# Fundamental Physics/Formulas

## Force

Force is a physical quantity that interacts with matter to perform a task

 Force Definition Notation Formula Motion Force Force that sets matter in motion ${\displaystyle F_{a}}$ ${\displaystyle ma}$ Impulse Force that sets a mass in motion ${\displaystyle F_{p}}$ ${\displaystyle {\frac {p}{t}}}$ Opposition force Force that opposes the interacting force with matter ${\displaystyle F_{-}}$ ${\displaystyle -F}$ Pressure force Force that acts on surface's area ${\displaystyle F_{A}}$ ${\displaystyle {\frac {F}{A}}}$ Friction Force Force opposes matter movement on a surface Elastic Force Force that restores matter equilibrium ${\displaystyle F_{x}}$ ${\displaystyle -kx}$ Circulation Force Force sets matter in circular motion ${\displaystyle F_{r}}$ ${\displaystyle \omega r}$ Centripetal Force Force that sets matter moves out of circulation motion ${\displaystyle F_{v}}$ ${\displaystyle m{\frac {v^{2}}{r}}}$ Centripugal Force Force that sets matter moves in of circulation motion ${\displaystyle F_{\omega }}$ ${\displaystyle m{\frac {\omega r}{t}}}$ Electrostatic Force Attraction force of 2 different polaity charges ${\displaystyle F_{q}}$ ${\displaystyle m{\frac {q_{+}q_{-}}{r^{2}}}}$ Electromotive Force Force sets electric charge in motion ${\displaystyle F_{E}}$ ${\displaystyle qE}$ Electromagnetomotive Force Force that sets moving electric charge to move perpendicular to the intial travel direction ${\displaystyle F_{B}}$ ${\displaystyle \pm qvB}$ Electromagnetic Force Summation of 2 force Electromotive force and Electromagnetomotive force ${\displaystyle F_{EB}}$ ${\displaystyle q(E\pm vB)}$

## Motion

Movement of matter from one place to another place caused by a force

#### Uniform linear motion

Motion that follows straight path of constant speed for example horizontal uniform linear motion, vertical uniform linear motion,

 Notation Horizontal uniform linear motion Vertical uniform linear motion Inclined uniform linear motion Distance s ${\displaystyle s}$ ${\displaystyle h}$ ${\displaystyle (v_{o}+a\Delta t)t=s_{o}+at\Delta t=s_{o}+v\Delta t}$ Time t ${\displaystyle t}$ ${\displaystyle t}$ ${\displaystyle t}$ Speed v ${\displaystyle {\frac {s}{t}}}$ ${\displaystyle {\frac {h}{t}}}$ ${\displaystyle v_{o}+a\Delta t}$ Acceleration a ${\displaystyle {\frac {v}{t}}}$ ${\displaystyle g={\frac {GM}{h^{2}}}}$ ${\displaystyle {\frac {v-v_{o}}{t-t_{o}}}}$ Force F ${\displaystyle ma}$ ${\displaystyle mg}$ ${\displaystyle m{\frac {|\Delta v}{\Delta t}}}$ Work W ${\displaystyle Fs}$ ${\displaystyle mgh}$ ${\displaystyle Ft(v_{o}+a\Delta t)}$ power E ${\displaystyle {\frac {W}{t}}}$ ${\displaystyle {\frac {mgh}{t}}}$ ${\displaystyle F(v_{o}+a\Delta t)}$

### Non uniform curve motion

Motion that does not follow a straight path

 Notation Formulas Distance s(t) ${\displaystyle \int v(t)dt}$ Time t ${\displaystyle t}$ Speed v(t) ${\displaystyle v(t)}$ Acceleration a(t) ${\displaystyle {\frac {d}{dt}}v(t)}$ Force F(t) ${\displaystyle m{\frac {d}{dt}}v(t)}$ Work W(t) ${\displaystyle F\int v(t)dt}$ Energy E(t) ${\displaystyle {\frac {F}{t}}\int v(t)dt}$

