![Primary Electromagnetic Radiation (P-EM-R) interaction with Carbon atom electron; the Radiation Magnetic Force (F mR ) embedded in P-EM-R [11] forced electron from point-1 to point-2 at high Binding Force Orbit (F bFE ), the Total Circular Magnetic Field (B CMFT ) formed Secondary Radiation Energy (E s ) and Forced Binding Energy (E bFE ). Electron' relativistic velocity and mass in distance (d 1 ) is controlled by frequency and angle ϕ, where CMF and the Electric Field (EF) are Flip-Flop (F-F), generating Secondary Electromagnetic Radiation (S-EM-R) at point-3, pulled by Electromagnetic Radiation Force (F EMR ) and released through lin-4 at angle ϕ with increased wavelength; then electron is ejected at angleϕ.](https://www.researchgate.net/profile/Mahmoud-E-Yousif/publication/299347018/figure/fig2/AS:388521979334658@1469642266869/Primary-Electromagnetic-Radiation-P-EM-R-interaction-with-Carbon-atom-electron-the_Q320.jpg)
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© 2016 Mahmoud E. Yousif. Volume 1 Issue 1 JAAP-1-004 Page 1 of 13
Journal of Advanced and Applied Physics
Received: Dec 14, 2015, Accepted: Mar 01, 2016, Published: Mar 04, 2016
J Adv Appl Phys, Volume 1, Issue 1
http://crescopublications.org/pdf/jaap/JAAP-1-004.pdf
Article Number: JAAP-1-004
Research Article Open Access
The Compton Effect Re-Visited
Mahmoud E. Yousif*
Physics Department - The University of Nairobi, P.O.Box 30197, Nairobi, Kenya
*Corresponding Author: Mahmoud E Yousif, Physics Department - The University of Nairobi, P.O.Box 30197, Nairobi, Kenya,
E-mail: yousif_474@yahoo.com
Citation: Mahmoud E. Yousif (2016) The Compton Effect Re-Visited. J Adv Appl Phys 1: 004.
Copyright: © 2016 Mahmoud E. Yousif. This is an open-access article distributed under the terms of the Creative Commons
Attribution License, which permits unrestricted Access, usage, distribution, and reproduction in any medium, provided the
original author and source are credited.
Abstract
The Primary Electromagnetic Radiation (P-EM-R) is suggested to interact with inter-atomic electron during Compton
Effect phenomena, producing Radiation Magnetic Force (
) moving electron to higher binding Energy, where an
increased in Total Circular Magnetic Field (
) automatically formed electron Forced Binding Energy (
) and
Secondary Radiation Energy (
); the
is added to the related Orbit Binding Energy (
) constituting
Electron’s Kinetic Energy (
), while
is transformed into Secondary Electromagnetic Radiation (S-EM-R) through
the Flip-Flop (F-F) mechanism, characterized by relativistic mass/velocity frequency and angle
1
controlled, ended
with increased S-EM-R wavelength releases at angle ϕ; a recoil force resulted from S-EM-R releases, ejecting electron
at an angle θ, the force is added to
to form electron’s energy (
); the
is also related to x-ray process of
production from energetic electron impinging anode in an x-rays tube; the paper accommodates Compton formulas
except the momentum photon; the paper is aimed at improving our understanding to the physical reality.
Keywords: Compton Effect; Generation of secondary electromagnetic radiation; X-ray production; Circular magnetic
field; Electron binding energy; Atomic structure.
PACS No:13.60.Fz;41.50.+h; 41.50.+h
1. INTRODUCTION
Compton stated in 1923, that “scattering is a quantum
phenomenon; and a radiation quantum carries with it
momentum as well as energy”[1], after trial with classical
solution till end of 1922[2], the interpretation consolidated
Einstein 1905 photoelectric effect[3], rejected by leading
contemporary scientists[4], while Bohr tried a different
model[5]; but Compton’s formula and experimental
verification, changed destiny of Einstein’s quantum
model[6].
Compton believed in the universal validity of classical
electrodynamics[2], neither motivated nor influenced by
Einstein’s 1905 light-quantum hypothesis[7], only
shifted to quantum after six years in classical physics[2],
implying he may have known about Einstein light-quantum.
However, the quantum theory of scattering only applied to
light elements[8], and failed to resolve the heavy atoms,
where recoil energy is smaller than the binding energy of
scattering electron[9], and CE was contested with a classical
model[10], in addition to discovery that Radiation Magnetic
Force (
) embedded Electromagnetic Radiation (EM-R),
similar to Planck’ Energy (
)[11], casting doubt on
photon existence and necessitate revision of CE.
© 2016 Mahmoud E. Yousif. Volume 1 Issue 1 JAAP-1-004 Page 2 of 13
At his era, Compton interpretation necessitate
billiard-ball of quanta, a situation expressed by Raman that
“the classical wave-principles are not easily reconcilable
with Compton effect because they have not been correctly
interpreted,”[10], that shortage resulted from lack of
understanding to nature of magnetism and magnetic force,
where a formula expressing interaction between charged
particle magnetic field with stationary magnetic fields give
same force but different mechanism[12], the spinning
magnetic field, and spinning magnetic force deduced fields
magnitudes and formulas for each charged particle and their
interaction with each other[13], helped in forming atomic
model in which the force by both the magnetic force
produced by revolving electron and nucleus, and the
electrostatic field are balanced with the centripetal force[11,
12], all of which suggested the Electromagnetic Radiation
(EM-R) to be produced through the Flip-Flop (F-F)
mechanism, of both the Circular Magnetic Field (CMF) and
the Electric Field (EF) of charged particles[14], rather than
charged acceleration[15]; the Flip-Flop (F-F) mechanism
showed EM-R energy to be concentrated in the magnetic
field as twisted CMF, all of which gives the condition
initiating EM-R production and nature of Planck’ Constant
(h)[16], helped in re-explaining the photoelectric effect by
deriving the Radiation Magnetic Force (
) embedded in
EM-R similarly to Planck’ energy formula, the
expels
electron from the atom, rather than the quanta (photon), it
also disclosed the origin of Planck’ constant[11].
