Top page ( correct Bohr model )

All atoms through de Broglie waves

Realistic atomic Neon structure

*(Fig.1) "Photon" is just abstract math symbol (= a ^{†} ), without physical shape.*

Quantum mechanics claims that the classical Coulomb force is caused by photon exchange.

But **clear** mechanisms of "*attractive*" and "**repulsive**" Coulomb forces remain **unknown**.

In fact, this **photon** causing *Coulomb* force is **virtual** photon, so **NOT** real ( see this, this, this ).

Surprisingly, this **virtual** photon is superluminal tachyon, **violating** Einstein's relativity ( see this, this ).

By the way, what is the physical **shape** and *size* of a single **photon** ?

Unfortunately, quantum mechanics cannot answer this **basic** question.

In QED, these *photons* must be described using **abstract** Feynman diagram.

This Feynman QED has **NO** ability to show photon's **clear** picture at all.

All quantum mechanics can show is **meaningless** math *symbols* ( see this, this p.3 ).

It contains only **rough** actions, "a photon is **created** (= a^{†} )", or "*annihilated* (= a )". That's all, **NOT** physics.

*(Fig.2) Light frequency (= f ) equal to c/λ (= light wavelength ) proves "Wave" !*

Though almost all textbooks say photoelectric effect proposed by Einstein proved **particle** nature of "**photon**", this *far-fetched* interpretation is clearly "**brainwashing**" by textbooks.

Electrons are "**emitted**" from metals, when illuminated by *light* of higher **frequency** than some threshold, irrelevant to its intensity. So they ( this, this, this ) affirmed that light is "**particle**".

But as you know, light **frequency** (= f ) is equal to c/λ (= **wavelength** ). See this site.

"Frequency" and "**wave**length" clearly mean "**wave**" ( NOT particle ! ) nature of light.

So, the idea "photoelectric effect = light *frequency* = photon " is one of **mind-controls** by textbooks and media, like Bohr's accelerating electron ( though it does **NOT** lose energy ).

In fact, Lamb (= Nobel winner ) argued that the photoelectric effect happens without photon.

**Imaginary** "photon" is necessary for quantum field theory such as Higgs and string theory.

But these photon's **operators** (= a^{†}, this, this p.5 ) are just **abstract** math *symbols* with **NO** realistic shapes.

*(Fig.3) The wavelength of radio wave (= one of lights = photon ? ) is 1000 meter !*

Though quantum mechanics claims that light is a photon, the existence of this *photon* is very **unrealistic**. The radio wave is one of lights with **long** wavelength ( > **1000** meters ! ).

As shown in this, this, low-frequency lights have wavelengths from 1 km to **100000 km** !

This means the **size** of a *single* photon in these radio waves is as **Big** as 100000 km ?

If a photon is so **Big**, we can easily **divide** a photon into **two** parts, which means a photon is **NOT** an elementary particle. So, a photon is just "media-hype", as shown in clear **discrepancy** between
NBC and insidescience.

Though the media ( this, this ) and universities **routinely** use the word "photon", they **cannot** answer "what **size** and shape of a photon ?". So **vague** photon represents " NOT asking" quantum mechanics.

Some say a photon has
**NO size** ( this, this ), some say a photon is point-like. But thinking *commonsensically*, it is **impossible** that light with **1000 meter** wavelength is a **point**-like particle.

*(Fig.4) Davisson-Germer experiment showed an electron is de Broglie wave.*

In Davisson-Germer experiment, they accelerated electrons by electric fields and made them reflected by nickel crystal.

de Broglie wavelength of an electron is gotten from the electric field strength and **interference** pattern of a *single* electron.

Experimental results **agreed** with de Broglie relation.

So **de Broglie** waves themselves are **realistic** concepts, though quantum mechanics **avoids** commenting it.

This experiment showed an single electron has *wave*-like property, in which the **opposite** wave phases **cancel** each other, and **expel** the electron.

*(Fig.5) One de Broglie wavelength of electron.*

When an electron moves, **electric** fields (= E ) around the electron also moves with it.

So this *spreading* electric field causes *de Broglie* waves, which can be confirmed by Davisson-Germer experiment.

We can naturally think this de Broglie wave is a kind of longitudinal waves through some *medium*.

If so, double slit interference can be explained by this "**real**" de Broglie waves, **NOT** by "fantasy" many-worlds.

