THE MOVEMENT OF AN ELECTRON AROUND THE ATOMIC NUCLEUS

8/10/2019 THE MOVEMENT OF AN ELECTRON AROUND THE ATOMIC NUCLEUS

1/8

1053

THE MOVEMENT OF AN ELECTRON

AROUND THE ATOMIC NUCLEUS

PETRESCU Florian Ion*

*Polytechnic University of BucharestRomania

Abstract:Movement of an electron around the atomic nucleus has today a great

importance in many engineering fields. Electronics, aeronautics, micro and

nano technology, electrical engineering, optics, lasers, nuclear power, compu-ting, equipment and automation, telecommunications, genetic engineering, bio-engineering, special processing, modern welding, robotics, energy and electro-magnetic wave field is today only a few of the many applications of electronic

engineering. This paper presents shortly a new and original relation which cal-culates the radius with that the electron is running around the atomic nucleus.

Key words: Electron, nucleus, nucleons, proton, neutron, atom, quantum

1. INTRODUCTION

This paper presents, shortly, a new and original relation (20) who determines the radiuswith that, the electron is running around the nucleus of an atom.In the picture number 1 one presents some electrons that are moving around the nucleus of

an atom;

Fig. 1Electrons that are moving around the atomic nucleus;atomic nucleus consists of nucleons (protons and neutrons)

One utilizes, two times the Lorenz relation (5), the Niels Bohr generalized equation (7),and a mass relation (4) which it was deduced from the kinematics energy relation written in two

modes: classical (1) and coulombian (2). Equalizing the mass relation (4) with Lorenz relation(5) one obtains the form (6) which is a relation between the squared electron speed (v2) and the

radius (r). The second relation (8), between v2and r, it was obtained by equalizing the mass of

Bohr equation (7) and the mass of Lorenz relation (5). In the system (8) (6) eliminating thesquared electron speed (v2), it determines the radius r, with that the electron is moving aroundthe atomic nucleus; see the relation (20). For a Bohr energetically level (n=a constant value),

one determines now two energetically below levels, which form an electronic layer. The author


2/8

1054

realizes by this a new atomic model, or a new quantum theory, which explains the existence ofelectron-clouds (without spin).

2. THE NEW RELATIONS

Writing the kinematics energy relation in two modes, classical (1) and coulombian (2) one

determines the relation (3):

2.2

1vmE

C (1)

r

eZE

C

..

.

8

1

0

2

(2)

r

eZvm

..

.

4

1.

0

22

(3)

From the relation (3), determining explicit the mass of the electron, it obtains the form (4):

rv

eZm

....4

.2

0

2

(4)

Now, we write the known relation Lorenz (5), for the mass of a corpuscle in function of the

corpuscle squared speed:

22

0.

vc

cmm

(5)

With the relations (4) and (5) one obtains the first essential expression (6):

rv

eZ

vc

cm

....4

..2

0

2

22

0

(6)

One utilizes now, the Niels Bohr generalized relation (7):

Zer

hnm

...

..2

2

0

2

(7)

It uses for the second time the Lorenz relation (5), together with the Bohr relation (7) and

in this mode one obtains the second essential expression (8):

Zer

hn

vc

cm

...

...2

2

0

2

22

0

(8)

Now, one keeps just the two essential expressions (6 and 8).

It writes (8) in the form (8):

Zecmrhnvc ........ 2

0

2

0

222 (8)

Elevating the relationship (8) to the square, to explicit the squared electron speed, it ob-

tains the form (9):
http://www.mediafire.com/download.php?5ywdzjj2m0dhttp://www.mediafire.com/download.php?5ywdzjj2m0d


3/8

1055

42

0

4

2242

0

2242

0

42

..

).......(

hn

cZemrhnv

(9)

The formula (9) can be put in the form (10):

2222 .. rckcv (10)

Where the constant k take the form (10):

42

0

4

242

0

2

..

