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

2. 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

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

4. B. EM Spectrum
HIGH
ENERGY
LOW
ENERGY

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

6. 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)

7. 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

8. 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

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

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

11. “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

12. 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)

13. 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

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

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

16. 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

17. 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

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

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

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

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

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

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

24. 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

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

26. 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

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

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

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

30. C. Quantum Numbers px py pz

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

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

33. 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

34. Feeling overwhelmed?
Read Section 4-2!