### Periodic motion

Motion that keeps repeat itself over a period of time

#### Circular motion

Motion that follows a circular path

##### Full circle motion

Motion that completes a circle

 Notation Formulas Distance s ${\displaystyle 2\pi r}$ Time t ${\displaystyle t}$ Speed v ${\displaystyle {\frac {2\pi r}{t}}=\omega r}$ Angular speed ω ${\displaystyle \omega {\frac {v}{r}}}$ Acceleration a ${\displaystyle vr}$ Force F ${\displaystyle mvr}$ Work W ${\displaystyle mvr2\pi }$ Energy E ${\displaystyle {\frac {mvr2\pi }{t}}=pr\omega }$
##### Circle's arc motion

Motion that follows an arc of a circle

 Notation Formulas Distance s ${\displaystyle \theta r}$ Time t ${\displaystyle t}$ Speed v ${\displaystyle {\frac {\theta r}{t}}}$ Angular speed ω ${\displaystyle \omega {\frac {v}{r}}}$ Acceleration a ${\displaystyle {\frac {\theta r}{t^{2}}}}$ Force F ${\displaystyle m{\frac {\theta r}{t^{2}}}}$ Work W ${\displaystyle p{\frac {\theta r}{t}}}$ Energy E ${\displaystyle p{\frac {\theta r}{t^{2}}}}$

#### Wave

##### Mathematical formula

A period motion of a sinusoidal motion

 Notation Formulas Distance s ${\displaystyle \lambda }$ Time t ${\displaystyle t}$ Speed v ${\displaystyle {\frac {\lambda }{t}}}$ Angular Speed ω ${\displaystyle \lambda f}$ Frequency f ${\displaystyle {\frac {1}{t}}}$ Wave equation f"(t) ${\displaystyle -\omega f(t)}$ Wave function f(t) ${\displaystyle ASin\omega t}$

#### Sinusoidal wave

Mathematiccaly sinusoidal can be represent by a wave equation and a wave function

Wave equation

${\displaystyle f^{''}(t)=-\omega f(t)}$

Wave function

${\displaystyle f(t)=ASin\omega t}$

#### Oscillation

##### Spring's Oscillation
 Spring's Oscillation Symbol Horizontal Vertical Spring's Oscillation equation ${\displaystyle f^{''}(t)}$ ${\displaystyle m{\frac {d}{dt}}x(t)=-kx(t)}$ ${\displaystyle m{\frac {d}{dt}}y(t)=-ky(t)}$ Spring's wave function ${\displaystyle f(t)}$ ${\displaystyle x(t)=ASin\omega t}$ ${\displaystyle y(t)=ASin\omega t}$ Angular speed ω ${\displaystyle {\sqrt {\frac {k}{m}}}}$ ${\displaystyle {\sqrt {\frac {k}{m}}}}$
##### Pendulum Oscillation

The differential equation which represents the motion of a simple pendulum is

${\displaystyle {\frac {d^{2}\theta }{dt^{2}}}+{\frac {g}{\ell }}\sin \theta =0}$  Eq. 1

where g is acceleration due to gravity, l is the length of the pendulum, and θ is the angular displacement.