Using these as a bases, this paper re-investigated
the Compton Effect and suggested the interaction of x-ray
and γ-rays Primary Electromagnetic Radiation (P-EM-R)
with inter-atomic electron, as a phenomenon in which the
embedded Radiation Magnetic Force (
), moved electron
towards the nucleus at the Force Binding Energy (
)
orbit, where the total produced CMF (
) interacted with
nucleus Spinning Magnetic Field (
1
), distributing
the
energy into Forced Binding Energy (
) and
Secondary Radiation Energy (
), the
is transformed into
Secondary Electromagnetic Radiation (S-EM-R) through the
Flip-Flop (F-F) mechanism, during which electron’s
relativistic mass and velocity are controlled by frequency
and angle
1
, S-EM-R is released at angle ϕ, afterward the
recoil force ejected electron at angle θ. A relation is
established between electrons energized by P-EM-R and x-
rays electrons accelerated in x-ray machine[17], it suggested
both to radiate
as S-EM-R. The method used is based on
creating a model from the ambiguous characteristics of the
CMF, then compared and testing the results with
reproducible derived data, given in Tables 1, 2, 3 and
Figures 1 and 2.
Eighty seven years ago, Raman stated that “the
classical wave-principles are not easily reconcilable with
Compton effect because they have not been correctly
interpreted,” he then asked “What would be the nature of the
secondary radiation emitted by the atom?” [10], the correct
interpretation of magnetic field relation with atom, and the
generation of electromagnetic radiation helped in this
explanation. This raised a question, of whether some
concepts (such as Compton Effects) are scientific truth, and
if so how a scientific truth can be accepted to become a final
truth?[18], particularly when it imposed such decisive
conclusion which diverted the course of the physical science
to such mathematical structure; while this reinterpretation
illustrates the phenomena as an amazing outstanding natural
mechanism; therefore, it is hoped that, this explanation
which also strengthened inter-atoms mechanism knowledge,
would restore sense of sanity within the scientific arena, and
may lead to a better understanding to the inner mechanism
of nature, and reduce inefficiency in x-ray generation [17]
among others, reflecting positively on future energy crises
and technological developments on this planet and in the
space, and to form a better understanding to our status in the
Universe based on accurate scientific knowledge.
2. The Interaction of Radiation Force and Energy
with Inter-atomic Electron
The interaction of x-ray, and γ-rays Prime Electromagnetic
Radiation (P-EM-R) in Compton Effects, with inter-atomic
electrons, forced electron to high binding energy orbit
shown in Figure 1, and given in Table 1, the force is
expressed by[11]
=
1
2
2
+
3
=
(1)
Where,
1
is the strong magnetic field or nucleus Spinning Magnetic Field (SMF) in Tesla,
2
is the Circular Magnetic Field
(CMF or
) produced by orbital electron in Tesla,
is the magnetic radius in meter, c is the velocity of light in m.s
-1
, is the
Prime Electromagnetic Radiation (P-EM-R) Frequency in Hz, y is the constant of radiation force with magnitude equal
1.9063181614361072009999849625463×10
-61
N
2
. Hz
-3
(or N
2
.s
3
.),
is threshold Force,
is Compton Effect Force and
is the Radiation Magnetic Force.
© 2016 Mahmoud E. Yousif. Volume 1 Issue 1 JAAP-1-004 Page 3 of 13
Figure 1: Cross section of atom, showing electron on left at orbit Magnetic Radius (r
m1
), and then moved to right by Radiation
Magnetic Force (F
mR
) embedded in Primary Electromagnetic Radiation (P-EM-R) to the Forced Binding Orbit (F
mFE
); energy is
divided to Secondary Radiation Energy (E
s
) by Secondary CMF (B
CMFS
) in green color and Electron Binding Energy (E
bFE
), of
Forced CMF (B
CMFE
) in black color.
The electron acquired energy is added to orbital energy[11],
and transferred into
, as
=
2
2
4
2
2
2
Where,
is the CMF at n
th
orbit,
is magnetic
radius of gyration at n
th
orbit.
Rearranging Eq. (2) and solving the physical constants, the
Total CMF (
)[12], is
=
4
3
Where,
shown in Figure 1 is forced orbital radius in
m,
is the constant of Primary Radiation Energy, equal
4.1493087273019205468914124949556×10
-58
T
2
. m
4
. Hz
-
1
.(T
2
. m
4
. S.) and
is the Total energetic CMF.
