1. November 13, 2007 1.Please staple both labs together and place in basket. a.Spectra lab 1 st, Flame test 2 nd 2.Then review by completing the following: 1.Name the 4 orbitals 2.Draw the 4 orbital shapes 3.Define an orbital 3.Today in class, we will continue to describe electrons using the quantum mechanical model of the atom. Homework:Important Dates: LEQ 11/29- Ch5 Test Read Ch5 11/26- E.C. due (pg 130) Study Guide

2. Quantum Mechanical Model From Bohr to present

3. 6.5 Quantum Mechanical Atom Electrons are outside the nucleus Electrons can’t be just anywhere – occupy regions of space Knowing the location and energy of an electron ( a wave) is limited in accuracy – Heisenberg Uncertainty Principle Orbitals – Regions in space where the electron is likely to be found – Regions are described mathematically as waves

4. Schrodinger Wave Equation In 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e - Wave function (  ) describes: 1. energy of e - with a given  2. probability of finding e - in a volume of space exactly approximate nl m Schrodinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems. Solutions to wave functions require integer quantum numbers n, l and m l. 7.5

5. Solutions to wave functions require integer quantum numbers n, l and m l Quantum numbers are much like an address, a place where the electrons are likely to be found  fn(n, l, m l, m s ) Each distinct set of 3 quantum numbers corresponds to an orbital

6. QUANTUM NUMBERS The shape, size, and energy of each orbital is a function of 3 quantum numbers which describe the location of an electron within an atom or ion n (principal) ---> energy level l (angular momentum) ---> shape of orbital m l (magnetic) ---> designates a particular suborbital The fourth quantum number is not derived from the wave function s(spin) ---> spin of the electron (clockwise or counterclockwise: ½ or – ½) s (spin) ---> spin of the electron (clockwise or counterclockwise: ½ or – ½)

7. Schrodinger Wave Equation  fn(n, l, m l, m s ) principal quantum number n n = 1, 2, 3, 4, …. n=1 n=2 n=3 7.6 distance of e - from the nucleus

8. e - density (1s orbital) falls off rapidly as distance from nucleus increases Where 90% of the e - density is found for the 1s orbital 7.6

9.  = fn(n, l, m l, m s ) angular momentum quantum number l for a given value of n, l = 0, 1, 2, 3, … n-1 n = 1, l = 0 n = 2, l = 0 or 1 n = 3, l = 0, 1, or 2 Shape of the “volume” of space that the e - occupies l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital Schrodinger Wave Equation 7.6

10. Types of Orbitals ( l ) s orbital p orbital d orbital l = 0l = 2l = 1

11. l = 0 (s orbitals) l = 1 (p orbitals) 7.6

12. p Orbitals this is a p sublevel with 3 orbitals These are called x, y, and z this is a p sublevel with 3 orbitals These are called x, y, and z There is a PLANAR NODE thru the nucleus, which is an area of zero probability of finding an electron 3p y orbital

13. p Orbitals The three p orbitals lie 90 o apart in space The three p orbitals lie 90 o apart in space

14. l = 2 (d sublevel with 5 orbitals) 7.6 d Orbitals

15. f Orbitals For l = 3 f sublevel with 7 orbitals f sublevel with 7 orbitals

16.  = fn(n, l, m l, m s ) magnetic quantum number m l for a given value of l m l = -l, …., 0, …. +l orientation of the orbital in space if l = 1 (p orbital), m l = -1, 0, or 1 if l = 2 (d orbital), m l = -2, -1, 0, 1, or 2 Schrodinger Wave Equation 7.6

17. m l = -1m l = 0m l = 1 m l = -2m l = -1m l = 0m l = 1m l = 2 7.6

18.  = fn(n, l, m l, m s ) spin quantum number m s m s = +½ or -½ Schrodinger Wave Equation m s = -½m s = +½ 7.6

19. Existence (and energy) of an electron in an atom is described by its unique wave function . Pauli exclusion principle - no two electrons in an atom can have the same four quantum numbers. Schrodinger Wave Equation  = fn(n, l, m l, m s ) Each seat is uniquely identified (E1, R12, S8) Each seat can hold only one individual at a time 7.6

20. Schrodinger Wave Equation  = fn(n, l, m l, m s ) Shell – electrons with the same value of n Subshell – electrons with the same values of n and l Orbital – electrons with the same values of n, l, and m l How many electrons can an orbital hold? If n, l, and m l are fixed, then m s = ½ or - ½  = (n, l, m l, ½ ) or  = (n, l, m l, - ½ ) An orbital can hold 2 electrons 7.6

21. Summary An electron has a 100% probability of being somewhere ORBITAL: The region in space where an electron is likely to be found The usual pictures of orbitals show the regions where the electron will be found 90% of the time http://www.falstad.com/qmatom/

22. 7.6 Summary

23. How many 2p orbitals are there in an atom? 2p n=2 l = 1 If l = 1, then m l = -1, 0, or +1 3 orbitals How many electrons can be placed in the 3d subshell? 3d n=3 l = 2 If l = 2, then m l = -2, -1, 0, +1, or +2 5 orbitals which can hold a total of 10 e - 7.6

24. Compare and contrast the Bohr and quantum mechanical models. Summary