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Chapter 7: Atomic Structure and Periodicity 7.1 Electromagnetic Radiation Comes from the sun and the stars Electromagnetic Radiation – radiant energy that exhibits wavelike behavior and travels through space at the speed of light (3.00 X 108 m/s) Wavelength – length of a wave (from crest to crest, trough to trough, or other corresponding points) Frequency – number of waves (cycles) per second that pass a given point in space - Page 139 “R O Y G Frequency Increases Wavelength Longer B I V” Formula! v = c/λ OR c = vλ λ (wavelength) is in meters v (frequency) is in sec-1 or hertz (hz) c (speed of light) is in m/s and is a constant Practice problem Given: v = 4.54 X 1014 s-1 λ=? 4.54 X 1014 s-1 = 3.00 X 108 m/s / λ λ = 6.61 X 10-7 m 7.2 The Nature of Matter Δ E = hv Δ E = change in energy for a system (in J/photon) h = Planck’s constant 6.626 X 10-34 J*sec v = frequency Δ E = hv = hc / λ Examples 1) What is the wavelength of blue light with a frequency of 8.3 x 1015 hz? 2) What is the frequency of red light with a wavelength of 4.2 x 10-5 m? 3) What is the energy of a photon of each of the above? 1) = c = 3 x 108 m/s = 3.6 x 10-8 m 8.3 x 1015hz 2) = c = 3 x 108 m/s = 7.1 x 1012 hz 4.2 x 10-5 m 3-1) E = h = (6.626 x 10-34 J·s)(8.3 x 1015hz) = 5.4 x 10-18 J 3-2) E = h = (6.626 x 10-34 J·s)(7.1 x 1012hz) = 4.7 x 10-21 J 2 ways to excite an electron 1. Heat 2. Electricity An electron jumps up an energy level, falls back down releasing a packet of energy (a photon) with a λ = 589.0 nm Find change in energy for this photon & per mol of photons. v=c/λ = 3.00 X 108 m/s / 5.89 X 10-7 m = 5.09 X 1014 hz Δ E = hv = (6.63x10-34Jsec)(5.09x1014 hz) = 3.37x10-19 J J/mol = 3.37 X 10-19 J | 6.02 X 1023 photons 1 photon | 1 mol Answer = 203.17 kJ/mol de Broglie’s Equation and the Dual Nature of Light E = mc2 & E = hν & E = hc/λ m = h/(λv) OR λ = h/(mv) v = velocity Dual nature of light: sometimes electromagnetic radiation exhibits wave properties, sometimes it shows characteristics of particle matter 7.3 Atomic Spectrum of Hydrogen Continuous spectrum – contains all the wavelengths over which the spectrum is continuous Line spectrum – contains certain specific wavelengths which are characteristics of the substances emitting those wavelengths There are specific energy levels among which an e- in a H atom can jump quantized 7.4 The Bohr Model E = -2.178 X 10-18 J [Z2] [n2] E = energy in J Z = nuclear charge/number of protons n = state energy level (farther away from nucleus = higher number) Lowest energy state: n=1 Highest energy state: n=∞ where it’s ionized Sample Problem Calculate E corresponding to n=3 in H atom. E = -2.178 X 10-18 J [12/32] = -2.42 X 10-19 J When you move there is a change in energy. Δ E = Efinal – Einitial Δ E = -2.178 X 10-18 J [z2/nf2 – z2/ni2] If going from 13, ni=1 and nf=3 ΔE=(-2.178 X 10-18J [12/32]) – (-2.178 X 10-18J [12/12]) ΔE = -2.178 X 10-18J [12/32 – 12/12 ] = 1.9 x 10-18 J 7.5 Quantum Mechanical Model of the Atom Electron is assumed to behave as a standing wave. Wave function of an electron represents the allowed coordinates where an electron may reside in the atom orbital Heisenberg’s uncertainty principle Can only know position or velocity As one is known more precisely, the other is known less precisely Δ x Δ (mv) ≥ h/4π Δ x = uncertainty in the particle’s position Δ (mv) = uncertainty in particle’s momentum h = Planck’s constant Smallest possible uncertainty = h/4π (h/4π)2 = probability distribution Radius of the sphere encloses 90% of the total electron probability Rules to Remember for Orbital Notation Aufbau Principle – electrons are added one at a time to the lowest energy level available until all electrons are accounted for Pauli Exclusion Principle – an orbital can hold a max of two electrons which have opposite spins Hund’s Rule: electrons occupy equal energy orbitals so that the max number of unpaired electrons results Orbital Shapes S orbital P orbitals D orbitals The Diagonal Rule An Example of Orbital Notation What is the orbital notation for nitrogen? N = 1s2 2s2 2p3 Draw the orbital diagram for nitrogen. 7.6 Quantum Numbers Name Designation Property of the orbital Possible range of values Principle quantum # Angular momentum # N Energy level l Shape (sublevel) 0 < integers < 7 0 n-1 Magnetic quantum # Ml Position of orbital Spin S Spin Integers from –3 to 3 +1/2 or –1/2 Orbital notation chart 7.12 Periodic Trends in Atomic Properties 1. Ionization energy – energy needed to remove an electron 1. Metals – low, nonmetals – high 2. Across a period IE increases (because nuclear force increases with a greater number of protons) 3. Going down a group IE decreases (because of the added energy levels) Successive IE: 1. After one e- is taken off, it is harder to take off the next e2. Shielding effect/penetration effect 3. When all e- are taken away, take away core e- 2. 3. Electron affinity – the opposite of IE – change in energy when adding an electron 1. Across a period EA increases 2. Going down a group EA decreases Atomic radius – distance from nucleus to outermost electron 1. Across a period AR decreases Zeff 2. Going down a group AR increases A metal ion is + and smaller than the original atom A nonmetal ion is – and larger than the original atom EXCEPTIONS TO GEN RULES? 7.13 Properties of a Group: Alkali Metals As you go down the group: – – – – – IE decreases AR increases Density increases Reactivity increases Melting point and boiling point decrease 7.13 Properties of a Group: Halogens Nonmetals As you go down the group: – – – – – IE decreases AR increases Density increases Reactivity decreases Melting point and boiling point increase