##### Electric Oscillation
 Electric's Oscillation RLC series at equilibrium RLC series at resonance LC series at equilibrium LC series at resonance Wave equation ${\displaystyle {\frac {d^{2}}{dt^{2}}}i(t)=-2\alpha {\frac {d}{dt}}i(t)-\beta i(t)}$ ${\displaystyle Z_{L}=-Z_{C}.Z_{t}=R}$ ${\displaystyle {\frac {d^{2}}{dt^{2}}}i(t)=-{\frac {1}{T}}}$ ${\displaystyle Z_{L}=-Z_{C}}$ Wave function ${\displaystyle x(t)=A(\alpha )Sin\omega t}$ ${\displaystyle i(\omega =0)=0}$ ${\displaystyle i(\omega =\omega _{o})={\frac {v}{R}}}$ ${\displaystyle i(\omega =0))=0}$ ${\displaystyle i(t)=ASin\omega t}$ ${\displaystyle V_{L}=-V_{C}}$ ${\displaystyle A(\alpha )=Ae^{-\alpha t}}$ ${\displaystyle \omega ={\sqrt {\beta -\alpha }}}$ ${\displaystyle {\sqrt {\frac {1}{T}}}}$ ${\displaystyle {\sqrt {\frac {1}{T}}}}$ ${\displaystyle {\sqrt {\frac {1}{T}}}}$ ${\displaystyle \beta ={\frac {1}{T}}}$ ${\displaystyle T=LC}$ ${\displaystyle LC}$ ${\displaystyle LC}$ ${\displaystyle LC}$ ${\displaystyle \alpha =\beta \gamma }$ ${\displaystyle \gamma =RC}$
##### Electromagnetic Oscillation
 Electromagnetic's Oscillation Formula Wave equation ${\displaystyle \nabla ^{2}E(t)=-\omega E(t)}$  ${\displaystyle \nabla ^{2}B(t)=-\omega B(t)}$ Wave function ${\displaystyle E(t)=ASin\omega t}$ ${\displaystyle B(t)=ASin\omega t}$ Angular speed ${\displaystyle \omega =\lambda f={\sqrt {\frac {1}{T}}}=C}$ Time constant ${\displaystyle T=\mu \epsilon }$ Wave hape

#### Momentum

Momentum is defined as motion of a mass at a speed caused by a force

${\displaystyle F=ma=m{\frac {v}{t}}}$

Moment

${\displaystyle p=mv=Ft}$
##### Momentum of a mass in motion
 Notation Formulas Mass m ${\displaystyle m}$ Speed v ${\displaystyle v}$ Moment p ${\displaystyle mv}$ Impulse(Force) F ${\displaystyle {\frac {p}{t}}}$ Work W ${\displaystyle pv}$ Energy E ${\displaystyle pa}$
##### Momentum of a relativistic mass in motion

Momentum refers to movement of a mass at a speed relative to the speed of light

 Notation Formulas Mass m ${\displaystyle m_{0}(\gamma -1)}$ Speed v ${\displaystyle \gamma ={\sqrt {1-{\frac {v^{2}}{C^{2}}}}}}$ Momentum p ${\displaystyle mv}$ Force F ${\displaystyle {\frac {p}{t}}}$ Work W ${\displaystyle pv}$ Energy E ${\displaystyle pa}$
##### Momentum of a massless quanta in motion

Momentum refers to movement of a mass at a speed equals to the speed of light

 Notation Formulas Speed v ${\displaystyle \omega ={\sqrt {\frac {1}{\mu \epsilon }}}=C=\lambda f}$ Work W ${\displaystyle pv=pC=p\lambda f=hf}$ Quanta h ${\displaystyle p\lambda }$ Momentum p ${\displaystyle {\frac {h}{\lambda }}}$ Wavelength ${\displaystyle {\frac {h}{p}}={\frac {C}{f}}}$
##### Momentum of electric charge
${\displaystyle F_{B}=F_{r}}$
${\displaystyle QvB=m{\frac {v^{2}}{r}}}$
${\displaystyle r={\frac {mv}{QB}}}$
${\displaystyle v={\frac {Q}{m}}Br}$
##### Momentum of free electron

Absorbing photon, electron becomes free electron travels outward off the atom's circular orbit

${\displaystyle hf=hf_{o}+{\frac {1}{2}}mv^{2}}$
${\displaystyle v={\sqrt {{\frac {2}{m}}(hf-hf_{o})}}={\sqrt {{\frac {2}{m}}(nhf_{o})}}}$
##### Momentum of a bind electron