**Longitudinal** wave consists of "*low*" (= **sparse** ) and "*high*" (= **dense** ) pressure areas.

It is thought that an electron **pushes** the field around it toward "dense" area, and is moving with "low" pressure area.

*(Fig.6) Relation between electron's velocity (= v ) and de Broglie wavelength (= λ ).*

According to de Broglie theory, the electron's **wavelength** (= **λ** ) is equal to λ = **h/mv**, where h is Planck constant, "**m**" is *mass*, and "**v**" is "*velocity*".

So as an electron moves **faster**, its de Broglie wavelength becomes **shorter**.
"Momentum" means "impluse (= Ft )", so bigger momentum can apply more **pressure** on *surrounding* **field**, and **compress** it.

*(Fig.7) "Field" is compressed enough to maintain its shape, resisting momentum. *

When an electron with mass "m" is moving at a velocity of "v", its momentum is "mv".

In Fig.7 left, "*field*" is only **slightly** compressed, which pressure is **lower** than electron's momentum.

In this case, the **stronger** momentum pressure causes "field" to be **more** compressed, *until* their forces are equal (= **balanced** ) to each other (= Fig.7 right ).

Once the pressures from particle's "momentum" and compressed field are **balanced**, this field *distortion* is **kept** as "de Broglie wave", meaning its potential energy ( like spring ) remains the same.

Total energy must be **conserved**, so if the field potential (= distortion ) energy remains the **same** (= de Broglie *wavelength* is unchanged ), particle's **kinetic** energy is also conserved, **keeping** "uniform motion".

*(Fig.8) Proton's mass (= M ), velocity (= V ). Electron's mass (= m ), velocity (= v ). *

A proton is about 1840 times **heavier** than an electron, so even when the proton is moving much **slower** than the electron, their *momentums* can be the same ( MV = mv ).

In this case, their **de Broglie** wavelengths are also the same ( λ = h/MV = h/mv ).

**Larger** mass of a proton means the **density** of "*positive*" field is much **higher** than "*nagetive*" field of an electron.

As a result, **denser** proton exerts **higher** pressure on surrounding "field", even if its speed is lower than an electron.

Considering "*dense* (= **+** )" and "*thin* (= **-** )" fields **attract** each other, Coulomb forces can be explained by the difference in field **density**. ( the same charges, "dense" - "dense", "thin" - "thin" **repel** each other. )

*(Fig.9) Wave phases at both ends fit each other = n × de Broglie wavelength. *

As seen in Bohr model, when an orbit is an **integer** (= n ) times de Broglie wavelength, their wave phases are **consistent** with each other, *avoiding* destructive interference, so **stable**.

In this page, we proved that **Schrodinger** equation also **satisfies** this "n × de Broglie wavelength" rule, *tacitly*, which is the reason both Bohr and Schrodinger hydrogens give the **same** energy levels.

Considering electron's **de Broglie** wave is one of longitudinal waves, their wave phases (= repeat of high and low pressure regions ) **harmonize** with each other, keeping **stable** wave states.

*(Fig.10) de Broglie wave ends fit.*

To avoid cancelling de Broglie wave, both ends of electron's wave in hydrogen atom need to **agree** with each other with respect to wave phases.

*(Fig.11) Photodetectors just see amplified "electric" current, NOT a photon itself. *

Though the media and textbooks repeatedly use the word of "**photon**",
those media said **nothing** about the shape and *size* of a single **photon**.

**Feynman** QED just shows *abstract* math symbols **without** physical shape as a "*photon*" ( see this p.2, this ).
For example, a photon is created (= a^{†} ), or annihilated (= a ). That's all. **NOT** physics.

A single photon detector just measures amplified "*electrons*", **cannot** see a **photon** itself. See this, this p.4
This **photodetector** depends on photoelectric effect, in which an electron is ejected by a photon (= *light* ).

Though textbooks ( this, this ) say photoelectric effect depending on light "**frequency**" proves photon "*particle*", the frequency (= c/**wave**length ! ) clearly means wave nature of light.

*(Fig.12) Emitted electromagnetic wave is always "transverse" wave ! *

It is known that electromagnetic wave is "transverse" wave, consisting of electric and magnetic fileds, they insist.

These electromagnetic waves (= light or photon ? ) are emitted ( or absorbed ), when each electron moves to lower ( higher ) energy levels.

