I. Waves & Particles(p. 91 - 94)
Ch. 4 - Electrons in Atoms
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. Waves
Agreater
amplitude
(intensity)
greater frequency
(color)
crest
origin
trough
A
B. EM Spectrum
LOW
ENERGY
HIGH
ENERGY
B. EM Spectrum
LOW
ENERGY
HIGH
ENERGY
R O Y G. B I V
red orange yellow green blue indigo violet
B. EM Spectrum
Frequency & wavelength are inversely proportional
c = c: speed of light (3.00 108 m/s): wavelength (m, nm, etc.): frequency (Hz)
B. EM Spectrum
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
EX: Find the frequency of a photon with a wavelength of 434 nm.
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)
vs.
Classical Theory Quantum Theory
C. Quantum Theory
Einstein (1905)
Observed - photoelectric effect
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
E: energy (J, joules)h: Planck’s constant (6.6262 10-34 J·s): frequency (Hz)
E = h
The energy of a photon is proportional to its frequency.
C. Quantum Theory
GIVEN:
E = ? = 4.57 1014 Hzh = 6.6262 10-34 J·s
WORK:
E = h
E = (6.6262 10-34 J·s)(4.57 1014 Hz)
E = 3.03 10-19 J
EX: Find the energy of a red photon with a frequency of 4.57 1014 Hz.
II. Bohr Model of the Atom(p. 94 - 97)
Ch. 4 - Electrons in Atoms
A. Line-Emission Spectrum
ground state
excited state
ENERGY IN PHOTON OUT
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
1
23
456 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
C. Other Elements
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
A. Electrons as Waves
Louis de Broglie (1924)
Applied wave-particle theory to e-
e- exhibit wave properties
EVIDENCE: DIFFRACTION PATTERNS
ELECTRONSVISIBLE LIGHT
B. Quantum Mechanics
Heisenberg Uncertainty Principle
Impossible to know both the velocity and position of an electron at the same time
B. Quantum Mechanics
σ3/2 Zπ
11s 0
eΨ a
Schrödinger Wave Equation (1926)
finite # of solutions quantized energy levels
defines probability of finding an e-
B. Quantum Mechanics
Radial Distribution CurveOrbital
Orbital (“electron cloud”)
Region in space where there is 90% probability of finding an e-
C. Quantum Numbers
UPPER LEVEL
Four Quantum Numbers:
Specify the “address” of each electron in an atom
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
s p d f
2. Angular Momentum Quantum # ( l )
Energy sublevel
Shape of the orbital
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 orbitalwithin each sublevel
C. Quantum Numbers
px py pz
C. Quantum Numbers
Orbitals combine to form a spherical shape.
2s
2pz2py
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
1. Principal # 2. Ang. Mom. # 3. Magnetic # 4. Spin #
energy level
sublevel (s,p,d,f)
orientation
electron
Pauli Exclusion Principle
No two electrons in an atom can have the same 4 quantum numbers.
Each e- has a unique “address”:
Feeling overwhelmed?
Read Section 4-2!
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