Releasing photon, electron becomes free electron travels inward off the circle orbit

${\displaystyle nhf=mvr2\pi }$
${\displaystyle r={\frac {1}{2\pi }}{\frac {nhf}{mv}}}$
${\displaystyle v={\frac {1}{2\pi }}{\frac {nhf}{mr}}}$
${\displaystyle n=2\pi r{\frac {mv}{hf}}}$

## Heat

### Temperature

Temperature is the measurement of heat's intensity . Temperature is denoted as T measured in degree o

#### Temperature measurements

There are 3 temperature measuring system

1. Degree Celcius, ${\displaystyle ^{o}C}$
2. Degree Kevin , ${\displaystyle ^{o}K}$
3. Degree Fahrenheit , ${\displaystyle ^{o}F}$

Conversion between systems of temperature can be done as shown below

 Convert from to ' Formulas Degree Fahrenheit Celsius °C = (°F – 32) / 1.8 Degree Celsius Fahrenheit °F = °C × 1.8 + 32 Degree Fahrenheit Kelvin K = (°F – 32) / 1.8 + 273.15

#### Standard temperatures

 Standard temperature Value Room temperature ${\displaystyle 25^{o}C}$ Boiling temperature ${\displaystyle 100^{o}C}$ Frozen temperature ${\displaystyle 0^{o}C}$

### Heat and matter

Heat and matter interact to create Heat transfer of three phases Heat conduction, Heat convection and Heat radiation

#### Heat absortion of matter

• Matter of dark color absorbs more heat energy than matter of bright color
• Matter of thin dimension absorbs more heat energy than matter of thich dimension

For example

Dark and thin clothes dry faster than bright and thick clothes

#### Heat Transfer

A process of heat interaction with matter through 3 phases of

##### Heat conduction

Matter change its temperature when it in contact with heat energy

${\displaystyle \Delta T=T_{2}-T_{1}}$
${\displaystyle E=mc\Delta T=mc(T_{2}-T_{1})}$
##### Heat convection

Matter absorbs heat energy to its maximum level and gives off visible light

${\displaystyle E=hf_{o}}$
${\displaystyle f_{o}={\frac {C}{\lambda _{o}}}}$

Matter is at its saturation . Matter is no longer absorbs heat energy and use the excess energy to release electron of its atom

${\displaystyle E=E_{o}+E_{e}=hf_{o}+{\frac {1}{2}}mv^{2}=hf}$
${\displaystyle v={\sqrt {{\frac {2}{m}}(hf-hf_{o})}}={\sqrt {{\frac {2}{m}}(nhf_{o})}}}$

#### Heat flow

Heat flows between 2 objects of different mass follows heat flow rule that heat flows from high temperature to low temperature

Heat energy absorb by mass 1

${\displaystyle Q_{1}=m_{1}cT_{1}}$

Heat energy absorb by mass 2

${\displaystyle Q_{2}=m_{2}cT_{2}}$

Direction of heat flow

${\displaystyle T_{1}>T_{2}}$
${\displaystyle Q_{1}-Q_{2}=m_{1}cT_{1}-m_{2}cT_{2}=(m_{1}-m_{2})c(T_{1}-T_{2})}$
${\displaystyle T_{2}>T_{1}}$
${\displaystyle Q_{2}-Q_{1}=m_{2}cT_{2}-m_{1}cT_{1}=(m_{2}-m_{1})c(T_{2}-T_{1})}$

## Light

### Speed of visible light

Speed of light is denoted as C which has a value

${\displaystyle C=3\times 10^{8}}$  m/s

### Measurement speed of visible light

 In vacuum ${\displaystyle v=C=299999000m/s}$ By Michael Morrison In air, as electromagnetic radiation ${\displaystyle v=\omega ={\sqrt {\frac {1}{\mu _{o}\epsilon _{o}}}}=C=\lambda f=3\times 10^{8}m/s}$ By James Clerk Maxwell In liquid ${\displaystyle v={\sqrt {1-{\frac {v^{2}}{C^{2}}}}}m/s}$ By Lorentz