The CMF (
2
)[19 - 21],of an electron accelerated to anode
in X-ray tube[17], is
=
2
4
Where,
is electron velocity in m s
-1
,
is x-ray
electron CMF.The CMF given by Eq. (4), increased in
similar manner to electron energized by P-EM-R given by
Eq. (2), therefore x-ray electron in anode’ atom is forced to
high binding energy given by
=
2
2
4
2
2
(5)
Where,
is x-ray potential difference in x-ray tube [17],
is the total CMF,given by
=
4
(6)
Where,
is the constant of energetic x-ray electron with
value equal to 6.2620909274304534364140772240757×10
-
25
T
2
. m
4
. J
-1
© 2016 Mahmoud E. Yousif. Volume 1 Issue 1 JAAP-1-004 Page 4 of 13
The CMF given by Eq. (3) is to be derived in term of
frequency, but substituting the right hand of Eq. (2) with
related energy frequency formula[11], the
is given by
=
5
(7)
Where,
is the constant of
it is equal to
1.3113864619620884691409896280354×10
-89
T
2
. Hz
-5
(T
2
.
s
5
), Eq. (7) can be used to derived both
and
.
1
=
+
1
1
E
135
367,029.
4658483
2231903
7704830
8617
8.874729689
1529720434
8544014082
09×10
+19
0.365014834
1219567126
5889764564
178
3.59315634065
5947445770593
7786494×10
+8
6.3405045419
760391112647
608201896×1
0
+9
5.1282267375
286042747447
351515155×1
0
-13
729,677.583
4042025704
6795009670
331
6.162432922
8965839056
2860828070
93×10
-14
90
o
299,987.
2086720
8492604
2753040
27357
7.253655727
6534786290
9840873251
28×10
+19
0.269717285
1708296813
3062730386
029
3.24845620981
4910163707441
1479329×10
+8
5.1822836538
285942427637
807969316×1
0
+9
5.0944005735
429321954694
027406879×1
0
-13
668,467.293
5493425892
8575416394
909
7.168909080
3229403705
3367789680
95×10
-14
45
o
136,138.
2439353
3233195
5952758
96553
3.291806864
8508373965
2320697169
12×10
+19
0.082450941
0332048953
5268793578
921
2.18834464382
8788474001222
9058646×10
+8
2.3516317438
986611251029
60797305×10
+
9
5.4589445765
631044770169
996463247×1
0
-13
392,182.018
9891304643
3793116635
934
1.296610857
4718205492
3300564867
62×10
-13
C(6)
No
-n
(eV)
1
6
489.9
1.184572487
8429169724
9752134578
×10
+17
1.780083459
5941409409
0883666170
15×10
-5
1.31274196260
5827226634465
2531452×10
+7
8.4635081047
008062118717
794052962×1
0
+6
8.8187626230
284588457052
737727899×1
0
-12
90.14743833
4972174884
0766845176
13
8.824442547
2833599423
8118096599
97×10
-12
1
=
+
1
1
E
170
409.8504
5521844
9876377
0527579
0976
9.910136219
2625271123
5506539182
95×10
+16
1.362125517
3314535791
6417292059
13×10
-5
1.20071064001
9498553345566
5790662×10
+7
7.0805694564
503493524718
251686851×1
0
+6
9.6415946942
633119493850
983665318×1
0
-12
68.98107288
3089199231
0037330961
11
1.008785654
9331927474
4633969918
35×10
-11
C(6)
No
-n
(eV)
1
5
392
9.478514293
4154613843
4432266882
56×10
+16
1.274114053
8221777053
0308609813
12×10
-5
1.17427193590
2251753589847
2334942×10
+7
6.7721885630
592284855148
755396537×1
0
+6
9.8586702105
030632991446
16399875×10
-
12
64.52400727
5953137756
1276518582
68
9.521660364
3997008722
2219422314
14×10
-12
4
64.4
1.557184491
0611115131
4228158130
71×10
+16
8.484143521
6617143446
3041781597
1×10
-7
4.75957946276
2838550094375
2463081×10
+6
1.1125738353
597303940488
72410086×10
+
6
2.4323072750
610659295497
282475041×1
0
-11
4.296561494
4730338592
2910634972
01
3.300333513
2273749885
1399530607
2×10
-11
3
47.8
1.155798426
5950486075
8076179482
11×10
+16
5.425266175
7901194610
1596215219
14×10
-7
4.10052625099
5243369034598
2032188×10
+6
8.2579238090
365082042757
921121284×1
0
+5
2.8232375663
244403037562
88331487×10
-
11
2.747477065
7346535371
5114774993
93
3.574225420
0986314728
4241816746
02×10
-11
2
24.3
5.875711666
5815232561
1140410337
1.966475844
1905183629
0665441705
2.92367291892
9534226832814
7079564×10
+6
4.1980658694
474299030104
968268769×1
3.9596630931
438034332815
039176218×1
0.995867687
8093979760
3000729672
4.847329330
4712610623
9856747938
© 2016 Mahmoud E. Yousif. Volume 1 Issue 1 JAAP-1-004 Page 5 of 13
91×10
+15
45×10
-7
0
+5
0
-11
399
2×10
-11
1
11.2
2.708146940
9758461098
1266361966
45×10
+15
6.153273791
9840666115
9028638113
88×10
-8
1.98488184567
2159939069043
0291252×10
+6
1.9349110180
169224244328
215827581×1
0
+5
5.8324679520
603608754985
470798925×1
0
-11
0.311615653
0366031727
2641366016
265
6.127435061
7545938710
2526913285
52×10
-11
Table 1: Parameters of Carbon atom (C6)[11] from the bottom left, electron’s number (No), binding energy (
-n), Ionization
Frequency (
), binding force (
), Orbit Velocity (
), Magentic Field (
1
), Magnetic Radius (
), Circular
Magnetic Field (
), and Electrostatic Radius (
). The first three electrons are moved to forced binding of angles (
1
)
45
, 90
, and 135
, has the same Primary Electromagnetic Radiation (P-EM-R) frequency, the Radiation Magnetic Force (
)
added binding orbit force to each, to occupy Forced Binding Energy (
) orbits. From top: released Angle (ϕ), Forced Binding
Energy (
=
1
+
), Ionization Frequency (
), Forced Binding Force (
), Electron Velocity (
), strong Nucleus
magnetic field (
1
), Forced Magnetic Radius (
), CMF (
), and the electrostatic Radius (
). Electron’ Energy (
) at
angle 170
is 409.8 eV, is forced between orbit 5&6.