...

hn

Zemk

(10)

Now one writes the essential relation (6) in the form (6):

2222

00 ........4 vceZvrcm (6)

Then, putting the relation (6) at the square, it obtains the formula (6):

).(.......16 22424220222

0 vceZvrcm (6)

In the relation (6) one introduce the squared velocity of the electron, taken from the ex-

pression (10) and one obtains the formula (11):

keZrckcm ..)...(...16 4222222

0

22

0 (11)

The (11) relationship can be arranged in the form (12):

2

0

22

0

422222

...16

..)..(

m

keZrckc (12)

One squares the relation (12) and it obtains the expression (13):

00

2222

...4

..)..(

m

keZrckc (13)

The relation (13) can be arranged to the form (14):

00

2222

...4

....

m

keZcrck (14)

From relation (14) it explicit the squared electron radius and one obtains the relation (15):

2

00

22

.....4

.1

ckm

eZ

kr

(15)

Now, one exchange in the relation (15), the constant k with its expression (10) and it ob-

tains the relation (16):

22

0

2

22

242

0

2

42

0

42

...4

.

...

..

cm

hn

Zem

hnr

(16)

The expression (16) can be put in the form (17):


4/8

1056

)....4

.1.(

...

..222

0

2

24

242

0

2

42

0

42

nhc

Ze

Zem

hnr

(17)

Extracting the square root of the expression (17), it obtains for the electron radius (r), the

expression (18).

222

0

2

24

2

0

2

0

2

....4

.1.

...

..

nhc

Ze

Zem

hnr

(18)

Physically there is only the positive solution (19):

222

0

2

24

2

0

2

0

2

....4

.1.

...

..

nhc

Ze

Zem

hnr

(19)

The relation (19) is writing in final form (20):

222

0

2

24

2

0

2

0

2

....4

.1.

...

..

nhc

Ze

Zem

hnr

(20)

The expression (20) its not just a new theory for calculating the radius with that the elec-tron is running around the nucleus of an atom, it is also a really new theory of an atomic model,

or a new quantum theory. For a value of the quantum number n (for a constant atomic numberZ), we havent just one energetically level (like in the Bohr model). Now we can find two ener-

getically below levels, which form an electronic layer, an electronic cloud. For example, for

n=1, we have two sublevels (two below levels).

3. USED NOTATIONS

The permissive constant (the permittivity):0

=8.85418*10-12

[2

2

.mN

C];

The Planck constant: h=6.626*10-34[J.s];

The rest mass of electron:0

m =9.1091*10-31[kg];

The Pythagoras number: =3.141592654 [ ];The electrical elementary load: e=-1.6021*10

-19[C];

The light speed in vacuum: c=2.997925*108[m/s];

n=the principal quantum number (the Bohr quantum number);Z=the number of protons from the atomic nucleus (the atomic number).

4. DETERMINING THE TWO DIFFERENT ELECTRON SPEED

VALUES

Relationship (6) may be writtenin the form (6):

016 2422424220222

0 ceZveZvrcm (6)

It can see easily that the relation (6) represents a two degree equation in v2.One calculates v

2with the formula (6

IVa):


5/8

1057

22

0

222

0

24242

0

22

0

28442

2

2,1.....16.2

8

rcm

reZcmeZeZv

(6

IVa)

Physically there is just the positive solution, and one keeps it for the relation (6IV

) (only the

positive sign):

22

0

222

0

24242

0

22

0

28442

2

.....16.2

8

rcm

reZcmeZeZv

(6

IV)

It can thinks that the relation (6IV) gives only one solution for the electron squared speed

(v2), but really there is two solutions for this parameter, v

2, because the value of the squared ra-

dius (r2) gives two physically solutions. It put the relation (6

IV) in the form (6

V):

2

42

2

0

222

0

2

22

42

22

0

22

0

2

2

2,18

2

1

811

reZ

cm

rc

eZ

cm

v

(6V)

The formula (6V) can be written in the form (6

VI), where the constant k1 takes the form

(6VII):

21

22

12

2,1

2

11

rk

rckv

(6

VI)

42

22

0

22

0

2

1.

....8

eZ

cmk

(6VII

)

Now one starts with relation (6VI) who can be written in the form (21):

1..1

.2

22

1

22

rck

cv (21)

One notes the radical with R (see the relation 22):

22

1 ..1 rckR (22)

In relation (22) one introduces for r2the expression (20) and it obtains the form (22):

).

