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The Wave-Particle Duality of Light and Quantum Mechanics

Explore the nature of light as both a wave and particle, delving into atomic spectra, quantum mechanical models, electron behavior, and quantum numbers in this comprehensive review chapter.

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The Wave-Particle Duality of Light and Quantum Mechanics

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  1. Chapter 6 Review and Breathe

  2. The Wave Nature of Light • Electromagnetic radiation is one way energy travels through space. • Wavelength is inversely proportional to frequency • =c/

  3. The Particle Nature of Light • Energy is gained or lost in whole number multiples. • ΔE=nh • This energy is Quantized. • Electromagnetic radiation is quantized as photons.

  4. Dual Nature of Light • Photons have energy of Ephoton = hc/ • Energy is also E=mc2 (c=speed of light) • Thus: m=E/c2 • Substitute E=hc/ in the above equation • m=hc/c2  • And finally: m=h/c  • Light acts as a wave and has mass

  5. Do particles have wave characteristics? • If a photon has mass m=h/c  while it is moving… • Then a particle moving at a velocity v has a wavelength using the equation m=h/v  • Solve for  and =h/mv • This is de Broglie’s equation.

  6. Atomic spectrum of Hydrogen • When light is passed through a prism one gets an emission spectrum. • When all wavelengths are possible one gets a continuous spectrum. • When energy is quantized the spectrum is a line spectrum, or discrete.

  7. How do electrons emit light?

  8. The Bohr model • Bohr proposed that in a hydrogen atom the electron orbits the nucleus in allowed circular orbits. • Each orbit has an energy associated with it. • E=-2.178x10-18J (Z2/n2)

  9. Quantum Mechanical Model • Bohr’s model doesn’t work for atoms larger than hydrogen. • Electrons are not behaving in a manner that agrees with the circular orbit model.

  10. Wave function • Electrons in the higher energy levels are acting more like standing waves than like particles. • Schrödinger looked at the wave function of the electron. This wave function describes the electron’s orbital.

  11. But where is the electron? • Heisenberg’s uncertainty principle states that we cannot know with certainty both how fast an electron is moving and where it is. • Δx * Δ(mv)> h/4 • Probability distribution

  12. Quantum numbers • each energy level is designated by the value n which is an integer from 1 (lowest energy or "ground state") on up • the number of types of orbitals possible on an energy level is also equal to n • the maximum number of actual orbitals on an energy level is equal to n2 • the maximum number of electrons in an orbital is equal to 2 • the maximum number of electrons on an energy level is equal to 2n2

  13. Quantum numbers • Principle quantum number, n=integral values 1, 2, 3 … Represents the energy level. • Angular quantum number, l = 0, 1, 2 etc for n-1. It represents the shape of the orbital. • Magnetic quantum number m= -l to l. It is related to the orientation of the orbital in relationship to other orbitals in the atom.

  14. Pauli Exclusion Principle • In given atom, no two electrons may have the same set of quantum numbers. This is known as the Pauli Exclusion Principle. • Since each orbital may hold up to two elections. Each election is assigned a separate spin. • +½ and -½

  15. Summary Table

  16. Angular quantum numbersTake note of the nodes! • For l= 0, 1, 2, and bottom row 3.

  17. As protons are added to a nucleus to build up elements, electrons are added too. These electrons are added into the lower energy orbitals first. Aufbau Principle

  18. Hund’s Rule • The lowest energy configuration In an orbital is one having the maximum number of unpaired electrons allowed by the Pauli Principle in a set of degenerative orbitals.

  19. Electron Configuration and the Periodic Table • Elements’ reactivity is based on its valence electrons. • The periodic table demonstrates the valence electrons of each group.

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