2. 6.3 Q UANTUM N UMBERS, O RBITALS, AND P ROBABILITY P ATTERNS Chemistry Ms. Pollock 2013 - 2014

3. Introduction ▪ Schrodinger’s wave equation gave correct description for electron behavior in almost every case ▪ Few scientists able to describe electron behavior during bonding or reactions – best understood by considering electrons to be particles ▪ Schrodinger’s equations used by Max Born to show probability of finding electron at point in space for which equation was solved

4. Introduction

5. Probability Patterns ▪ Dots represent position of electron at different points in time ▪ Electron spending more time near nucleus than anywhere else ▪ Boundary of atom placed at 90% of probability

6. Probability Patterns ▪ No actual boundary in atom ▪ Simple for first electron in atom ▪ More complicated atoms = more complicated probability plots

7. Probability Patterns

8. The Principal Quantum Number ▪ Quantum numbers solutions to Schrodinger’s equation ▪ Completely describe energy of electron ▪ No two electrons same four quantum numbers – Pauli exclusion principle (Wolfgang Pauli)

9. The Principal Quantum Number ▪ Number of Sub-levels and Electrons by Principal Quantum Number ▪ Principal quantum number positive integer that indicates main energy level within atom ▪ Sub-levels within every principle quantum number ▪ Principal number equal to number of sub-levels within energy level Principal Quantum Number Number of Sub-Levels Total Number of Electrons 112 228 3318 4432

10. The Principal Quantum Number ▪ Largest known atom just over 100 electrons ▪ 7 principal energy levels in known atoms ▪ Sub-levels identified by letters s, p, d, f, g, h, i ▪ Only currently described for four energy levels

11. Orbitals ▪ Defined in quantum mechanics as area in electron cloud where probability of finding electron high ▪ Number of orbitals in energy level = square of principal quantum number

12. Orbitals Principal Energy Level (n) Number of Orbitals Present S p d f Total Number of Orbitals (n 2 ) Maximum Number of Electrons (2n 2 ) 1 112 2 1 348 3 1 3 5918 4 1 3 5 71632 Relationship between n (principal quantum number), number of orbitals, and maximum number of electrons in principal energy level

13. Orbitals ▪ Each orbital probability pattern determined by intepreting Schrodinger’s equation ▪ Each shape representative of single orbital ▪ Probability pattern result of various positions of electrons

14. Orbitals