1. Quantum Model of the Atom
Electrons in Atoms
Quantum Model of the Atom

2. Schrödinger Wave Equation (1926)
defines probability of finding an e-

3. Orbital (“electron cloud”)
Region in space where there is 90% probability of finding an e-
Orbital

4. Orbital
A 3-dimensional space around a nucleus in which electrons are most likely to be found
Shape represents electron density (not a path the electron follows)
Each orbital can hold up to 2 electrons

5. Quantum Numbers Four Quantum Numbers:
Specify the “address” of each electron in an atom
UPPER LEVEL

6. Describes the arrangement and space occupied by electrons in atoms
Quantum Mechanics
Describes the arrangement and space occupied by electrons in atoms

7. Quantum Mechanics
Describes the arrangement of electrons in atoms in terms of:
Main or principal energy levels or shells (n)
(Oklahoma City)
Energy sublevels or subshells
(Britton Road)
Orbitals
(house # 200)
Electron spin
(room # 4)

8. Quantum Numbers 1. Principal Quantum Number ( n )
Energy level or shell
Size of the orbital

9. Principal Quantum Number (n)
Contain electrons that are
Close in energy
Similar distance from nucleus
Have values of n = 1, 2, 3, 4, 5, 6…..

10. Energy Levels (Shells)
The first shell (n = 1) is lowest in energy, 2nd level next and so on 1<2<3<4
Low energy electrons are closest to the nucleus

11. Quantum Numbers f d s p 2. Angular Momentum Quantum # ( l )
Energy sublevel or subshell
Shape of the orbital f d s p

12. Subshells Energy sublevels within energy level
All electrons in a subshell have the same energy
Designated s, p, d, f ..
Sublevel energy: s<p<d<f

13. n = # of energy sublevels per energy level
Main
Energy
Levels Sublevels
n=4 4s, 4p, 4d, 4f
n=3 3s, 3p, 3d
n=2 2s, 2p
n=1 1s

14. Sublevels in n = 1,2, 3
n = 3 3d 3p 3s
n = 2 2p 2s
n = 1 1s

15. Quantum Numbers 3. Magnetic Quantum Number ( ml )
Orientation of orbital
Specifies the exact orbital within each sublevel

16. s subshell contains 1 s orbital

17. p subshell contains 3 p orbitalspx pz py

18. d subshell contains 5 d orbitals

19. f subshell contains 7 f orbitals

20. Quantum Numbers n = # of energy sublevels per energy level
n2 = # of orbitals per energy level
Sublevel sets: 1 s, 3 p, 5 d, 7 f

21. Number of Electrons Each orbital can hold up to 2 electrons
Maximum number of electrons in any energy level = 2n2
n =1 2(1)2 = 2
n =2 2(2)2 = 8
n =3 2(3)2 = 18

22. Electrons Allowed All 2s electrons have the same energy
All 2p electrons have the same energy which is slightly higher than the energy of the 2s electrons
s sublevel 2 electrons
p sublevel 6 electrons
d sublevel 10 electrons
f sublevel 14 electrons

23. Quantum Numbers 2s 2px 2py 2pz
Orbitals combine to form a spherical shape. 2s
2pz
2py
2px

24. Quantum Numbers 4. Spin Quantum Number ( ms ) Electron spin  +½ or -½
An orbital can hold 2 electrons that spin in opposite directions

25. Quantum Numbers Pauli Exclusion Principle
No two electrons in an atom can have the same 4 quantum numbers.
Each e- has a unique “address”
1. Principal # 
2. Ang. Mom. # 
3. Magnetic # 
4. Spin # 
energy level
sublevel (s,p,d,f)
orbital
electron spin

26. Pauli Exclusion Principle
Each orbital can hold TWO electrons with opposite spins.

27. A. Number of electrons in a p orbital
1e or 2e
B. Number of orbitals in a p subshell 3
C. Number of orbitals in 4d subshell 5
D. Maximum number of electrons in a 3d subshell
10e

28. ORBITAL DIAGRAM Shows the electrons in each orbital
Circles, boxes, or lines are used to represent orbitals
Arrows or half-arrows represent electrons

29. l = s subshell
1 p
2 d
3 f

30. s orbital ml

31. p orbital Ml

32. d orbital Ml

33. f orbital Ml

34. electron spin
ms +1/ /2

35. 7s 6p 5d Orbital diagram n l ml ms 7 +1/2 6 1 -1 5 2 -2 -1/2 -1 0 +1
+1/2 6 1 -1 5 2 -2
-1/2 7s 6p 5d

36. 4f 4d 5f Orbital diagram n l ml ms 4 3 -3 +1/2 2 -1 -1/2 5 4d 5f

37. Feeling overwhelmed?
Read Section 4-2!