QUANTUM MODEL OF HYDROGEN ATOM

prof. Ing. Pavel Ošmera, CSc.

Brno University of Technology

osmera @fme.vutbr.cz

 

September 14-16, 2011

5th Meeting on Chemistry and Life 2011

Main ideas and differences

MENDEL2010

a) spiral structure as the fractal-spiral structure b) fractal-ring structure

Fractals seem to be very powerful in describing natural objects on all scales. Fractal dimension and fractal measure, are crucial parameters for such description.

a) b) c)Vortex structures: a) the vortex VB at the drain hole of bath-tub,

b) the vortex tornado-vortex VT

  c) the vortex in the PET bottle

Topological transformation

MENDEL2009

The vortex-fractal-ring structure of the electron

Mauritsson Johan: online.itp.ucsb.edu/online/atto06/mauritsson/

The fractal ring structure of the electron

MENDEL2010

The fractal ring structure of the electron

MENDEL2007

2

2

2

2 2 N

r

v

N

mNFF

e

eeaoa

NrNr

r

veFF

e

e

e

oooA

2

2

4222

22

22

Aa FF

NrNr

r

veN

r

v

N

m

e

e

e

oo

e

ee

2

2

422

2

222

222

2

2

2

2

4 e

o

e

oe v

v

m

er

2

cvv eo

mm

er

e

oe

152

2

1089.04

22

2 1

8 ee

oe vm

er

MENDEL2007

NrN

r

Nr

vNe

NrN

r

r

vqF

e

e

e

oo

e

e

oe

oooA

2

2

422

2

42 22

22

22

221

2

2

24

N

r

N

e

Fe

o

oC

oCoA FF

2

2

22

22

24

2

2

42

Nr

Ne

NrNr

Nr

vNe

eo

e

e

e

oo

22

1 22 c

voo

o 2

cvo

Amper‘s law Coulom‘s law

2cmE eoo

0 evv2

543

cvvvvo

25255

4244

3233

222 2

1

2

1

2

1

2

1cmNv

N

mNv

N

mNv

N

mNv

N

mE eo

eoeoeoo

eoo

This result is in coincidence with the well-known Einstein’s law.

The levitating electron in the field of the proton

The electron-proton structure of hydrogen

d

proton

elektron

026)1(3 36222232 oo dnddnd

n=7

MENDEL2010

MENDEL2007

n=1

n=1

eVh

emE

o

eio 6.13

8 22

4

eVeVE

E ior 36.1

6.1322

The line spectrum of hydrogen atom

Perhaps the decreasing width Δλ2n of spectrum lines (as Δλ23 = λa - λb) depends on energy Eio and kinetic energy Er . This energy can vary in the interval {Ea, Eb} for {λa, λb} and ΔEλ = Eb - Ea = Eio/(20π2) = Er /20 = 0.069eV (for n1=2 a different size n2>n1). It can be caused by precession of the electron. λa λb