Then, why are these electromagnetic waves always "**transverse**" ( *NOT* longitudinal ) waves ?

*(Fig.13) From "circular" Bohr model to "elliptical" Sommerfeld model.*

In 1916, Arnold Sommerfeld extended Bohr's circular orbit to "**elliptical**" one.

Sommerfeld elliptical orbit also **satisfies** an integer number of de Broglie wavelength.

This condition is expressed as Sommerfeld **quantization** rule in **both** radial and angular directions, as shown on this site (p.119) and this site (p.12).

In these quantum theories ( including Schrodinger equation ), **stable** de Broglie waves are **indispensable** for stable orbits. Between them, electromagnetic *transverse* waves are emitted.

*(Fig.14) Crash between de Broglie waves causes "transverse" EM waves. *

When each orbit is **NOT** an integer times de Broglie wavelength, the **phases** of these de Broglie waves do **NOT** fit each other, so "**crash**" between de Broglie waves happens.

When "**upper**" and "**lower**" de Broglie waves *crash* into each other, electromagnetic waves are emitted to the **right** ( or left ), which becomes "**transverse**" wave, naturally.

*(Fig.15) "Upper" and "lower" wave pressures prevent longitudinal emission. *

If "**longitudinal**" wave is emitted **instead** of "transverse" wave in energy transitions, its direction is **parallel** to two "crashing" de Broglie waves (= upper and lower in Fig.15 ).

But thinking commonsensically, this "**longitudinal**" emission is **impossible**.

**Pressures** from upper and lower de Broglie waves **prevent** longitudinal waves from being emitted in "*parallel*" direction.

Only directions **perpendicular** to these two de Broglie waves are allowed, when *electromagnetic* waves are emitted, which naturally becomes "**transverse**" wave.

As shown in helium, when two de Broglie waves cross **perpendicularly**, their phases are *independent* and **NOT** interfering with each other, which does **NOT** cause "crash".

*(Fig.16) Electromagnetic wave is emitted in "pressure-free" directions ← "transverse".*

When two de Broglie waves **crash** into each other from "upper" and "lower" directions, their energies are emitted in **horizontal** (= *transverse* ) direction, which has **NO** de Broglie wave pressures.

This emitted electromagnetic wave **takes over** "*oscillating* (= up and down ) energies" from **de Broglie** waves to satisfy total energy conservation.

This *oscillating* direction in "crashed" **de Broglie** waves is the origin of **transverse** wave *inside* emitted electromagnetic wave, as shown in Fig.16.

In circular orbits, an electron is **periodically** moving in **closed** system, so its de Broglie wave is oscillating up and down ( or right and left ), meaning the *average* momentum is **zero** in transverse direction.

*(Fig.17) True figure of electromagnetic wave ↓ transverse and longitudinal mixed. *

As seen in Compton scattering, the electromagnetic wave also has the property of **de Broglie** wave in the direction of travel (= to the right in Fig.16 ).

Crash between two de Broglie waves is thought to **push** electromagnetic waves in the **right** direction, as a form of "**longitudinal**" de Brolgie wave.

So the electromagnetic wave has both "**transverse**" (= original de Broglie wave oscillating direction ) and "**longitudinal**" (= pushed out ) directions inside one wave.

Due to the **balance** in the field pressure, high-pressure area in transverse direction is low-pressure in longitudinal direction. They are **alternating**.

In Maxwell equation, changing electric field originally means the electric *current* (= **de Broglie** wave ). This page proved **magnetic** field is generated by **de Broglie** waves, which can be *applied* to this electromagentic wave.

*(Fig.18) "Longitudinal" waves are NOT absorbed. Why ?*

If each electron can **absorb** "*longitudinal*" waves in addition to transverse electromagnetic waves, we can also **see** "longitudinal" wave with various **colors** through chemical reaction inside eyes. But we **cannot**.

This fact shows there are some reasons why each electron in energy transition can absorb **only** "*transverse*" electromagnetic wave, like in case of "emission"

*(Fig.19) "Longitudinal" waves "avoid" each other !*

To transfer the energy of one "longitudinal" wave to another de Broglie (= longitudinal ) wave of electron, they must **crash** into each other in the **parallel** direction.