Electron shown in Figure 1, in natural orbit has
large CMF and radius[12], and since P-EM-R is divided into
Secondary Radiation Energy (
) and ejected Electron
Kinetic Energy (
) [22], therefore when electron receive P-
EM-R as
in Eq.(3), it form the Forced Orbit CMF
(
) touching
1
at an increased magnitudes, reducing
gyrating radius to Forced Electron Radius (
); and
formed the Secondary CMF (
) touching
1
at higher
magnitudes; both connections determined division of
into
and
, given by
=
+
=
4
+
4
(8)
Eq. (7) also derived
, P-EM-R (
), and the
, as
=
5
5
(9)
Where,
is the P-EM-R frequency and
is the secondary
radiation frequency, in Table 2.
The
in Eq. (6), is divided between x-ray CMF
similar to Eq.(8) it is
=
+
=
4
+
4
(10)
Where,
is x-ray Secondary Radiation CMF and
is energetic electron CMF.
The amount of
in Eq. (8 or 9) is developed into the
secondary radiation energy, as
=
=
2
2
4
2
2
(11)
Where,
is the P-EM-R energy,
is the forced binding
energy, and
is the Secondary Radiation Energy.
Since measured electrons energies always higher than
calculated[5], and target atoms necessarily contain bound
electrons[6]; therefore binding energy in Eq. (2) is added to
in Eq. (8), forming the Electron Kinetic Energy (
)
=
+
=
2
2
4
2
2
+
2
2
4
2
2
(12)
Where,
is the binding energy of the orbital electron
given in Eq. (2)[11],
is the forced binding energy
subtracted from the P-EM-R,shown in Eq. (11).
While x-ray electron kinetic energy (
) is derived from
in Eq. (10), as
=
=
2
2
4
2
2
(13)
Where,
is x-ray electron binding energy, and
is x-
ray electron kinetic energy.
The Secondary Radiation Energy (
), represented by
in Eq. (10) is
=
=
2
2
4
2
2
(14)
© 2016 Mahmoud E. Yousif. Volume 1 Issue 1 JAAP-1-004 Page 6 of 13
From Eq. (11&12) energy distribution is guided by the conservation of energy as
=
+
=
2
2
4
2
2
+
2
2
4
2
2
(15)
The above principle of conservation of energy, is in the core
of Compton’s formulas [22]
= +
2
1
1
2
1
(16)
Where, mc
2
1
1β
c
2
1 is the kinetic energy of the
recoiling electron.
The Forced Radius of Gyration (
) is derived from Eq.
(4), is
=
(17)
As CMF distribution is the essential parameter, therefore
from Eq. (5),
is given by
=
2
2
2
2
4
(18)
Eq. (18) is important in deriving
when
and
is
given, as in Table 1. After getting radius,
is derived from
Eq. (17), and the strong magnetic field
1
in Table 1, is
1
=
3
(19)
Table 1, gives
in P-EM-R interaction with inter-atomic
electrons in Carbon atom (C6), forcing each of first four
electrons to high Forced Electron Binding Energy (
).
From these, the x-ray
, given by Eq.(14) is similar to
Compton
, given by Eq. (11), and x-ray
given by Eq.
(15), is similar to
given by Eq. (12); therefore, existence
of forced orbit electron energized by high frequency
radiation, is synonymous in characteristics to energetic X-
rays electrons forced into temporarily orbit in anode atom.
3. Generation of Secondary Radiation
Since the secondary X-rays are emitted by fast moving
electrons[8], and tertiary radiation was suggested to be
produced by photoelectrons, liberated by the primary X-rays
stroking neighbouring atom and emitted bremsstrahlung
radiation[9], and no scattered γ-radiation have the original
wavelength[5], showing a lower energy phenomenon, and as
anode bombardment by energetic electrons produced X-
rays[17], suggested a link with energetic Compton electron;
and since any substance struck by cathode rays emitted x-
rays, and rays are intense from high atomic weight target[5],
and Bremsstrahlung x-rays are produced when an energetic
electron passes close to the nucleus[17], and that the shortest
radiation/particle bursts (such as x-ray and γ-rays) are
produced by highest power laser, having high magnetic
field[23], all three example simplying the influence of
nucleus
1
on x-rays production; thus the long lasting
Maxwell’s electron acceleration generating EM-R [15],
thought to divert attention from E-MR Flip-Flop (F-F)
mechanism[14], therefore electron existence with
at
, and both
and
possess the Primary
, and
since
and
are separated in frame shown in Figure 1;
while electron maintain Electric Field (EF) at point-2 before
moving to point-3 along distance
1
in Figure 2, therefore
two interconnected phenomena occurred, (1) the
release
phenomenon and (2)
Electron Ejection phenomenon.
