Wave Nature of Light

1. Wave Nature of Light • Rutherford’s model of the atom could not explain chemical behavior • Bohr and others described the arrangement of electrons around the nucleus • These arrangements could account for differences between the elements • Bohr’s model was based on spectroscopic evidence

2. Electromagnetic Radiation • Light can be described as though it is a wave Parts of a wave • Amplitude and wavelength Crest Trough

3. Wave Stuff • Amplitude: Vertical distance from crest to midline (brightness/intensity) • Wavelength: Horizontal distance from crest to crest (meters) (color) • Velocity: Rate at which wave travels (3.00x108 m/s in a vacuum) (constant) • Frequency: # waves that pass a given point per unit time (waves/sec, cps, hertz, s-1)

7. Electromagnetic Spectrum

9. High frequency Low frequency

11. Wave Math • Velocity = wavelength x frequency • Velocity = c Wavelength = l Frequency = n • c = ln • Since c is constant, l and n are inversely related

12. Example problems • Find the frequency of purple light (wavelength 455 nm). • Solution: c = ln, or n = c/l Wavelength must be in meters, since c is in m/s: 455 nm = 4.55x10-7 m n = (3.00x108 m/s)/(4.55x10-7 m) = 6.59x1014s-1

13. Example #2 • Find the wavelength of red light with a frequency of 4.56x1014s-1. • c = ln or l = c/n • l = (3.00x108 m/s)/(4.56x1014s-1) = 6.58x10-7m (658 nm)

14. Particle Nature of Light • Light also acts as a particle: proposed by Newton • Max Planck and glowing blackbodies: energy is quantized • Smallest energy unit available is a quantum • Energy of quanta depends on the frequency of the energy: E = hn

15. Particle Nature of Light • h is Planck’s constant: 6.626x10-34Js • Energy is directly proportional to frequency • Energy is inversely proportional to wavelength: E = hn andn = c/l so E = hc/l

16. Light Particle Sample Problem • Find the energy of a microwave photon having a wavelength of 3.42x10-2m. • Solution: E = hc/l = (6.626x10-34Js)(3.00x108m/s)/3.42x10-2m = 5.81x10-24J

17. Photoelectric Effect • Certain metals will eject electrons when exposed to light • Number of electrons ejected depends only on the intensity of light • No electrons ejected by light below certain frequency

18. Photoelectric Effect • Could not be explained by wave model of light • Einstein explained effect using quantum theory of light • He won the Nobel Prize for his work (not for relativity)

19. Photoelectric Effect Simulator

20. Atomic Emission Spectra • When elements are zapped with energy, they give off light • Light is first shone through a slit • When light is shone through a prism, colors are separated • Only some of the colors appear as fine lines against a dark background

22. Emission spectra of common fluorescent bulbs

23. Emission Spectrum Setup

24. Absorption Spectra • In absorption spectra, light is shone through cold gas or liquid • Light then goes through a slit and prism or grating • Resulting spectrum is continuous except for dark lines

25. Absorption Spectrum

26. Absorption Spectrum of Chlorophyll Liquids tend to have less distinct absorption spectra

27. Gas Absorption Spectra

28. Absorption Spectrum Setup

29. Spectra Types

30. Bohr Model of the Atom • Bohr wanted to explain the presence of sharp lines in the hydrogen spectrum • He proposed that hydrogen’s electron could only have certain distinct energies • These energies were integral multiples of some minimum energy • The energy levels correspond to differently sized orbits

31. Bohr’s Atom • Spectral lines were due to electrons jumping from one level to another. • Incoming energy promotes an electron to a higher energy level • When the electron returns to the lower level it releases energy

32. Quantum Numbers • Bohr assignedthe energy levels numbers • The Principle Quantum Number (n) represents the main energy level • n can only have non-zero integral values • n = 1, 2, 3, ...

