Hydrogen Atom: Wave Function Hydrogen Atom: more quantum numbers Bohr Model Quantum Physics According to Bohr’s Model, the energy levels of an electron in a Hydrogen atom:

2π 2m k 2e4 E = − e n = 1,2,3,.... n n2h2

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Quantum Numbers for Allowed Electron States in an Atom Pauli Exclusion Principle

n = Principal Quantum Number (1,2,3,...) No two electrons in an atom can be in 2 2 4 2π mek e *Determines energy (Bohr) En = − 2 2 the same quantum state (n, l, ml, ms) n h l = Orbital Quantum Number (0,1,2,...n-1) h *Determines angular momentum L = l(l + 1) 2π * l < n always true!

ml = Magnetic Quantum Number (-l,...,-1,0,1,...l) h *Component of l along some z axis L = m z l 2π

1 1 m = Spin Quantum Number (− ,+ ) s 2 2 *”Spin Up” or “Spin Down” 12/5/10 3 12/5/10 4

1 Probability Functions for a few states of H Nomenclature

Example: 1 electron in the ground state of Hydrogen

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Example Periodic Table & Pauli Exclusion Principle

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2 Filling Energy Levels Filling Energy Levels

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Periodic Table & Pauli Exclusion Periodic Table & Pauli Exclusion

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3 Photons & Matter Laser (Light Amplification by stimulated emission http://www.youtube.com/watch?v=5uAMTcaKLpI

Ruby is an aluminum oxide crystal in which some Al atoms have been replaced with chromium. Chromium atoms absorb green and blue light and emit or reflect only red light. 12/5/10 13 12/5/10 14

Laser (Light Amplification by stimulated emission) Laser (Light Amplification by stimulated emission)

1. High-voltage electricity causes the quartz flash tube to emit an 3. Mirrors at each end reflect intense burst of light, exciting the photons back and forth, some of the atoms in the ruby continuing this process of crystal to higher energy levels. stimulated emission and amplification.

2. At a specific energy level, some atoms emit photons. At first, photons are emitted in all 4. The photons leave through directions. Photons from one the partially silvered mirror at atom stimulate emission of one end. This is laser light. photons from other atoms and the light intensity is amplified.

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4 Ruby Laser Energy Levels Helium-Neon Laser Energy Levels

Key to the laser: population inversion

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Helium-Neon Laser

15% helium, 85% neon λ = 632.8 nm (E = 1.96 eV)

Characteristics of laser beams: coherent (photons have the same frequency in phase, and the same direction of propagation), very small angular divergence, intense.

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