The wavelength, phases and velocities are **different** between de Broglie waves with *different* "**masses**", which causes "crash" between two different de Broglie waves.

As a result, two different "longitudinal" ( de Broglie ) waves tend to **avoid** each other to prevent "crash". This is the reason why "longitudinal" wave **cannot** be absorbed into an electron.

Besides this reason, when a particle with **different** *mass* is absorbed into other particles, it **cannot** satisfy both energy and **momentum** conservation, as seen in antiparticle generation.

*(Fig.20) "Transverse" wave can approach de Broglie wave "perpendicularly". *

On the other hand, transverse electromagnetic waves can **approach** other electron's de Broglie waves from the **perpendicular** direction.

As shown in helium case, "*perpendicular*" means two de Broglie waves can approach each other independently ( in phase ), **NOT** disturbing other waves.

After they approach and **cross** each other, **transverse** *oscillation* energies stored in electromagnetic waves
are **transferred** and absorbed into electron's de Broglie wave, **safely**.

This is thought to be the main reason why each electron can absorb **only** "*transverse*" ( NOT longitudinal ) electromangetic wave.

*(Fig.21) Unstable muon (= particle ? ) decays into an electron and neutrino instantly !*

**Unstable** muon's lifetime is very short (= about 2.2 microsecond ), it decays into an electron and *neutrino* instantly. So, calling muon "elementary particle" is very **unreasonable**.

We can naturally think this *transient* muon is a "**composite**" state consisting of an electron and neutrino. It is known that this neutrino **always** travels at light speed.

And this neutrino can pass through the earth, **different** from ordinary "particles".

From these two properties, we can naturally think this neutrino is **de Broglie** wave *oscillation*, **NOT** a particle.

*(Fig.22) Why "neutrino" and "light" always travel at light-speed c ? *

It is known both neutrino and electromagnetic wave **always** travel at **light-speed** c.

"**Constant**" speed means these things are some **oscillations** travelling in the same **common** *medium*.

From *fatal* paradoxes of special relativity, we can naturally think Michelson-Morley experiment (= denied "**absolute**" ether ) proved "*medium*" moving **with** the earth. See also this page.

*(Fig.23) Neutrino can cause only "Compton" scattering. *

If "neutrino" can be absorbed into an electron in energy transition, we can "**see**" (= chemical reaction inside eyes ) these neutrinos like electromagnetic waves. But we **cannot**.

As I said in this section, if we think **neutrino** is one of "*longitudinal*" **de Broglie** waves, two different de Broglie waves tend to **crash** and avoid each other in parallel direction.

As a result, these neutrinos can **pass** (= avoid ) other particles de Broglie waves, **NOT** interacting with each other. Neutrino can interact with electrons **only** through Compton-like **scattering**.

*(Fig.24) Transverse wave can approach electrons, "perpendicularly" and safely.*

Different from longitudinal neutrino, **transverse** *electromagnetic* wave can **approach** other electron's de Broglie waves from the "**perpendicular**" direction.

Its energy is **stored** in "*transverse*" direction, so after approaching and crossing electron's de Broglie waves, this stored oscillating energy is **transferred** to other electrons, safely.

This is the **true** mechanism of light "absorption" and photoelectric effect.

*(Fig.25) If "transverse" oscillation disappears, longitudinal component also disappears. *

Different from neutrino, the electromagnetic waves are very **susceptible** to environment.

One of reasons is easy absorption into electrons, because they can cross each other perpendicularly.

As shown in Fig.25, inside electromagnetic waves, both "transverse" and "longitudinal" directions contains the **opposite** oscillations in **small** areas.

So when transverse oscillation **disappears** ( by absorption ), the opposite longitudinal oscillations *cancel* each other, and **disappears**, too.

As seen in balanced field **pressures**, even when only transverse oscillations are **disturbed** and slowed down, it instantly **affects** "longitudinal" oscillation, to keep their field balance.

Even when longitudinal wave can pass through other waves perpendicularly and safely, "transverse" oscillation may be **caught** by them.
It can explain the light "**slow-down**" inside various *medium* such as **water**,

*(Fig.26) Magnetic (= Lorentz ) force between two wires = de Broglie waves. *

As shown on this site and this, according to Lorentz magnetic force, two wires carrying electric currents in the **same** direction **attract **each other. And the **opposite** currents **repel** each other.