.21(

.1

1

2

1

kc

k

k

ck

R (22)

In relation (22) one exchanges the two constant k1and k with the two values from expres-

sions (6VII

) respective (10) and itobtains for (22) the form (22):

)8

.21(

81

222

0

2

24

0

242

0

242

42

0

442

0

22

0

2

chn

Zem

ZemeZ

hncmR

(22)

Oneput the expression (22) in the form (22):


6/8

1058

)4

1(8

12222

0

24

48

4444

0

2

nhc

Ze

Ze

nhcR

(22)

The expression (22) will be written in the form (22IV

):

24

2222

0

48

4444

0

2 8.281

Ze

nhc

Ze

nhcR

(22IV)

The expression (22IV) can be restricted to the forms (22V) and (22VI):

2

24

2222

0 )8

1(Ze

nhcR

(22V)

24

2222

0

.

....81

Ze

nhcR

(22VI)

One note with E the expression (23):

2

2

4

222

0 ...8

Z

n

e

hcE

(23)

This expression must be evaluated:

2

2

2

2682

764

162242 06551.3756410626.6

106021.1

10997925.21085418.88

Z

n

Z

nE

(23)

For Zmax=92, we have a minimum of expression E (23):

2

min *438098477.4 nE (23)

It can see easily that Emin > 1:

1min E (24)

Now one can write the expression (22VI) in the forms (22VII) a and b:

11 ER (22VIIa

)

12 ER (22VIIb

)

Only now the expression (21) can be evaluated and reduced to two forms (21Ia) and respec-

tive (21Ib):

11

.2 221

E

cv (21

Ia)

11

.2 222

E

cv (21

Ib)

The two relations take the forms (21II) a and b:


7/8

1059

2

2

2

1E

cv (21

IIa)

12

22

2

E

cv (21

IIb)

If one replaces E with its expression (23) it obtains for the electron speeds the relations

(21III

) a and b:

2220

242

1

...4 nh

Zev

(21IIIa)

1.

....424

2222

0

22

2

Ze

nhc

cv

(21IIIb

)

5. DETERMINING THE MASSES AND THE ENERGY OF

THE ATOMIC ELECTRON IN MOVEMENT

The exact squared speeds can be written in the forms (25, 26):

2222

0

2242

11....4

..

nhc

cZevrr

(25)

242222

0

2242

22.....4

..

Zenhc

cZevrr

(26)

With these velocities one can write the two adequate masses (27), (28):

22220

24

011

....4

.

1 nhc

Ze

mmrr

(27)

242222

0

24

022

.....4

.1

Zenhc

Ze

mmrr

(28)

The total electron energy can be written in the forms (29) and (30):


8/8

1060

2222

0

24

2

011

....4

.1

.

nhc

Ze

cmWrr

(29)

242222

0

24

2

022

.....4

.1

.

Zenhc

Ze

cmWrr

(30)

The frequency of pumping, between the two near energetically below levels can be writtenin the form (31):

)

.....4.1

1

....4.1

1(

.

242222

0

24

2222

0

24

2

021

Zenhc

Ze

nhc

Zeh

cm

h

WW

(31)

6. CONCLUSIONS

The paper introduces a new and original relation (20) who determines the radius with that

the electron is running around the atomic nucleus. It explains the two sublevels without spin-theory. The paper realizes a new atomic model and a new quantum theory. It determines as wellthe frequency of pumping between the two near energetically sublevels, with possible applica-tions in LASER, MASER, IRASER industry, and the prediction of new elements.

7. REFERENCES

[1] David Halliday, Robert, R., - Physics, Part II, Edit. John Wiley & Sons, Inc. - New York, London,

Sydney, 1966

[2] Petrescu-Prahova, M., Petrescu-Prahova, I., - Fizica-Manual pentru anul IV liceu, secia real, Editura

Didactici Pedagogic, Bucureti, 1976

THE MOVEMENT OF AN ELECTRON AROUND THE ATOMIC NUCLEUS

Documents

Transcript of THE MOVEMENT OF AN ELECTRON AROUND THE ATOMIC NUCLEUS