### Visible light

#### Characteristics

Visible light travels at a constant speed in vacuum and in air which has a value

${\displaystyle C=3\times 10^{8}}$  m/s

Travels as Electromagnetic wave of wavelength

${\displaystyle \lambda =400-700nm}$  m

Of Threshold frequency

${\displaystyle f_{o}={\frac {C}{f_{o}}}={\frac {3\times 10^{8}}{400-700nm}}}$  Hz

#### Composite colors

Visible light passes through prism decomposes itself into its composites color light of 6 colors

 Colors Wavelength Angle of refraction Red Orange Yellow Green Blue Violet

### Light and matter

Light and matter interacts with each other to create the following effects

## Sound

### Measurement speed of sound

 Material medium Value In air ${\displaystyle v=}$ In water ${\displaystyle v=}$ In solid ${\displaystyle v=}$

### Audible sound

#### Sound spectrum

Audible sound to human's ears is in the frequency range 20Hz - 20KHz . Sound above 20KHz is called Ultrasound . Sound below 20Hz is called Infrasound

#### Audible sound wave in air

In air, audible sound travels as wave of thick and thin columns of air

 Medium Speed Frequency Wavelength In air ${\displaystyle v=300m/s}$ ${\displaystyle f=20Hz-20KHz}$ ${\displaystyle \lambda ={\frac {300m/s}{20Hz-20KHz}}}$

### Sound and matter

Sound and matter interacts with each other to create the following effects

## Electricity

### Electricity and a straight line conductor

 Characteristis Symbols Formulas Voltage ${\displaystyle V}$ ${\displaystyle V}$ Current ${\displaystyle I}$ ${\displaystyle I}$ Resistance ${\displaystyle R}$ ${\displaystyle R={\frac {V}{I}}}$ Conductance ${\displaystyle G}$ ${\displaystyle G={\frac {I}{V}}={\frac {1}{R}}}$ Electromagnet's Field strength ${\displaystyle B}$ ${\displaystyle B=LI={\frac {N\mu }{l}}I}$ Resistance change ${\displaystyle R(T)}$ ${\displaystyle E(T)=R_{o}+nT}$ ${\displaystyle E(T)=R_{o}e^{nT}}$ Power generated ${\displaystyle E_{V}}$ ${\displaystyle E_{V}=IV}$ Power loss ${\displaystyle E_{R}}$ ${\displaystyle E_{R}=I^{2}R(T)}$ Power transmitted ${\displaystyle E}$ ${\displaystyle E=E_{E}-E_{R}}$

### Electromagnet

 For a straight line conductor ${\displaystyle B=LI={\frac {\mu }{2\pi r}}I}$ For a circular loop made from straight line conductor ${\displaystyle B=LI={\frac {\mu }{2r}}I}$ For a coil of N circular loops made from straight line conductor ${\displaystyle B=LI={\frac {N\mu }{l}}I}$