The electric current is the flow of ( moving ) charged particles (= **electron** ).

*Moving* electrons generate their de Broglie waves, so it is clear this **de Broglie** wave has something to do with **magnetic** force !

*(Fig.27) The opposite de Broglie waves (= currents ) have the "opposite" oscillating velocities. *

As I said, electron's de Broglie waves propagating in the **opposite** directions contain the **opposite** *oscillating* fields in the **same**-phase areas, so these opposite waves **crash** and **repel** each other.

The electric **currents** are moving **electrons** (= *de Broglie* waves ).

So the repulsive **de Broglie** waves express the electric currents **repelling** each other by **magnetic** forces.

*(Fig.28) de Broglie waves in the same direction contain the same oscillation.*

When two de Broglie waves propagate in the **same** direction, their oscillations are the same and **harmonize** with each other (= **constructive** interference ).

As a result, two de Broglie waves ( electric currents ) in the same direction **attract** each other, which is thought to be Lorentz "**magnetic**" force. It is similar to Magnus effect.

*(Fig.M1) Hydrogen and helium de Broglie wave models.*

It is known that one-electron hydrogen has magnetic moment (= Bohr magneton ), and two-electron helium shows no magnetic property.

*Spin*-spin magnetic interaction is too weak to explain **Pauli** exclusion principle. So spin is **unreal**.

Here we use "**realistic**" *de Broglie* wave model of helium to explain it.

*(Fig.M2) Opposite wave phases in the same direction cancel magnetic in He.*

For two electrons' de Broglie waves to **avoid** canceling each other, they have to be perpendicular to each other in "realistic" helium model.

e1 ( e2 ) electron and e2 ( e1 ) **opposite** wave phase are moving in the **same** direction, as shown in Fig.M2. So these *opposite* phases ( in the *same* direction ) cancel each other at the point of a **distant** detector.

As I said, **magnetic** field is related to **de Broglie** wave (= electron's movement ), so these canceled ( from a distant place ) wave phases show "average **zero**" magnetic property of helium.

*(Fig.29) "Independent" protons, electrons are just the "same" amount !? *

It is said that the proton is composed of three quarks with **fractional** charges.

But this *fractional* charges ( +2/3e, -1/3e ) can **NEVER** be *isolated*, so quark has **NO** real evidence. See this and this.

They just **jumped** to a conclusion that Jets (= only electrons and lights can be detected ) may be quark or gluon. In standard model, quarks are just **meaningless** math *symbols* with **NO** physical shapes.

Originally, fractional charges such as +2/3 (= up ) and -1/3 (= down ) quarks are completely **independent** from (= *NO* relation with ) electrons. ( Why 3/4e, 4/7e is **impossible** ? )

But the **sum** of them (= 2 × up + 1 × down quarks ) becomes just **+e** charge *proton*, which number is "*accidentally*" just the Same as **-e** charge **electron** in the universe ! ← **Too good** to be true!

On the other hand, the number of positron, which is said to be the **partner** of electron, is much **smaller** than electrons, and **unstable** antiparticles *disappear* **instantly** (= within 10^{-12} seconds ! ).

And these antiparticles **disobey** *basic* physical law such as total **momenum** conservation.

So standard model based on these quarks **lacks** reality.

*(Fig.30) Imbalance in "field pressure" causes plus, minus charges. *

Quantum mechanics **cannot** answer "why the universe contains exactly the **same** amount of plus, minus charges" as protons and electrons. And they have **NO** definite answer, "why a proton is much **heavier** than an electron".

If we suppose *Coulomb* force is caused by the **difference** in field **pressures** (= density ), we **can** naturally answer all these basic questions.

In Fig.30 upper, some amount of field matters are **transferred** to another places.

This causes a **pair** of "**thin**" area with *lower* pressure, and "**dense**" area with "*higher*" pressure in the field.

If the field matters are **unevenly** distributed, they try to go **back** to the *uniform* density, which is the origin of **Coulomb** attraction. "Dense" proton is naturally **heavier** than "thin" electron.

Due to pressure **balance**, the combinations of "dense-dense (= +, + )" and "thin-thin (= -, - )" areas **repel** each other, which is why the **same** charges **repel** each other in Coulomb forces.

