# I. Waves & Particles (p. 91 - 94) Ch. 4 - Electrons in Atoms I. Waves & Particles (p. 91 - 94)

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I. Waves & Particles (p. 91 - 94)
Ch. 4 - Electrons in Atoms I. Waves & Particles (p )

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

 A A  A. Waves crest greater amplitude (intensity) origin trough
greater frequency (color)

B. EM Spectrum HIGH ENERGY LOW ENERGY

B. EM Spectrum HIGH ENERGY LOW ENERGY R O Y G. B I V red orange yellow
green blue indigo violet

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)

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

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

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

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

“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

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)

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

II. Bohr Model of the Atom (p. 94 - 97)
Ch. 4 - Electrons in Atoms II. Bohr Model of the Atom (p )

A. Line-Emission Spectrum
excited state ENERGY IN PHOTON OUT ground state

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

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

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

C. Other Elements Examples: Iron
Now, we can calculate for all elements and their electrons – next section 

III. Quantum Model of the Atom (p. 98 - 104)
Ch. 4 - Electrons in Atoms III. Quantum Model of the Atom (p )

A. Electrons as Waves Louis de Broglie (1924)
Applied wave-particle theory to e- e- exhibit wave properties EVIDENCE: DIFFRACTION PATTERNS VISIBLE LIGHT ELECTRONS

B. Quantum Mechanics Heisenberg Uncertainty Principle
Impossible to know both the velocity and position of an electron at the same time

B. Quantum Mechanics Schrödinger Wave Equation (1926)
finite # of solutions  quantized energy levels defines probability of finding an e-

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

C. Quantum Numbers Four Quantum Numbers:
Specify the “address” of each electron in an atom UPPER LEVEL

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

C. Quantum Numbers f d s p 2. Angular Momentum Quantum # ( l )
Energy sublevel Shape of the orbital f d s p

C. Quantum Numbers n = # of sublevels per level
n2 = # of orbitals per level Sublevel sets: 1 s, 3 p, 5 d, 7 f

C. Quantum Numbers 3. Magnetic Quantum Number ( ml )
Orientation of orbital around the nucleus Specifies the exact orbital within each sublevel

C. Quantum Numbers px py pz

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

C. Quantum Numbers 4. Spin Quantum Number ( ms )
Electron spin  +½ or -½ An orbital can hold 2 electrons that spin in opposite directions.

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