### Electric Oscillation

 Electric's Oscillation RLC series at equilibrium RLC series at resonance LC series at equilibrium LC series at resonance Wave equation ${\displaystyle {\frac {d^{2}}{dt^{2}}}i(t)=-2\alpha {\frac {d}{dt}}i(t)-\beta i(t)}$ ${\displaystyle Z_{L}=-Z_{C}.Z_{t}=R}$ ${\displaystyle {\frac {d^{2}}{dt^{2}}}i(t)=-{\frac {1}{T}}}$ ${\displaystyle Z_{L}=-Z_{C}}$ Wave function ${\displaystyle x(t)=A(\alpha )Sin\omega t}$ ${\displaystyle i(\omega =0)=0}$ ${\displaystyle i(\omega =\omega _{o})={\frac {v}{R}}}$ ${\displaystyle i(\omega =0))=0}$ ${\displaystyle i(t)=ASin\omega t}$ ${\displaystyle V_{L}=-V_{C}}$ ${\displaystyle A(\alpha )=Ae^{-\alpha t}}$ ${\displaystyle \omega ={\sqrt {\beta -\alpha }}}$ ${\displaystyle {\sqrt {\frac {1}{T}}}}$ ${\displaystyle {\sqrt {\frac {1}{T}}}}$ ${\displaystyle {\sqrt {\frac {1}{T}}}}$ ${\displaystyle \beta ={\frac {1}{T}}}$ ${\displaystyle T=LC}$ ${\displaystyle LC}$ ${\displaystyle LC}$ ${\displaystyle LC}$ ${\displaystyle \alpha =\beta \gamma }$ ${\displaystyle \gamma =RC}$

## Electromagnetism

Electric current interacts with magnetic material to generate Magnetic field

### Electromagnetic Field

 Electromagnetic Field Definition symbol formula Straight line conductor The magnetic field is made up of circular magnetic circles rotate counterclockwise or clockwise direction ${\displaystyle B}$ ${\displaystyle B=LI={\frac {\mu }{2\pi r}}I}$ Circular loop conductor The magnetic field is made up of circular magnetic circle around a point charge that moves around the circular loop ${\displaystyle B}$ ${\displaystyle B=LI={\frac {\mu }{2r}}I}$ Coil of N circular loop conductor The magnetic field is made up of elliptic magnetic lines running from North pole [N] to South pole [S] With North pole [N] corresponds to positive polarity (+) and South pole [S] corresponds to negative polarity (-) ${\displaystyle B}$ ${\displaystyle B=LI={\frac {N\mu }{l}}I}$ ${\displaystyle \phi =-NB=-NLI}$ ${\displaystyle H={\frac {B}{\mu }}={\frac {\phi }{N\mu }}}$

### Electromagnetic Induction

For a Faraday's coil of N circular loops . The magnetic field is made up of elliptic magnetic lines running from North pole [N] to South pole [S]

 Magnetic Potential Difference ${\displaystyle V_{L}}$ ${\displaystyle {\frac {dB}{dt}}=L{\frac {dI}{dt}}}$ Induced Magnetic Voltage ${\displaystyle \epsilon }$ ${\displaystyle -{\frac {d\phi }{dt}}=-N{\frac {dB}{dt}}=-NL{\frac {dI}{dt}}}$

### Electromagnetization

Process of generating permanent electromagnet from a magnetic material placed in the turns of the magnetic coil

${\displaystyle B=LI={\frac {N\mu }{l}}I}$
${\displaystyle H={\frac {B}{\mu }}={\frac {\phi }{N\mu }}}$

Maxwell's Electromagnetization Vector Equation

${\displaystyle \nabla \cdot D=\rho }$
${\displaystyle \nabla \times E=-\nabla B}$
${\displaystyle \nabla \cdot B=0}$
${\displaystyle \nabla \times H=J+\nabla B}$

### Electromagnetic Wave Oscillation

 Electromagnetic Wave Vectore Equation ${\displaystyle \nabla \cdot E=0}$ ${\displaystyle \nabla \times E={\frac {1}{T}}E}$ ${\displaystyle \nabla \cdot B=0}$ ${\displaystyle \nabla \times B={\frac {1}{T}}B}$ ${\displaystyle T=\mu \epsilon }$ Electromagnetic Wave Equation ${\displaystyle \nabla ^{2}E=-\omega E}$ ${\displaystyle \nabla ^{2}B=-\omega B}$ Electromagnetic Wave Function ${\displaystyle E=ASin\omega t}$ ${\displaystyle B=ASin\omega t}$ ${\displaystyle \omega ={\sqrt {\frac {1}{\mu \epsilon }}}=C=\lambda f}$ Electromagnetic Wave Radiation ${\displaystyle v=\omega ={\sqrt {\frac {1}{\mu \epsilon }}}=C=\lambda f}$ ${\displaystyle E=pv=pC=p\lambda f=hf}$ ${\displaystyle h=p\lambda }$

