Bellringer:  = ? = c   = 7.5  10-3 m = 2.998  108 m/s Find the frequency in Hertz of microwave radiation with a wavelength of 7.5  10-3 m. GIVEN:  = ?  = 7.5  10-3 m c = 2.998  108 m/s WORK: = c  = 2.998  108 m/s 7.5  10-3 m  = 4.0 x 1010 s-1  = 4.0 x 1010 Hz Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem 1

Find the energy of a red photon with a frequency of 4.57  1014 Hz. GIVEN: E = ?  = 4.57  1014 Hz h = 6.626  10-34 J· s WORK: E = h E = (6.6262  10-34 J· s) (4.57  1014 Hz) E = 3.03  10-19 J Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem 2

Example problem using BOTH Equations… Find the energy of a photon with a wavelength of 1.0 x 10-3 nm. c = λv E = hv GIVEN: h = 6.626 x 10-34 J s c = 3.00 x 108 m/s  = ?  = 1.0 x 10-3 nm = ???? m WORK:  = c   = 3.00  108 m/s 1.0 x 10-12 m  = 3.0 x 1020 s-1 E = (6.626 x 10-34 J s)(3.0 x 1020s-1) E = 1.99 x 10-13 J

Copyright © 2006 Pearson Benjamin Cummings. All rights reserved. 4

Chemist Humor Question: Why does hamburger have lower energy than steak? Answer: Because it’s in the ground state. 5

The Quantum Mechanical model It is based on the energy and possible location of an electron. how likely it is to find an electron is described in terms of probability. (ie. Propeller blades) Based on work done by Shrodinger…

Atomic Orbitals The energy levels of electrons are labeled by principal quantum numbers (n) Each energy sublevel corresponds to an orbital of a different shape, which describes where the electron is likely to be found.

Atomic Orbitals

Electron Probability vs. Distance Quantum Mechanics Orbital (“electron cloud”) Region in space where there is 90% probability of finding an electron 90% probability of finding the electron Orbital Electron Probability vs. Distance 40 30 Electron Probability (%) 20 10 50 100 150 200 250 Distance from the Nucleus (pm) Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

The Shapes of the s, p, and d Orbitals Sketch these in your notes s orbital p orbitals • p orbitals – Orbitals with l = 1 are p orbitals and contain a nodal plane that includes the nucleus, giving rise to a “dumbbell shape.” – The size and complexity of the p orbitals for any atom increase as the principal quantum number n increases. • d orbitals – Orbitals with l = 2 are d orbitals and have more complex shapes with at least two nodal surfaces. • f orbitals – Orbitals with l = 3 are f orbitals, and each f orbital has three nodal surfaces, so their shapes are complex. d orbitals

Please write this in your notes.

(a) 1s orbital (b) 2s and 2p orbitals Electron Orbitals: Electron orbitals Equivalent Electron shells (a) 1s orbital (b) 2s and 2p orbitals c) Neon Ne-10: 1s, 2s and 2p 1999, Addison, Wesley, Longman, Inc.

Copyright © 2006 Pearson Benjamin Cummings. All rights reserved.

1s Orbital Sphere around the nucleus The one tells you that the electron is in the orbital closest to the nucleus S tells you about the shape

2s Orbital Similar to 1s except the electron is most likely in the region farther from the nucleus

p Orbitals At the first energy level there is only the 1s orbital, after the second energy level there are 2p orbitals Look like dumbbells In the three directions

Four Energy Sub-Levels Energy Level Sub-level # of Orbitals # electrons s Sphere 1 2 p Dumbbell 3 6 d 4-Lobed 5 10 f 6-8 Lobed 7 14

Remember…. MAX NUMBER OF ELECTRONS IN AN ENERGY LEVEL MAX # OF ELECTRONS 1 2 8 3 18 4 32 5 50