2. CHEMISTRY 161 Chapter 7 Quantum Theory and Electronic Structure of the Atom www.chem.hawaii.edu/Bil301/welcome.html

3. REVISION 1. light can be described as a wave (wavelength) and a particle (momentum) 2. electrons can be described as a particle (momentum) and a wave (wavelength) 3. light is emitted/absorbed from atoms/molecules in discrete quanta

4. e-e- THE BOHR ATOM QUANTUM NUMBERS n = 4 n = 3 n = 2 n = 1 absorption emission ionization energy

5. HEISENBERG’S UNCERTAINTY PRINCIPLE  x is the uncertainty in the particle’s position  p is the uncertainty in the particle’s momentum in the microscopic world you cannot determine the momentum and location of a particle simultaneously

6. THE HEISENBERG UNCERTAINTY PRINCIPLE if particle is big thenuncertainty small

7. This means we have no idea of the velocity of an electron if we try to tie it down! Alternatively if we pin down velocity we have no idea where the electron is! So for electrons we cannot know precisely where they are!

8. we cannot describe the electron as following a known path such as a circular orbit Bohr’s model is therefore fundamentally incorrect in its description of how the electron behaves. we cannot know precisely where electrons are!

9. Schroedinger (1926) H  = E 

10. The probability of finding an electron at a given location is proportional to the square of . 22 Born (1927)

11. PARTICLE IN A BOX

12. orbit of an electron at radius r (Bohr) probability of finding an electron at a radius r (Schroedinger, Born) H  = E 

13. 1. Schroedinger equation defines energy states an electron can occupy H  = E  2. square of wave function defines distribution of electrons around the nucleus high electron density - high probability of finding an electron at this location low electron density - low probability of finding an electron at this location atomic orbital wave function of an electron in an atom each wave function corresponds to defined energy of electron an orbital can be filled up with two electrons

14. 22

15. QUANTUM NUMBERS 1.principle quantum number 2. angular momentum quantum number 3. magnetic quantum number 4. spin quantum number

16. 1. principle quantum number n n = 1, 2, 3, 4, 5… hydrogen atom: n determines the energy of an atomic orbital measure of the average distance of an electron from nucleus n increases → energy increases n increases → average distance increases

17. e-e- n = 4 n = 3 n = 2 n = 1 n = 1 2 3 4 5 6 K L M N O P ‘shell’ maximum numbers of electrons in each shell 2 n 2 radial distribution maximum of electron density corresponds to Bohr radii

18. 2. angular momentum quantum number l = 0, 1, … (n-1) l = 0 1 2 3 4 5 s p d f g h define the shape of the orbital

19. sperical polar cloverleaf

20. 3. magnetic quantum number m l = -l, (-l + 1), … 0…… (+l-1) +l defines orientation of an orbital in space

21. 4. spin quantum number m s = -1/2; + 1/2

22. SUMMARY ORBITALS AND QUANTUM NUMBERS 1.principle quantum number 2. angular momentum quantum number 3. magnetic quantum number 4. spin quantum number n = 1, 2, 3, 4, 5… l = 0, 1, … (n-1) m l = -l, (-l + 1), … 0…… (+l-1) +l m s = -1/2; + 1/2

23. Homework Chapter 7, pages 263-267 problems