*(Fig.31) An proton is 1840 times heavier (= denser ) than an electron. *

It is known that a *proton* is about 1840 times **heavier** than a electron. If we suppose, a proton (= positive field ) is 1840 times **denser** than an electron (= negative field ), this big difference in **mass** can be explained.

Due to **imbalance** in field densities (= "positive" is dense, "negative" is thin ), the **opposite** charges **attract** and start to move towards each other.

Total momentum must be **conserved** due to the law of *action* and *reaction*.

So a "light" electron must move much ( 1840 × ) **faster** than a heavy proton during the same time.

*(Fig.32) The same momentum causes the same de Broglie wavelength. *

According do de Broglie theory, de Broglie wavelength (= λ ) is determined by the particle's **momentum** ( λ = h/p ), irrespective of particle's kinds.

So even when a proton's velocity is **lower**, it can cause the **same** de Broglie wavelength (= distortion of the field ) as an electron, if they have the same *momentum*.

Because "**denser**" proton can **distort** the surrounding field as much as "thin" electron, even when proton is moving more slowly.

*(Fig.33) "Thin" area (= negative ) is kept due to conservation of total energy. *

Of course, total energy must be **conserved**, so once "*distortion*" of the field is formed, its imbalance (= potential **energy** ) is conserved. As a result each positive and negative **charges** are *conserved*.

In Fig.33 left, some field particle is attracted toward "thin" negative field, and accelerated (= kinetic energy increases ). It moves until it reaches the same potential energy (= imbalance ), **keeping** negative charge .

*(Fig.34) Positive charge is conserved due to energy conservation. *

Also in the positive proton, the **conservation** of total ( potential ) energy keeps the original amount of charge. In Fig.34 left, some field particle is pushed **outward** by high-pressure positive field.

This force is changed into particle's kinetic energy, and it continues until the pressure in the center is **lower** enough to get them **back** to the *original* places, due to conservation of potential energy.

This is the mechanism in which each positive charge (= +e ) is **conserved**.

The point is, when field becomes **dense** enough to cause "+e", the surrounding field **cannot** enter the central part, even when the field is **expanded** in Fig.34 middle.

If total charge is **smaller** than this +e, the surrouding field matters can **enter** the central part, when the proton is expanded, which tears up a proton into *scattered* pieces (= potential energy splits into smaller kinetic energies ).

This theory can explain why the nature adopts **only** "±e" as "quantum **charge**".

*(Fig.35) de Broglie relation.*

According to de **Broglie** relation, the momentum ( p = mv ) is expressed as ( p = h/λ ).

Here, p = momentum, m = mass, v = velocity, h = Planck constant, λ = wavelength.

As shown on this site, total energy (= E ) of electromagnetic wave is linearly **proportional** to *frequency* (= f ) through the relation of **E = hf**, which is confirmed in photoelectric effects.

Surprisingly, in any **other** particles such as electrons and protons, their *frequency* is **proportional** to their total **energy**, if de Broglie relation is satisfied ! Here we explain it.

*(Fig.36) Electron is slower ( v → 1/2 v ), its wavelength becomes longer ( λ → 2λ ).*

When an electron's velocty (= v ) becomes half (= 1/2 ), its total ( kinetic ) energy (= E ) becomes **1/4** of the original value, because E is proportional to a **square** of velocity ( E = 1/2 mv^{2} ).

According to de Broglie relation ( mv = h/λ ), the electron's wavelength becomes **twice** ( λ → 2λ ), when the velocity becomes **half**.

Considering wave relation ( v = fλ ), the electron's **frequency** (= f ) becomes **1/4** of the original value in this case.

As you see, also in **electron**'s de Broglie wave, the energy is **proportional** to frequency ( E/f = constant ) !

*(Fig.37) Momentum ( p = h/λ ) is constant.*

Here we think about the case when the momentum (= p ) is **common** in both of "light" electron and "heavy" proton.

So through de Broglie relation ( λ = h/p ), their wavelengths (= λ ) are the **same**, too.

Due to **heavier** mass ( M_{p} ) of proton, the velocity (= V ) of proton becomes much **lower** than that (= v ) of electron.

So the total kinetic energy ( E = 1/2 M_{p}V^{2} ) of proton is much **smaller** than electron (= 1/2 mv^{2} ).

*(Fig.38) Energy (= E ) is proportional to frequency (= f ) in electron and proton.*

Again, through the wave relation of v = fλ, we can find the proton's frequency.