© 2016 Mahmoud E. Yousif. Volume 1 Issue 1 JAAP-1-004 Page 7 of 13
Figure 2: Primary Electromagnetic Radiation (P-EM-R) interaction with Carbon atom electron; the Radiation Magnetic Force
(F
mR
) embedded in P-EM-R [11] forced electron from point-1 to point-2 at high Binding Force Orbit (F
bFE
), the Total Circular
Magnetic Field (B
CMFT
) formed Secondary Radiation Energy (E
s
) and Forced Binding Energy (E
bFE
). Electron’ relativistic velocity
and mass in distance (d
1
) is controlled by frequency and angle ϕ, where CMF and the Electric Field (EF) are Flip-Flop (F-F),
generating Secondary Electromagnetic Radiation (S-EM-R) at point-3, pulled by Electromagnetic Radiation Force (F
EMR
) and
released through lin-4 at angle ϕ with increased wavelength; then electron is ejected at angleϕ.
In
(
) release phenomenon, the interaction of the
with Nucleus
1
, shown in Figure 1, and given in
Table 1, resulted in the Constant state of Radiation (
)
initiated the Flip-Flop (F-F) mechanism producing the
Electromagnetic Radiation (EM-R), the
is[16]
=
1
(20)
Where,
is the Flip-Flop (F-F) radius (or magnetic
radius
, it is quarter of wavelength), and
is the EM-R
constant equal 5.3585813301090455233656153661379×10
-
3
T.m[16].
This occurred, when electron in Figure 2 start moving from
point-2 to point-3 along distance
1
, initiate the Flip-Flop
(F-F) mechanism; where the combined CMF-EF Flip-Flop
(F-F), producing the Secondary Electromagnetic Radiation
(S-EM-R)[14], the Flipping Time (
)is[16]
=
4
1
=
1
(21)
Where, is the S-EM-R frequency, and
is the Flipping-
Time[16], given in Table 2.
The F-F ended at point-3 in Figure 2, where
in Eq. (11),
is transformed into S-EM-R[14], and released through line-
4, parameters of which are in Table 2, the frequency is
=
2
2
4
2
2
(22)
© 2016 Mahmoud E. Yousif. Volume 1 Issue 1 JAAP-1-004 Page 8 of 13
The wavelength of which is given by
`
=
2
2
2
4
(23)
The S-EM-R is produced at line-3, but pulled and released at
line-4, force causing this is
=
1
r
2
(24)
Where,
is Electromagnetic Radiation Force in Newton,
given in Table 3.
The S-EM-R will be released at speed of light, given by[16]
=
1
=
1
(25)
Where, ε is the permittivity of free space, μ is the
permeability of free space.
4. Kinematics of the Compton Interaction
Kinematics of Compton interaction were solved based on
wave particle duality[24]; while as shown in Figure 2, S-
EM-R production is carried between poin-2 and point-3,
along arc
1
, travelled by electron during the Flip-Flop (F-
F) mechanism, therefore this length is given by
1
=
=
2
1
360
(26)
Where,
1
in Fig. 2, is the angle formed between line-1
where P-EM-R interacted and forced electron from point-1
to point-2, and line-2, where S-EM-R is produced at point-3,
is electron velocity in m.
1
,
is the Flipping time (1/)
in s and
1
is the arc distance in m.
Since Compton Effects is characterized by S-EM-R
increased in wavelength, and the increase is greater at large
angles[22], therefore
reduction by
is the main factor in
wavelength increases; while
1
increased by increases in
1
,
and by
, and since
1
is equal to ϕ, hence substituting
with(
`
4
)[16] in Eq. (26), therefore, angle
1
is
1
= =
360 (4)
2
`
(27)
From Eq. (27), the S-EM-R wavelength is
`
=
360 (4)
2
1
(28)
Since the energy of ejected electron varied with the angle of
recoil from the direction of the beam[5], and electrons with
forward velocity of about 0.7 the speed of light been
detected[8], therefore, electron movement between Point-2
and Point-3 in Figure 2, during the F-F mechanism, created
relativistic velocity (
), hence from Eq. (27),
is
=
2
1
360 (4)
(29)
Where,
is the relativistic velocity in m.
1
, and since
`
is equal the speed of light c, hence
=
2
1
360 (4)
(30)
Solving constants in Eq. (30), the
during distance
1
in
Figure 2, is
=
1
(31)
Where,
is the constant of velocity while radiating S-EM-
R at specific angle
1
its equal to
1.3089969389957471826927680763665e+6 m.
1
. Degree
-
1
.
The equivalence of radiation energy and kinetic energy, for
the above
is given by
= =
2
2
(32)
Modeling Eq. (32), and substituting
with Eq. (30), the
Relativistic Mass is given by
=
2(360)
2
(4)
2
4
2
2
1
2
(33)
Solving the physical constants into digits, therefore,
, is
given by
=
1
2
(34)
Where,
is the constant of relativistic mass it is equal to
7.7340880807314632074240051521845×10
-46
kg. degree
2
.
Hz
-1
(or kg. degree
-2
. S).Table 2 give electron parameters
during distance
1
, where electron movement shown in Fig.
2 is synchronized with fast occurs
, by controlling and
changing
and
.
