The Physical www.aetherenergy.com. The monographs, meticulously Nature of Electric Charge, Massbound and describing the experiments, thought processes and Research Volume Massfree”, p. 35. conclusions can be found at www.aetherometry.com. 11. Correa PN & Correa AN (2002) “Aether Power from Acknowledgement Pulsed Plasmas”, Labofex Experimental and Applied Plasma Physics, Toronto, Canada, p. 3 Frontier The author would like to thank Dr. Beverly Rubik and 4. for her suggestions and support. 12. Reich, Wilhelm (1953) Biographical Material, This research did not receive any specific grant “History of the Discovery of the Life Energy”, Science from funding agencies in the public, commercial, or not- (American Period 1939-1952), Documentary Volume of for-profit sectors. A-XI-E, “The Einstein Affair”, Orgone Institute Press, The author declares no competing interests. Orgonon, Rangeley, Maine.

Journal References

1. Pauling, Linus (1988) “General Chemistry”, Dover Global Publications, Inc., New York, p. 81.

2. Correa PN & Correa AN (1997, 2001) “Non- Equivalence Between Work Performed by Charge Against Gravity and the Electric Energy of the Same ‘Charge Gas’ Quantum”, Akronos Publishing,

Concord, Canada, ABRI monograph S2-01, p. 13 and 14.