As shown in Fig.38, between proton and electron, the relation of energy (= E ) **proportional** to frequency (= f ) **holds** true.

So not only in electromagnetic wave but also in electrons and protons, the **frequency** has an **important** meaning to determine their total **energy**.

*(Fig.39) Total energy in electron and proton.*

Using Fig.37, we find the proton's kinetic energy is much smaller than electron due to its large mass, even when their momentums are the same.

*(Fig.40) Ratio of electron's to proton's masses.*

Proton (= M_{p} ) is much **heavier** ( 1836 × ) than electron's mass (= m_{e} ).

*(Fig.41) Frequency = velocity / wavelength.*

Through wave relation, we find the proton's frequency becomes much **smaller** than electron.

( Here the wavelengths ( momentums ) of electron and proton are the **same**. )

*(Fig.42) Light's energy is proportional to its frequency, too.*

It is known that light's energy is also proportional to its frequency through the relation of **E = hf**.

The important point is that the speed of the light is always **constant** "c", different from other particles.

This means there is **NO** concept such as "acceleration" in light ( and neutrino ).

When electron's ( or proton's ) wavelength changes, **both** of its velocity and momentum changes.

So the electron's frequency is inversely proportional to a **square** of wavelength, as shown in Fig.36.

On the other hand, due to **neglecting** light speed change, the light frequency is just inversely proportional to its wavelength.

As you see, de Broglie wavelength ( λ = h/p ) expresses "**contraction**" ( or expansion ) of the field by the *momentum* (= impulse ), compared to its equilibrium state, **irrelevant** to the *velocities* of various particles.

*(Fig.43) *

Here we investigate the relation between electron's frequency (= f_{e} ) and emitted light's frequency (= f ).

In Fig.43, total kinetic energy of electron (= 1/2mv^{2} ) is equal to light's energy (= hf ) **emitted** from the electron.

*(Fig.44)*

Using wave relation ( v = fλ ) and de Broglie relation ( λ=h/p ), we find that the **electron**'s ( de Broglie ) frequency (= f_{e} ) is **two times** bigger than the emitted **light** frequency (= f ).

*(Fig.45) Oscillating electron emits light and gradually loses its energy. *

In Fig.45, we think about the case in which oscillating electron **gradually** *emits* light and loses its kinetic energy.

The initial electron's frequency is equivalent to **2** × f (= emitted light frequency ), as shown in Fig.44.

The more light the electron emits, it loses more energy, and its oscillation becomes **slower** ( to be zero ).

It means the **average** electron's frequency becomes **half** of the original value (= 1/2 × f_{e} = **f** ) .

As a result, we can prove there is an **important** relation between electron's and emitted light frequencies. Planck constant (= h ) connects light and electron.

*(Fig.46) Transition from excited ( n = 2, f=4 ) state to ground state ( n =1, f = 2 ).*

In Fig.46, the excited state of 2 × de Broglie wavelength **returns** to ground state (= 1 × de Broglie wavelength ).

Accelerated by Coulomb force, the final **frequency** of *de Broglie* wave of excited **electron** becomes f = **4**.

We can think the **afterimage** of stable ground state de Broglie wave **remains** during excitation, and it is supposed to be f = **2**.

These two de Broglie frequencies before and after transition are **different**, so they **don't** fit each other.

The **crash** between these two de Broglie waves causes **swell** with the frequency ( 4-2 = **2** ), which is the **difference** between two states.

The excited de Broglie wave is **attenuated**, while it emits light.

So the **average** frequency of emitted light becomes half of 2 (= **1** ), as is explained in Fig.45.

*(Fig.47) Transition from excited ( n = 2, f=2 ) state to ground state ( n =1, f = 4 ). *

In fact, according to Virial theorem, kinetic energy T is the **absolute** value of total energy E ( T = |E| ).

As I said in Fig.36, electron's frequency (= f ) is **proportional** to its *kinetic* energy.

So the electron frequency in the upper energy level is lower than the lower level, like their kinetic energies. Also in this case, the frequency difference becomes 4 - 2 = 2, like Fig.46.

So the difference in **total** energies is just **equal** to the *difference* in **kinetic** energies (= frequency ) in these bound state orbits, which can explain photoelectric effect correctly in the **realistic** way. See this.

2015/5/17 updated. Feel free to link to this site.