© 2016 Mahmoud E. Yousif. Volume 1 Issue 1 JAAP-1-004 Page 9 of 13
=
=
(
)
1
angle
563,95
4.8963
035196
609603
757157
1431
2.2
×10
-12
1.3612
704393
533233
195595
275896
553×10
+5
427,82
7.8523
681873
290044
229567
4879
2.9×10
-
12
7.25×1
0
-13
1.034482
7586206
8965517
2413793
1034×10
+20
9.666666
6666666
6666666
6666666
6667×10
-
21
3.951002
8509483
8478029
3233794
2192×10
-
29
5.890486
2254808
6232211
7456343
6493×10
+7
5.694136
6846315
0024471
3541132
1943×10
-
13
0.21
10
45
o
θ
24.5
o
563,95
4.8963
035196
609603
757157
1431
2.2
×10
-12
2.9997
600867
208492
604275
304027
357×10
+5
263,97
8.8876
314347
349176
226754
4075
4.7×10
-
12
1.175×
10
-12
6.382978
7234042
5531914
8936170
2128×10
+19
1.566666
6666666
6666666
6666666
6667×10
-
20
6.094632
0573139
9779938
8498937
8917×10
-
30
1.178097
2450961
7246442
3491268
7299×10
+8
1.845685
6839840
0352759
6802987
6768×10
-
12
0.22
27
90
o
θ
47.8
o
563,95
4.8963
035196
609603
757157
1431
2.2
×10
-12
3.6701
826584
832231
903770
483086
17×10
+
5
196,93
6.6304
551973
419226
708848
5261
6.3×10
-
12
1.575×
10
-12
4.761904
7619047
6190476
1904761
9048×10
+19
2.1e-20
2.020795
1089506
7299168
4370018
2075×10
-
30
1.767145
8676442
5869663
5236903
0948×10
+8
3.711006
3220529
4326293
3997496
499×10×
10
0.14
35
135
θ
69.4
o
10,339.
173098
897860
450940
221454
762
1.2
×10
-10
398.65
045521
844987
637705
275790
976
9940.5
226436
794105
745631
686968
527
1.2481
242851
517785
837437
332070
301×10
-10
3.1203
107128
794464
593593
330175
753×10
-11
2.403606
7847483
5057498
6262009
7013×10
+18
4.160414
2838392
6194581
2444023
4337×10
-
19
6.432424
4237672
9893073
3745340
1683×10
-
32
2.225294
7962927
7021057
7705729
8231×10
+8
9.258148
2562496
2187446
7381173
7206×10
-
11
0.00
16
170
θ
85.1
o
=
=
(
)
1
Angle
Table 2: The relativistic parameters of the electron during the generation of the Secondary Electromagnetic Radiation (S-EM-R),
at distance d
1
in Figure 2. On the left is the Primary Electromagnetic Radiation (P-EM-R) Energy (
), P-EM-R Wavelength (
),
the Electron’ Forced Binding Energy (
), the S-EM-R Energy (
), the S-EM-R Wavelength (
), S-EM-R Magnetic Radius
(
), S-EM-R Frequency (
), the Flipping Time (t
F
), the Relativistic Mass (
), the Relativistic Velocity (
), the operational arc
length (d
1
), the Radiation Magnetic Force (
) which expel the recoil electron, and the angle through which S-EM-R is released
(ϕ), and the angle θ through which electron is ejected.
© 2016 Mahmoud E. Yousif. Volume 1 Issue 1 JAAP-1-004 Page 10 of 13
Since Compton formulas in essence related both P-EM-R
and S-EM-R wavelengths and angle, and S-EM-R
wavelength with the ejected electron’ angle[8, 22] as shown
in Figure 2, therefore, S-EM-R giving in Table 2, is derived
using Compton formula, given by
`
= +
0
(1 ) (35)
Where,
0
is equal to 2.424632062160358924301299057755×10
-
12
. Although Eq. (35) was derived from the principle of
conservation of momentum [22], but it originated from the
energy of the system[5], therefore this greatly tested formula
is valid in our model.
Table 3: The Electromagnetic Radiation Force (
), resulted from Strong Spinning Magnetic Field (
1
) interaction with the
CMF (
) of the produced Secondary Electromagnetic Radiation (S-EM-R) after completing the Flip-Flop (F-F) mechanism;
pulls S-EM-R from
1
to ϕ. The data could also be used in Eq. (49) to derived speed of light (c).
5. The Ejected Electron
When S-EM-R is released, its part in
given by Eq. (1), ceased to exist, and turned into recoil force, given by
=
1
2
2
`3
= =
(36)
When S-EM-R is released,
impart electron with force,
the velocity of which is
=
1
2
2
`3
(37)
Where,
is secondary electron velocity.
Since forced binding energy doesn’t released with
,
therefore electron
is added to the electron energy,
therefore, the ejected electron energy is given by
=
+
=
2
2
+
2
2
4
2
2
(38)
Where,
is the electron kinetic energy in J.When S-EM-R
is released, x-ray electron is attracted by
potential on
anode[17], given in Eq. (5), thus for electron to accelerate
towards anode,
must exceed
, hence
(39)
Since angle ϕ and θ are related[22], therefore Compton
ejection formula is used
=
1 +
1
2
(40)
Where,
2
, and θ is the angle made by the ejected
electron with the forward direction of propagation of the
beam, in Figure 2.
6. Results and Discussion
The re-interpretation of Compton Effect illustrated in
Figures1&2 and given in Tables 1&2, shows the
phenomenon as an inter-atomic mechanism, that received
primary electromagnetic radiation, utilized some of the
incoming radiation energy in moving to higher orbital level,
then radiating major energy as secondary electromagnetic
radiation.
