Quantum Mechanics

Nature of Quantum Mechanics

Electromagnetic Waves

• Frequency $\nu$
  • Number of waves per second.
• Wavelength $/lambda$
  • Distance between two peaks.
• Speed ((c))
  • $c=\lambda \nu$

Quanta

• Discreteness of Energy:
• Radiation in discrete quantities: $hv$
• Atomic Absorption/Emission:
• Atoms absorb/emit energy at: $hv,2hv,3hv,\dots$

Energy of a Photon

• Formula: $E_{\text{photon}}=hv=\frac{hc}{\lambda }$

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Photoelectric Effect

Definition

• Radiation causes electron emission when certain frequency threshold is exceeded.
• Einstein: Light as particles (photons) explained with $E=hv$

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The Bohr Model

Electron Orbits

• Electrons have specific energy levels.
• Energy Level Formula: $E_n=-\frac{Z^2\times 2.178\times 10^{-18}\text{ J}}{n^2}$

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Quantum Mechanics Development

Planck’s Contribution

• Radiation Discreteness: Energy as quanta

Heisenberg and Schrödinger

• Wave Functions and Uncertainty:
  • Principle Quantum Numbers
  • Orientation with Magnetic Quantum Numbers

Wave-Particle Duality

• de Broglie’s Wavelength: $\lambda =\frac{h}{mu}$

Uncertainty Principle

• Heisenberg’s Principle: $\Delta x\Delta p\ge \frac{h}{4\pi }$

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Useful Formula Sheet

• Electromagnetic Waves: $c=\lambda \nu$

• Photon Energy: $E_{\text{photon}}=hv=\frac{hc}{\lambda }$

• Bohr Energy Levels: $E_n=-\frac{Z^2\times 2.178\times 10^{-18}\text{ J}}{n^2}$

• de Broglie’s Wavelength: $\lambda =\frac{h}{mu}$

• Heisenberg’s Uncertainty Principle: $\Delta x\Delta p\ge \frac{h}{4\pi }$ Where:

• (c) is the speed of light ((2.998 \times 10^8 , \text{m/s}))

• (\lambda) is wavelength

• (\nu) is frequency

• (h) is Planck’s constant ((6.626 \times 10^{-34} , \text{Js}))

• (Z) is atomic number

• (n) is principal quantum number

• (m) is mass

• (u) is velocity# Nature of Quantum Mechanics

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