# Photon

## Photon source

 Electromagnetic wave radiation Coil of N turns ${\displaystyle E=hf}$ Sun Celestial planet ${\displaystyle E=hf}$ Electric light Light bulb ${\displaystyle E=hf}$

## Photon's chracteristics

Photon is energy of a Quanta that travels as electromagnetic wave at speed of light

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

With

${\displaystyle E}$ - Photon
${\displaystyle f}$ - frequency of photon's wave
${\displaystyle \omega }$ - angular frequency of photon's wave
${\displaystyle h}$ - Planck's constant

### Photon's State

Photon is observed to exist in 2 states

Radiant Photon exists at frequency ${\displaystyle f=f_{o}}$ process the following identities

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

Non radiant Photon exists at frequency ${\displaystyle f.f_{o}}$

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

Uncertainty of Photon's state Photon exists in 2 states at specific frequency . The chance to find one of its state (successful rate of finding photon) is 1/2 where h = p λ . h and p do not change, only wavelength changes with frequency . Hence, Uncertainty principle

Photon cannot exist in 2 states at the same time


Mathematically, Uncertainty principle can be expressed as

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

### Photon's Quantization

${\displaystyle E=hf}$
${\displaystyle h=p\lambda }$

### Wave Particle Duality

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

## Photon's effects

Photon interacts with matter to create Heat transfer of three phases Heat conduction, Heat convection and Heat radiation

 Heat transfer Explanation Mathematical formulas Heat conduction matter absorbs photon's energy creates change in matter's temperature ${\displaystyle \Delta T=T_{1}-T_{o}}$${\displaystyle E=mC\Delta T}$ Heat convection matter conducts photon's energy to the maximum at threshold frequency ${\displaystyle f_{o}={\frac {C}{\lambda _{o}}}}$${\displaystyle E=hf_{o}}$ Heat radiation matter ejects electron off its atom at frequency greater than threshold frequency ${\displaystyle f={\frac {C}{\lambda }}}$${\displaystyle E=hf}$ provided that f>fo