ϕ
(
)
1
45
o
7.25e-13
7.39114666221937313567
67108498454e+9
394160.85381530235324
973627791679
0.4593911008284080858
6763932961252
90
o
1.175e-12
4.56049474902897491350
26513754365e+9
117875.57925509022830
191328032704
0.2226551720909207521
992781893694
135
o
1.575e-12
3.40227386038669557039
08668991352e+9
56665.289400230247119
717347572822
0.1434725279719041536
3660922387734
170
3.1203107128794464
593593330175753e-
11
1.71732299222345902656
3223533089e+8
32.435746762855858215
365265380161
0.0016270197492474151
1371325008135
© 2016 Mahmoud E. Yousif. Volume 1 Issue 1 JAAP-1-004 Page 11 of 13
The Forced Binding Energy (
) shown in Figure 1, and
given in Table 1 illustrate an important part of inter-atomic
characteristic of balance of magnetic force plus electrostatic
force with the centripetal force at the natural orbit[11, 12],
when such balance is violated by excitation potential, an
spectral line is radiated, but when x-ray or γ-rays forced
electron to higher orbit, the nucleus magnetic field help to
transform this energy into higher radiation.
In Compton Effect, the Primary Radiation Energy (
) is
reduced by Electron’ Kinetic Energy(
) to form the
secondary Energy (
); therefore the energy of the produced
Secondary Electromagnetic Radiation(S-EM-R) energy, is
always less by the amount of Electron’ Kinetic Energy (
),
leading to an increase in the wavelength.
When Secondary Electromagnetic Radiation (S-EM-R) is
produced, an Electromagnetic Radiation Force (
) is
established between the nucleus magnetic field(
1
) and the
radiation CMF(
), pulling Secondary Electromagnetic
Radiation (S-EM-R) to emerged at angle ϕ.
When Secondary Electromagnetic Radiation (S-EM-R) is
released, the Radiation Magnetic Force (
) stops abruptly
and turned into recoil force ejecting electron at specific
angle θ; while if anode potential is higher than x-ray
electron energy (
) electron will flow as anode current, if
anode potential is less than electron energy (
) electron
will be ejected from the atom.
At high Prime Electromagnetic Radiation (P-EM-R)
frequency, the Radiation Magnetic Force (
) is high,
forcing electron to high binding energy near nucleus, thus
great energy is deduced by electron as binding energy
(
), explains the discrepancy of Compton effect at high
energies.
At low x-ray frequency, forced binding energy (
) given
by ϕ
1
=17
o
in Tables 1&2 is little, the Prime Radiation
Energy (
) and the Secondary Radiation Energy (
) are
nearly equal.
Discrepancy between high and low energies, shown in Table
1, by forced binding energy (
) 409.8 eV at 170
o
which
is 3.8% of the Prime Electromagnetic Radiation (P-EM-R);
while forced binding energy (
) at 135
o
reached 367
keV or 65% of the P-EM-R.
This explains the discrepancy in Compton Secondary
Electromagnetic Radiation (S-EM-R) ratio over Prime
Electromagnetic Radiation (P-EM-R) at Soft X-rays (SX)
which is 99%and 0.13% at end of γ-rays at 3.08 fm[8], due
to the very high forced binding energy (
).
Although the frequency of the Prime Electromagnetic
Radiation (P-EM-R) in Table 1 is equal for 45
o
, 90
o
and
135
o
, but at 45
o
, the Secondary Energy (
) reached 76% of
Prime Electromagnetic Radiation (P-EM-R), while at 135
o
it
is only 35%, hence each ray interacted with specific electron
in specific orbit.
From above, it is clear why Compton Effect will not occur
from electrons with binding energies greater than the energy
transfer.
For Compton Effect to occurred, forced binding energy
(
) should be greater than the orbit binding energy
(
).
7. Conclusion
Compton Effect is reinterpreted based on the ambiguous
characteristics of the Circular Magnetic Field (CMF)
discovered in 1819 by Hans Christian Oersted[25], although
it represents an important element in the dynamics of
microscopic world[12], but neglected by physicists.This line
include the knowledge of the nucleus strong magnetic field
(
1
) [13], and the Flip-Flop (F-F) mechanism suggested to
generate Electromagnetic Radiation (
)[11], while the
Radiation Magnetic Force (
) was suggested to
embedded EM-R (as
=
3
). The
embedded in
the X-ray and γ-rays Primary Electromagnetic Radiation (P-
EM-R) interacted with the inter-atomic electron, and forced
electron to move to high binding energy at temporarily
forced orbit, where the CMF is automatically divided into a
binding energy responsible of the gyration of electron in this
temporary orbit, and high secondary energy shown in Figure
1.
A relation been established between X-rays tube energetic
electrons and inter-atomic electrons energized by Radiation
Magnetic Energy (
); the penetration of x-ray electrons
into high forced binding orbit of anode’s atoms, created the
same state of inter-atomic electron forced by the Radiation
Magnetic Force (
), shown in Figure 1.
Both the Total Radiation Circular Magnetic Field (
)
created by primary electromagnetic radiation, and the Total
X-Ray CMF (
), created by energetic x-ray tube
electron, are divided to form the Secondary CMF (
),
and the Forced Binding Electron energy CMF (
);
hence both CMF formed Electron Kinetic Energy (
) and
the Secondary Radiation Energy (
s
).