λa λb

MENDEL2010

neutron proton

4

22

2

2

exp2

2

4

1

4

1

4 r

re

r

e

r

A

r

eFFF o

ooo

4

2

2

2 1

4 r

r

r

eFFF o

o

2

2

3

2

5

2

3

2 21

2

42

4 r

r

r

e

r

r

r

e

dr

dF o

o

o

o

for ro

ooo

Kr

e

dr

dF 3

2

4

orr 22,1 Fmax

MENDEL2007

3

22

4

2

2

2

4

2

2

2

3

1

4

1

4

1

4 r

r

r

edr

r

r

r

edr

r

r

r

eE o

o

o

o

o

o

3

22

3

22

4

2

2

2

3

1

43

1

4

1

4 r

r

r

e

r

r

r

edr

r

r

r

eE o

or r

o

o

o

oo

mr

r oEo

111005.33

For Eo=0

eVr

e

r

e

r

r

r

eE

ooooo

o

ooo 13.18

1

63

21

43

1

4

22

3

22

eVeVr

eE

oo

13.183

22.27

3

21

4

2

min

Hzm

Kf

e

oo

14103.92

1

sf

To

o1510075.1

1

ooo

Kr

e

dr

dF

3

2

4

MENDEL2007

3

22

4

2

2

2

4

2

2

2

3

1

4

1

4

1

4 r

r

r

edr

r

r

r

edr

r

r

r

eE o

o

o

o

o

o

3

22

3

22

4

2

2

2

3

1

43

1

4

1

4 r

r

r

e

r

r

r

edr

r

r

r

eE o

or r

o

o

o

oo

4

24

2

2

4

24

2

2

4

2

2

2

11

4

1

4

1

4 d

dn

d

e

d

dn

d

e

d

dn

d

eFFF o

o

o

o

on

on

2

242

3

242

3

22

31

1

43

1

43

1

4 d

dn

d

e

d

dn

d

e

d

dn

d

eEE o

o

o

o

on

oinn

4

2

2

2 1

4 r

r

r

eFFF o

o

ond odn2

n=1

n=1

n=1 to 7

MENDEL2010

de Broglie’s equation

)( eee vrmS

22

1 hvr

N

mNS ee

ez

nre 22 2

2n

re

4er

22

1

4

hvmvr

N

mNS eeee

ez

eevm

h

)( eee vrmS

eee

z vrN

mNS

20

2

2 1

8 eee vm

er

h

eve

0

2

2

2

20

4

220

2

02

2

20

2

2

2

4

8

1

8 em

h

e

h

m

e

vm

er

eeeee

se

eeeez mh

em

h

h

emrvmS

2

1

22

1

22 2

20

0

2

2

1sm

ISM z

e

e

v

rT

2

e

e

e

e r

ve

v

r

NN

e

TQ

I

2

12

2

2erS

Be

zee

ee

e

ez m

eS

m

e

m

mr

r

veISM

2

12

The spin of the electron

Magnetic momentum Mz

μB is Bohr magneton

2

2

2

2

4 e

o

e

oe v

v

m

er

eeeeoee

o

e

o

e

oe vm

hnn

vm

e

v

c

m

e

v

v

m

er

2

1

2

1

44422

2

2

2

22

2

2

2

2

nhv

e

eo

1

2

2

2

2

1eer vmE

h

e

nv

oen 2

1 2

222

4

22

8

1

2

1

h

em

nvmE

o

eenern

eVh

emE

o

eio 6.13

8 22

4

112

2

1029.5 em

hrd

e

oBo

2

cvo

Quantum physics

eVeVE

E ior 36.1

6.1322

18

1

4

3

3

21

48

16.13

1 2

222

4

22

2

22

4

22

h

em

ndn

e

h

em

neV

nE

o

e

ooo

eno

onoen ddnr22

2

oe dr2

enr

enr

eeee me

hn

e

hn

m

e

vm

e2

20

2

4

220

22

02

2

20

2

2

2

4

8

1

8

MENDEL2010

2

22

2

22

222 em

hn

em

hndr

e

o

e

oonen

0263 323 oo rrrr

r1 = 0.7223517245ro ~ 0.382Å,

r2 = 1.792517214ro ~ 0.948Å

on En

E2

1

h

ev

oe 2

2

max 1371

max

ev

c

the couple constant α

4

2

2

2

4 r

r

r

nneFFF ope

o

02

4 4

2

2

2

r

r

r

eF o

o

mr

r oc

111075.32

mrd ccp11105.72 mrd op

11106.102

Covalent bond

221

112

1122

NNr

NNN

NrNTp e

eoe

mNN

rp e 15

21 1000693.011

mTDpD oeoeC15

11 100996.022

122 CNDp mND

p C 1512 10666.0

2

mDpD Cph15

12 10232.12

mD

R phph

1510616.02

oeNDp 32

mND

p oe 153 10290.0

2

mDDpD oeCC15

132 10736.022

mDDD phCp15

2 1070.22

mD

R pp

151035.12

The spin of the electron

Vortex structures with spin 1/2

MENDEL2010

the vortex structure of the electromagnetic field (photons)

MENDEL2009

the structure of the electric field the structure of the magnetic field

Lim, T.T.: serve.me.nus.edu.sg/limtt/

Lim, T.T.: serve.me.nus.edu.sg/limtt/

Examples of spiral structures: a), b) galaxies, c), d) the Earth’s hurricane

Jupiter’s spot

History (2004)

alpha particle

Vortex structuresOne hole Two holes

Structure of light as a ring particle or a wave energy structure

Logarithm of complex number (Re) dark matter

Polarization of a light rayPhoton coming though the sheet with two holes. a) The photon before the way through, b) the photon vortex structure is split to two sub-vortex structures (e.g.: osmeron rays), c) the photon behind the sheet

Forces between two gravitational parallel fibers

Vortex structure of light rays

Example: how we can measure the wavelength of light

Diffraction on the DVD surface

ZElement Z configuration

O 8 1s22s22p4

Oxygen

the classical structure model of the water molecule H2O

Element A=Z+N configuration

C 12 1s22s22p2

Carbon

atoms

nucleus

H He T

D

O C N

F

Ne

MENDEL2010

benzene molecule

Ball lightning

Plasma Ball

MENDEL2010

PhotonMENDEL2011

Electromagnetic field of the electron MENDEL2011

The structure of water MENDEL2011

The structure of the gold MENDEL2011

Structure the of hydrogen atom

The structure of hydrogen with one layer of the electromagnetic field

http://www.youtube.com/watch?v=OsW8zctD7CM MENDEL2011 magnetic liquid

Conclusions The annular-vortex model might be better than a classical planetary one. Vortex structures can explain the electromagnetic field. Fractals seem to be very powerful in describing natural objects on all scales. To understand the electromagnetic field requires a high degree of imagination.

The degree of imagination that is required is much more extreme than that required for some of the ancient ideas. The modern ideas are much harder to imagine. We use mathematical equations and rules, and make a lot of pictures. We can’t allow ourselves to seriously imagine things, which are obviously in contradiction to the known laws of nature. And so our kind of imagination is quite a difficult game (or a puzzle). One has to have the imagination to think of something that has never seen before, never been heard before. At the same time the thoughts are restricted or limited by the conditions that come from our knowledge of the way nature really is. The problem of creating something which is new, but which is consistent with everything, which has been seen before, is one of extreme difficulty.