1. Electronic Structure of Atoms
- The Quantum Mechanical Model

2. Quantum Mechanics
Schrödinger and de Broglie thought that an electron was similar to a standing wave
nodes = dots
must be a whole number of half wavelengths to avoid interference

3. Quantum Mechanics
only certain circular orbits have a circumference in which whole half wavelengths will fit
an electron must only be at certain distances from the nucleus or else there will be interference

4. Schrödinger Equation where
: wave function- describes the 3D position of the electron; each is called an orbital
: operator- set of mathematical instructions that produces the total energy of atom when applied to 
many solutions are found to equation but each includes position for each amount of energy (E)

5. Heisenberg Uncertainty Principle
we cannot know the exact position and momentum (motion) of the electron
as more is known about position, less is known about momentum
uncertainties are inversely proportional
where
∆x: uncertainty in position
∆m : uncertainty in mometum
minimum uncertainty is h/4

6. Meaning of Wave Function
the wave function itself does not have concrete meaning
the square of the wave function represents the probability of finding an electron at a certain point
easily represented as probability distribution where the deepness of color indicates the probability

7. Meaning of Wave Function
(a) electron density map
probability of finding an electron is highest at short distances from nucleus
(b) calculated probability of finding an electron at certain distances from nucleus in the 1s orbital

8. Meaning of Wave Function
(a) space around the nucleus is broken into shells
(b) when the total probability for each shell is summed
probability of finding electron is greatest near nucleus
volume of each shell increases

9. Electronic Structure of Atoms
- Quantum Numbers
- Orbital Shapes and Energies
- Electron Spin and Pauli’s Principle

10. Quantum Numbers
specify the properties of atomic orbitals and of electrons in orbitals
the first three numbers come from the Schrödinger equation and describe:
main energy level
shape
orientation
4th describes state of electron

11. 1st Quantum Number Principal Quantum Number: n
main energy level (or shell) occupied by electron
values are all positive integers (1,2,3,…)
As n increases
size of orbital is larger
electron has higher energy
the electron’s average distance from the nucleus increases

12. 1st Quantum Number
Energy

13. 2nd Quantum Number Angular Momentum Quantum Number: l
indicates the shape of the orbital (sublevel or subshell)
the number of possible shapes (or l values) for an energy level is equal to n
the possible values of l are 0 and all positive integers less than or equal to n - 1

14. 2nd Quantum Number s orbitals: 1: s spherical l value of 0
1st occur at n=1

15. 2nd Quantum Number p orbitals: 3 2px, 2py, 2pz dumbbell-shaped
l value of 1
1st occur at n=2
for n>2, shape is same but size increases

16. 2nd Quantum Number d orbitals: 5: 3dxz, 3dyz, 3dxy, 3dx2-y2, dz2
mostly cloverleaf
l value of 2
1st occur at n=3
for n>3, same shape but larger size

17. 2nd Quantum Number f orbitals: 7 types various shapes l value of 3
begin in n=4

18. 2nd Quantum Number
other shapes can exist in energy levels as long as they follow the rules
g (l=4) starts in 5 with 9 orbitals
h (l=5) starts in 6 with 11 orbitals, etc
but no known elements have electrons in them at ground state

19. 2nd Quantum Number
Level
Sublevels
Sublevels

20. 3rd Quantum Number Magnetic Quantum Number: ml
indicates the orientation of an orbital around the nucleus
has values from +l  -l
specifies the exact orbital that the electron is contained in
each orbital holds maximum of 2 electrons
total number of orbitals is equal to n2 for an energy level
number of possible ml values for a certain subshell is equal to 2l + 1

21. 3rd Quantum Number

22. Total # of Orbitals in Level
Energy Level
(n)
Sublevels in Level
# Orbitals in Sublevel
Total # of Orbitals in Level 1 s 2 4 p 3 9 d 5 16 f 7

23. 4th Quantum Number Spin Quantum Number: ms
indicates the spin state of the electron
only 2 possible directions
only 2 possible values: +½ and -½
paired electrons must
have opposite spins
maximum number of
electrons in an energy
level is 2n2