Electromagnetic wave radiation is generated from Electromagnetic wave propagates at speed of visible light

${\displaystyle v=\omega ={\sqrt {\frac {1}{\mu \epsilon }}}=C=\lambda f}$
${\displaystyle E=pv=pC=p\lambda f=hf}$
${\displaystyle h=p\lambda }$

Electromagnetic Wave Radiation of Radian Photon just like visible light perceive by human eyes

${\displaystyle v=\omega _{o}={\sqrt {\frac {1}{\mu _{o}\epsilon _{o}}}}=C=\lambda _{o}f_{o}}$
${\displaystyle E=pv=pC=p\lambda _{o}f=hf_{o}}$
${\displaystyle h=p\lambda _{o}}$

Electromagnetic Wave Radiation of Non radiant photon that can free electron off matter's atom

${\displaystyle v=\omega ={\sqrt {\frac {1}{\mu \epsilon }}}=C=\lambda f}$
${\displaystyle E=pv=pC=p\lambda f=hf}$
${\displaystyle h=p\lambda }$
##### Heinseinberg's Uncertainty Principle
Photon can only exist in one state at a time

${\displaystyle \Delta p\Delta \lambda ={\frac {1}{2}}{\frac {h}{2\pi }}={\frac {\hbar }{2}}}$
${\displaystyle \hbar ={\frac {h}{2\pi }}}$

#### Quantization

Photon is energy of a quantity that process no mass known as Quanta travels at speed of light

${\displaystyle v=C=\lambda f}$
${\displaystyle W=pv=pC=p\lambda f=\lambda f=hf}$
${\displaystyle h=p\lambda }$
##### Quanta's Wave-Particle Duality

Quanta processes Wave-Particle Duality . Sometimes, behave like wave of wavelength λ . Sometimes, behave like particle of a momentum p

Wave like . ${\displaystyle \lambda ={\frac {h}{p}}}$
Particle like . ${\displaystyle p={\frac {h}{\lambda }}={\frac {C}{f}}}$

## Quantum Physics

${\displaystyle E(t)=ASin\omega t}$
${\displaystyle B(t)=ASin\omega t}$
${\displaystyle \omega =\lambda f={\sqrt {\frac {1}{\mu \epsilon }}}=C}$
${\displaystyle v=\omega }$
${\displaystyle E=pv=pC=p\lambda f=hf}$
${\displaystyle h=p\lambda }$

Radiation interact with matter to create Heat transfer of three phases Heat conduction, Heat convection and Heat radiation

Heat conduction Matter absorbs photon's energy and release heat into the surrounding

${\displaystyle \Delta T=T_{1}-T_{o}}$
${\displaystyle E=mC\Delta T}$

Heat convection Matter absorbs photon's energy to the mazximum at Threshold frequency fo and release visible light into the surrounding

${\displaystyle f_{o}={\frac {C}{\lambda _{o}}}}$
${\displaystyle E=hf_{o}}$

Heat radiation Matter's atom releases its electron into the surrounding at frequency greater than threshold frequency fo

${\displaystyle f={\frac {C}{f}}}$
${\displaystyle E=hf}$

### Photon

#### Photon's characteristics

Photon is defined as energy of a Quanta travels at speed of visible light

${\displaystyle E=hf=h{\frac {\omega }{2\pi }}=\hbar \omega }$
${\displaystyle p={\frac {h}{\lambda }}=h{\frac {k}{2\pi }}=\hbar k}$
${\displaystyle h=p\lambda }$
${\displaystyle \omega ={\frac {E}{\hbar }}}$
${\displaystyle k={\frac {p}{\hbar }}}$
${\displaystyle \hbar ={\frac {E}{\omega }}={\frac {p}{k}}={\frac {h}{2\pi }}}$

#### Photon's states

Photon exists in 2 states .

