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**I. Waves & Particles (p. 91 - 94)**

Ch. 4 - Electrons in Atoms I. Waves & Particles (p )

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**A. Waves Wavelength () - length of one complete wave**

Frequency () - # of waves that pass a point during a certain time period hertz (Hz) = 1/s Amplitude (A) - distance from the origin to the trough or crest

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** A A A. Waves crest greater amplitude (intensity) origin trough**

greater frequency (color)

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B. EM Spectrum HIGH ENERGY LOW ENERGY

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**B. EM Spectrum HIGH ENERGY LOW ENERGY R O Y G. B I V red orange yellow**

green blue indigo violet

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**c = B. EM Spectrum c: speed of light (3.00 108 m/s)**

Frequency & wavelength are inversely proportional c = c: speed of light (3.00 108 m/s) : wavelength (m, nm, etc.) : frequency (Hz)

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**B. EM Spectrum = ? = c = 434 nm = 4.34 10-7 m**

EX: Find the frequency of a photon with a wavelength of 434 nm. GIVEN: = ? = 434 nm = 4.34 10-7 m c = 3.00 108 m/s WORK: = c = 3.00 108 m/s 4.34 10-7 m = 6.91 1014 Hz

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**C. Quantum Theory Planck (1900)**

Observed - emission of light from hot objects Concluded - energy is emitted in small, specific amounts (quanta) Quantum - minimum amount of energy change

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C. Quantum Theory Planck (1900) Classical Theory Quantum Theory vs.

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C. Quantum Theory Einstein (1905) Observed - photoelectric effect

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**“wave-particle duality”**

C. Quantum Theory Einstein (1905) Concluded - light has properties of both waves and particles “wave-particle duality” Photon - particle of light that carries a quantum of energy

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C. Quantum Theory The energy of a photon is proportional to its frequency. E = h E: energy (J, joules) h: Planck’s constant ( J·s) : frequency (Hz)

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**C. Quantum Theory E = ? E = h = 4.57 1014 Hz**

EX: Find the energy of a red photon with a frequency of 4.57 1014 Hz. GIVEN: E = ? = 4.57 1014 Hz h = J·s WORK: E = h E = ( J·s) (4.57 1014 Hz) E = 3.03 J

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**II. Bohr Model of the Atom (p. 94 - 97)**

Ch. 4 - Electrons in Atoms II. Bohr Model of the Atom (p )

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**A. Line-Emission Spectrum**

excited state ENERGY IN PHOTON OUT ground state

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B. Bohr Model e- exist only in orbits with specific amounts of energy called energy levels Therefore… e- can only gain or lose certain amounts of energy only certain photons are produced

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B. Bohr Model 6 Energy of photon depends on the difference in energy levels Bohr’s calculated energies matched the IR, visible, and UV lines for the H atom 5 4 3 2 1

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**C. Other Elements Helium**

Each element has a unique bright-line emission spectrum. “Atomic Fingerprint” Helium Bohr’s calculations only worked for hydrogen!

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**C. Other Elements Examples: Iron**

Now, we can calculate for all elements and their electrons – next section

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**III. Quantum Model of the Atom (p. 98 - 104)**

Ch. 4 - Electrons in Atoms III. Quantum Model of the Atom (p )

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**A. Electrons as Waves Louis de Broglie (1924)**

Applied wave-particle theory to e- e- exhibit wave properties EVIDENCE: DIFFRACTION PATTERNS VISIBLE LIGHT ELECTRONS

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**B. Quantum Mechanics Heisenberg Uncertainty Principle**

Impossible to know both the velocity and position of an electron at the same time

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**B. Quantum Mechanics Schrödinger Wave Equation (1926)**

finite # of solutions quantized energy levels defines probability of finding an e-

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**Radial Distribution Curve**

B. Quantum Mechanics Orbital (“electron cloud”) Region in space where there is 90% probability of finding an e- Orbital Radial Distribution Curve

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**C. Quantum Numbers Four Quantum Numbers:**

Specify the “address” of each electron in an atom UPPER LEVEL

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**C. Quantum Numbers 1. Principal Quantum Number ( n )**

Main energy level occupied the e- Size of the orbital n2 = # of orbitals in the energy level

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**C. Quantum Numbers f d s p 2. Angular Momentum Quantum # ( l )**

Energy sublevel Shape of the orbital f d s p

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**C. Quantum Numbers n = # of sublevels per level**

n2 = # of orbitals per level Sublevel sets: 1 s, 3 p, 5 d, 7 f

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**C. Quantum Numbers 3. Magnetic Quantum Number ( ml )**

Orientation of orbital around the nucleus Specifies the exact orbital within each sublevel

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C. Quantum Numbers px py pz

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**C. Quantum Numbers 2s 2px 2py 2pz**

Orbitals combine to form a spherical shape. 2s 2pz 2py 2px

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**C. Quantum Numbers 4. Spin Quantum Number ( ms )**

Electron spin +½ or -½ An orbital can hold 2 electrons that spin in opposite directions.

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**C. Quantum Numbers Pauli Exclusion Principle**

No two electrons in an atom can have the same 4 quantum numbers. Each e- has a unique “address”: 1. Principal # 2. Ang. Mom. # 3. Magnetic # 4. Spin # energy level sublevel (s,p,d,f) orientation electron

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Feeling overwhelmed? Read Section 4-2!

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