Wave-Particle Duality

Quanta process Wave-Particle duality

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

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

Quanta's States

Quanta exist in 2 states

Radiant photon at Threshold frequency . ${\displaystyle f_{o}={\frac {C}{\lambda _{o}}}}$ of a quantum energy ${\displaystyle E=hf_{o}}$

Non-Radiant photon at frequency greater Threshold frequency . ${\displaystyle f_{o}={\frac {C}{\lambda _{o}}}}$ of a quantum energy ${\displaystyle E=hf}$

Heiseinberg Uncertainty Priciple

states that

Quanta's energy , Photon , cannot exist in 2 states at the same times

There are 2 states of photons chances to find photon as radiant photon or Non-radiant photon is one half 1/2 which can be expressed mathematically as

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

Electromagnetic Wave Radiation

Experiment shows that electromagnetic wave radiation carries quantum energy

${\displaystyle E=hf_{o}}$ at ${\displaystyle f_{o}={\frac {C}{\lambda _{o}}}}$ of a Radiant photon that produce visible light

${\displaystyle E=hf}$ at ${\displaystyle f>{\frac {C}{\lambda _{o}}}}$ of a Non-Radiant photon that produce electricity made of free electron

This can be deduce from , electromagnetic wave equation

${\displaystyle \nabla ^{2}E=-\omega E}$

${\displaystyle \nabla ^{2}E=-\omega B}$

Solving equation above, we have electromagnetic function

${\displaystyle E=A\sin \omega t}$

${\displaystyle B=A\sin \omega t}$

${\displaystyle \omega ={\sqrt {\frac {1}{\mu \epsilon }}}=C=\lambda f}$

Electromagnetic wave radiation produces quantum energy travels at speed of light

• Speed . ${\displaystyle v={\sqrt {\frac {1}{\mu \epsilon }}}=C=\lambda f}$
• Quantum energy . ${\displaystyle E=pv=pC=p\lambda f=hf}$
• Quantum . ${\displaystyle h=p\lambda }$
• Wavelength . ${\displaystyle \lambda ={\frac {h}{p}}}$
• Momentum . ${\displaystyle p={\frac {h}{\lambda }}}$

Atom Decay

Experiment shows that . When atom absorbs electromagnetic radiation quantum energy . Electron of atom is released from atom going out off atom . When atom releases electromagnetic radiation quantum energy . Electron of atom is released from atom going inside atom

Free electron going out of atom

${\displaystyle hf=hf_{o}+{\frac {1}{2}}mv^{2}}$

${\displaystyle v={\sqrt {{\frac {2}{m}}(hf-hf_{o})}}={\sqrt {{\frac {2}{m}}(nhf_{o})}}}$

Free electron going inside of atom

${\displaystyle nhf=mvr2\pi }$

${\displaystyle r={\frac {1}{2\pi }}{\frac {nhf}{mv}}}$

${\displaystyle v={\frac {1}{2\pi }}{\frac {nhf}{mr}}}$

${\displaystyle n=2\pi {\frac {mv}{hf}}}$

Matter Decay

Alpha decay unstable radioactive material decays to become more stable . This type of decay releases Relative mass and Alpha photon travels at a speed relative to speed of light

${\displaystyle m=m_{o}(\gamma -1)}$

${\displaystyle v=\gamma ={\sqrt {1-{\frac {v^{2}}{C^{2}}}}}}$

Beta decay unstable isotope material decays to become more stable . This type of decay releases Relative mass and Beta photon travels at a speed equals to speed of light

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

${\displaystyle E=hf_{o}}$

${\displaystyle h=p\lambda _{o}}$

Gamma decay collision of electron . This type of decay releases Relative mass and Gamma photon travels at a speed equals to speed of light