33. Why quantum numbers? • Louis de Broglie: Wave-particle duality • As a wave: E = hc/l • As a particle: E = mc2 • Combined: hc/l = mc2 l= hc/mc2 = h/mc • For objects moving slower than light, replace c with v (velocity): l = h/mv

34. Particle wavelength problems • Every particle has a wavelength • The larger the particle, the shorter the wavelength • Example: Calculate the wavelength of an electron moving at 0.80c (mass = 9.109×10-31 kilograms). • Solution: l = h/mv = 6.626x10-34Js/[(9.109×10-31kg)(0.80)(3.00x108m/s)] = 3.0x10-12m (smaller than an atom, bigger than a nucleus)

35. Particle wavelength problems • Find the wavelength of a baseball (145g) thrown toward home plate at 95.0 mph (42.5 m/s) • Solution: l = h/mv = 6.626x10-34Js/[(0.145kg)(42.5m/s)] = 1.08x10-34m (much smaller than a nucleus)

36. Back to quantum numbers • Only certain orbits are allowed because they are the only ones in which an integral number of wavelengths can “fit”. • “In-between” orbitals would require a fractional number of wavelengths. “I think it is safe to say that no one understands quantum mechanics.”Physicist Richard P. Feynman

37. Heisenberg Uncertainty Principle • It is impossible to know both the position and momentum of an electron simultaneously • Electrons are both particles and waves • It’s in their nature to be indeterminate • Can be thought of as being “smeared out” over a region of space • Indeterminacy is related to Planck’s constant

38. More Energy Levels • The fine lines in emission spectra are actually made up of several even finer lines • Each energy level has sublevels • Each sublevel has a shape • Each sublevel has one or more orbitals • Each orbital holds two electrons • How do we sort all this out?

39. Using Quantum Numbers! • Four quantum numbers are needed in Schrödinger’s equation to describe the probability function of an electron • n = principle quantum number = 1, 2, 3, ... Main energy level – determines size of orbital • l = azimuthal quantum number = 0, 1, ... n-1 Sublevel – determines orbital shape

40. Well-used quantum numbers • s: l = 0 (first two columns of PT) p: l = 1 (last six columns of PT) d: l = 2 (middle ten columns of PT) f: l = 3 (bottom two rows of PT) • m = magnetic quantum number = - l to +l Specifies orbital – determines orientation • s = spin quantum number = ±½ Specifies spin

41. Orbital shapes • s orbital: spherical • Every energy level has an s orbital: 1s, 2s, etc. • Higher level s orbitals are lobed • Nodes are areas of minimum electron density • One node is added for each level • s sublevel: one orbital, two electrons

42. p orbital • p orbitals are dumbbell shaped • p sublevel (l = 1) consists of three orbitals: px py pz (six electrons) • Three p orbitals are orthogonal to each other • Only present after first main energy level (n>1)

43. d orbital • d orbital is cloverleaf-shaped • Five orbitals, ten electrons make up d sublevel • Only available when n>2

44. f orbitals • Complicated shape • Seven orbitals, fourteen electrons • Only available when n>3

47. Allowed quantum number combinations • Pauli exclusion principle: no two electrons can have the same set of four quantum numbers • Aufbau principle:electrons fill the lowest energy state available first • Lower numbers mean lower energy (n and l) • Various m and s states are degenerate (of equal energy)

48. n l m s 1 0 0 +½ 1 0 0 -½ 1s sublevel – 2e- 2 0 0 +½ 2 0 0 -½ 2s sublevel – 2e- n l m s 2 1 -1 +½ 2 1 0 +½ 2 1 1 +½ 2 1 -1 -½ 2 1 0 -½ 2 1 1 -½ 2p sublevel – 6e- Allowed Quantum Number Combinations

49. 3s and 3p are similar to 2s and 2p 3d sublevel: n l m s 3 2 -2 +½ 3 2 -2 -½ 3 2 -1 +½ 3 2 -1 -½ n l m s 3 2 0 +½ 3 2 0 -½ 3 2 1 +½ 3 2 1 -½ 3 2 2 +½ 3 2 2 -½ 3d sublevel - 10e- Allowed Quantum Number Combinations

50. Electron configurations • Electron configurations show the location of every electron in the atom • Electrons follow three rules: Pauli exclusion principle, Aufbau principle, Hund’s rule • Each orbital is represented by a box and a symbol, and each electron by an arrow.