Chapter 8. * Interference (constructive and destructive) * Diffraction and Refraction

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1 Chapter 8 (1) Electromagnetic Radiation (EMR) (a) Wavelength (λ), frequency (ν), speed (c), Amplitude (A) c = λν (c = x 10 8 m s 1 ) (b) Properties of light (EMR): * Interference (constructive and destructive) * Diffraction and Refraction (c) The Electromagnetic Spectrum: * Regions: γ rays, x rays, UV, Visible, IR, microwave, radio (d) Interaction of EMR with Matter: * Microwave (rotational), IR (vibrational), Visible (electronic)

2 (2) Observations Classical Physics Couldn t Solve I: Atomic Line Spectra It was discovered that gas phase elements emitted a discrete set of wavelengths after white light was shined on them, when continuous light was expected. These Line Spectra are unique to each element and act as fingerprints. Johan Balmer in 1885 empirically derived an equation to solve for the Balmer Series of H (the visible emission lines). ν = x s n 2 Where n is an integer greater than 2, giving discrete behavior to electron energy levels. Balmer could not explain why this behavior existed!

3 II: Blackbody Radiation Blackbody radiation is that from a heated body (like hot metal). Max Planck in 1900 proposed that the energy of a system is discrete, not continuous (as thought at the time), to explain the emission data. The difference in two energy levels in a system was a quantum. A quantum to energy was like an atom to matter. Planck s equation: E = hν = hc (h = Planck s constant = x J s) λ What is the energy (in J photon 1 and kj mol 1 ) of UV light (λ = 285 nm)? E = hc = x J s x 10 8 m 1 1 x 10 9 nm = x J λ photon s 285 nm 1 m photon E = x J x photon 1 kj = kj 420. kj photon 1 mol 1000 J mol mol

4 III: The Photoelectric Effect When metal was irradiated by light, electrons were found to be ejected, but only at a minimum frequency (threshold frequency). As the light frequency increased, the kinetic energy (E K ) of the ejected electrons also increased. As the light intensity increased, the number of electrons ejected increased, but not the energy. Albert Einstein explained this in 1905 using Planck s quantum concept. Einstein proposed the particle of light or the photon. E K = hν Φ where: E K = kinetic energy of ejected electron hν = energy of absorbed photon of light Φ = binding energy (or Work Function) of the electron Note: This was Einstein s ONLY Nobel Prize!!!

5 (3) Bohr Model and Electron Transitions * Neils Bohr in 1913 explained the Atomic Line Spectrum for hydrogen using quantum concepts applied to electron energies. * Electrons moved in quantized orbits (n) with set distances from the nucleus and energies: tiny nucleus

6 Radius: r n = n 2 a o (a o = 53 pm, and n is an integer) Orbit Energy: E n = R H (R H = Rydberg constant = x J) n 2 E E Excitation: Absorption of energy (+) with n i < n f. Relaxation: Release of energy ( ) with n i > n f. The energy of the e transition, E must equal the photon energy (E = hν)

7 Energetics of Electron Transitions: E = x J 1 1 Note: E photon = E n i 2 n f 2 emitted Example: What photon wavelength is required to promote an electron in the n = 1 orbit of a H atom to the n = 5 orbit? E = x J 1 1 = x J 1 1 = x J n i 2 n f E photon = E = hc so: λ λ = hc Ε λ = x J s x 10 8 m 1 1 x 10 9 nm s x J 1 m λ = nm -----> nm (the UV region)

8 (4) Models of Electrons in Atoms I: The Bohr Model: This Planetary Model by Neils Bohr in 1913 assumes electrons move in set orbits like planets around the sun. This is the most common, but least accurate model. II: The Wave Mechanical Model: This mathematical model was derived by Erwin Schrodinger in 1927 and is the most accurate model, but least understandable. It treats electrons as standing matter waves (as proposed by Louis de Broglie), and uses Heisenberg s Uncertainty Principle. Schrodinger s Equation (HΨ= EΨ) solves for electron location in terms of orbitals (3 D regions of space about the atom). III: The Electron Shell Model This model places orbitals of similar energies into shells which relate to Periods (rows) on the Periodic Table. This is a blending of the 1 st two models.

9 (5) Quantum Numbers and Orbitals Principle Quantum #, n: orbital size/energy * all integers >0 (relates to electron shell or level) Angular Momentum Quantum #, l: orbital shape * all integers from 0 to n 1 (relates to subshell) * l = 0 (s); l = 1 (p); l = 2 (d) and l = 3 (f subshell) Magnetic Quantum #, m l : orbital orientation * all integers from l to +l (# orbitals in subshell) Electron Spin Quantum #, m s : up or down * Only two values: +½ or ½ l = 1 (subshell) Notation: 3p x n = 3 (shell) m l = 1 (orbital)

10 (6) Electron Configurations * Shows distribution of electrons among orbitals. * Follow these three rules: (i) Aufbau Principle: Fill lowest energy subshells 1 st. (1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p, etc.) * Based on electron shielding and orbital penetration. (ii) Pauli Exclusion Principle: No two electrons can have the same 4 quantum # s (2 e s/orbital max). (iii) Hund s Rule: For degenerate orbitals in a subshell, keep electrons separated until they must be paired.

11 Example Electron Configuration Problem For the element Zinc with 30 electrons: (a) Expanded spdf notation (almost never used.big pain!): 1s 2 2s 2 2p x2 2p y2 2p z2 3s 2 3p x2 3p y2 3p z2 4s 2 3d xy2 3d xz2 3d yz2 3d z22 3d 2 x2 y2 (b) Condensed spdf notation (most common): 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 2 Valence e s (highest n subshell) (c) Noble Gas Core notation ( short cut!): [Ar] 4s 2 3d 10 (d) Orbital Box Diagram (my favorite!): Forms a +2 cation 1s 2s 2p 3s 3p 4s 3d Diamagnetic (all e s paired)