Radiant photon at ${\displaystyle f_{o}}$  carries quantum energy of energy of visible light ${\displaystyle E=hf_{o}}$
Non radiant photon at ${\displaystyle f>f_{o}}$  carries quantum energy greater than energy of visible light ${\displaystyle E=hf}$  with f > fo

Photon cannot exist in 2 states at the same time . The chances of finding photon at any one state is one half . This is the uncertainty principle proposed by schroduinger which can be expressed mathematicaaly as

${\displaystyle \Delta p\Delta \lambda ={\frac {1}{2}}{\frac {h}{2\pi }}={\frac {h}{4\pi }}={\frac {\hbar }{2}}}$

Photon has a spectrumand are found in the frequenct bands below

VF
UVF
X
γ

### Quanta

#### Mathematical formula

${\displaystyle h=p\lambda ={\frac {E}{C}}\lambda }$

#### Wave-Particle duality

Quanta processes Wave-Particle duality

Some time Quanta behaves as a particle of a momentum

${\displaystyle p={\frac {h}{\lambda }}}$

Some other time Quanta behaves as a wave of wavelength

${\displaystyle \lambda ={\frac {h}{p}}={\frac {C}{f}}}$

### Relativity

#### Relativistic mass in motion

 Symbol Mathematical formula Speed ${\displaystyle v}$ ${\displaystyle {\sqrt {1-{\frac {v^{2}}{C^{2}}}}}}$ Mass ${\displaystyle m}$ ${\displaystyle m=m_{o}(v-1)}$ Moment ${\displaystyle p}$ ${\displaystyle mv}$ Energy ${\displaystyle E}$ ${\displaystyle pv}$

#### Massless quanta in motion

 Symbol Mathematical formula Speed ${\displaystyle v}$ ${\displaystyle C=\lambda f}$ Energy ${\displaystyle E}$ ${\displaystyle pv=pC=p\lambda f=hf}$ Quanta ${\displaystyle h}$ ${\displaystyle h=p\lambda }$ Moment ${\displaystyle p}$ ${\displaystyle {\frac {h}{\lambda }}}$ Wave length ${\displaystyle \lambda }$ ${\displaystyle {\frac {C}{f}}={\frac {h}{p}}}$

#### Mass change

At speed relative to speed of visible light

${\displaystyle v=\gamma ={\sqrt {1-{\frac {v^{2}}{C^{2}}}}}}$  . ${\displaystyle M=m_{o}(\gamma -1)}$

At speed equals to speed of visible light

${\displaystyle v=C=\lambda f}$  . ${\displaystyle h=p\lambda ={\frac {E}{C}}\lambda }$

### Einstein's relativity theory

#### Newton's motion's speed

When matter travels at any speed less than speed of visible light, matter does not change its mass

 Speed of motion Mathematical formula of speed Mathematical formula of mass At any speed less than speed of visible light ${\displaystyle v=v}$ ${\displaystyle m=m}$

#### Einstein's motion's speed

When matter travels at a speed relative to or equal to the speed of visible light it is sometimes, erroneously said to change it's mass as space/time dilation changes the observable force needed to accelerate it under Newton's 2nd Law [F=ma]. The rest mass, usually designated m(subscript=0) remains the same.

 Speed of motion Mathematical formula of speed Mathematical formula of mass At speed relative to speed of visible light ${\displaystyle v={\sqrt {1-{\frac {v^{2}}{C^{2}}}}}}$ ${\displaystyle m=m_{o}(v-1)}$ At speed equals to speed of visible light ${\displaystyle v=C=\lambda f}$ ${\displaystyle h=p\lambda ={\frac {E}{C}}\lambda }$