© 2016 Mahmoud E. Yousif. Volume 1 Issue 1 JAAP-1-004 Page 12 of 13
As electron start moving in the short arc distance (d
1
) in
Figure 2, within the Flipping Time (
=
1
), the Flip-Flop
(F-F) mechanism to transform both the CMF and the
Electric Field (EF) into the secondary radiation, is also
performed within this short time, thus F-F is synchronized
with electron’ velocity, this is by controlling electron’
velocity through angle ϕ and electron’ mass by frequency
and angle ϕ, at the end of which the secondary
electromagnetic radiation is generated at angle ϕ
1
but pulled
by electromagnetic Radiation Force (
)to emerge at
angle ϕ, examples of the force is given in Table 3, the
secondary electromagnetic radiation is given in Table 2 and
shown in Figure 2, which is in core of this phenomenon,
formulas are derived to express the increased wavelength
and reduced frequency of the generated secondary
electromagnetic radiation. Compton formulas are valid in
producing the increased secondary wavelength, and when
this radiation is released, the recoil force ejected the electron
at angle θ, this angle is derived using Compton formula.
In this interpretation, the Compton Effect combined several
microscopic phenomena, such as the temporarily occupation
of electron at high binding energy in atom due to the
Radiation Magnetic Force (
) embedded in EM-R, as
given in Table 1 for each of the four primary radiation
frequencies; the synchronization within distance (d
1
) while
electron is moving while carried Flip-Flop (F-F) mechanism,
is another mechanism the details of which is given in Table
2, it required electron’ velocity (
R
) and mass (
) to be
controlled by the secondary radiation frequency and ejected
angle ϕ for the later, and by the angle ϕ for the former, the
related data in Table 2, give more weight to the Flip-Flop
(F-F) mechanism over the acceleration[15] mechanism. This
mechanism showed the correct suggestion by Raman, and
some of his contemporary physicists who interpreted
Compton Effects as secondary radiation generated inside the
atom [9, 10], but as shown the line taken by physics during
that period can’t substantiate such explanation.
In Compton effect, the reduction of forced binding energy
(
) from Prime Energy (
), increased radiated
Secondary Energy (
) wavelength, and justified the
Secondary Electromagnetic Radiation (S-EM-R)
mechanism, as energy is conserved, while electromagnetic
radiation as spreading waves is maintained, and doesn’t
required the conservation of momentum[22].
References
1. Compton, A. H. "A Quantum Theory of the Scattering of X-Rays by Light Elements", Physical Review, vol. 21, pp. 483,
1923.
2. Jenkin, J. G., E. M. Jauncey and the Compton Effect, PhysPerspect, vol. 4320; 321; 323, 2002.
3. Einstein, A. & into English, T., Concerning an Heuristic point of view toward the emission and transformation of light,
American Journal of Physics, vol. 33, pp. 367, 1965.
4. Millikan, R. A., A Direct Photoelectric Determination of Planck’s “h” Physical Review, vol. 7, pp. 384, 1916.
5. Compton, A. H. and S. K. Allison, X-rays in Theory and Experiment D. Van Nostrand New York, pp. 222, 216, 211, 4, 217,
48, 1935.
6. Cooper, M. J., Compton scattering and electron momentum determination, Rep ProgPhys, Printed in Great Britainvol. 48,
pp. 418, 1985.
7. Stuewer, R. H. Historical Questions and Physical Inquiry, Univ. of Minnesota, 2014.
8. Compton, A. H. Secondary Radiations Produced by X-Rays, and Some of Their Applications to Physical Problems, Bulletin
of the National Research Council 4 Google Books, 1922.
9. Mehra, J. (Author), R. Helmut (Contributor),The Historical Development of Quantum Theory, Springer, vol. 1, 2001.
10. Raman, C. V. A classical derivation of the Compton Effect, Indian J. Phys, vol. 3, pp.361,1928.
11. Yousif, M. E. The Photoelectric Effects-Radiation Based With Atomic Model, International Journal of Fundamental Physical
Sciences (IJFPS), vol. 5, pp.23, 26, 25, 20, 30, 2015.
12. Yousif, M. E. The Magnetic Interaction. Comprehensive Theory Articles, Journal of Theoretics, vol. 5, pp.7, 6, 2003a.
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2003b.
14. Yousif, M. E. The Electromagnetic Radiation Mechanism, International Journal of Fundamental Physical Sciences (IJFPS),
vol. 4, pp. 76, 78, 2014a.
15. Newman, J. Physics of the life sciences: Springer, pp. 471, 2008.
16. Yousif, M. E. Electromagnetic Radiation Energy and Planck’ Constant, International Journal of Innovative Research in
Advanced Engineering (IJIRAE), vol. 1, pp.439, 437, 440 2014b.
17. Zink, F. E. X-ray tubes, Imaging & Therapeutic Technology, September-October, vol. 17, pp. 1259, 1268, 1260, 1261, 1260,
1997.
18. Sachs, M. Einstein versus Bohr, Open Court, 1988.
19. Alonso, M. and E. J. Finn, Fundamental University Physics V. II Field and Waves, Addison and Wesley, Massachusetts, pp.
30, 19675.
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20. Ballif, J. R. Conceptual Physics,Wiley N. Y. pp. 338, 1969.
21. Fuch, W. R. Modern PhysicsWeidenfield& Nicolson (Educational) Ltd: and The Macmillan for Translation, Zurich, 1967.
22. Compton, A. H. X Rays And ElectronsD.VanNostrand, universal library, pp.232, 266, 267, 263, 270, 267, 266, 1926.
23. Itakura, K. et al., (edited) “Proceedings of International Conference on Physics in Intense Fields, PIF, 2010.
24. Attix, F. H. Introduction to Radiological Physics and Radiation Dosimetry, Wiley, New York, pp. 126, 1986.
25. Nightingale, E Magnetism and Electricity, G. Bell and Sons Ltd, London, 1958.
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