1. Quantum Mechanical Model of the Atom

2. Many scientists contributed to the development of the quantum mechanical model of the atom.
Bohr
Planck
DeBroglie
Heisenberg
Schrodinger
Pauli

3. What was already known.. Early 1900’s…believed that
Energy is quantized
Electrons have both wave and matter properties
Electrons can be at a variety of specific energy levels in an atom
Energy levels are called orbits (Bohr model)
Proposed that electron had both wave and matter properties

4. Next round of research Goal was to describe electrons in atoms
Ultimately describe for each electron:
Energy level & size of the region it occupies (n)
3-D shape of the region it occupies (l)
Orientation of the region/orbital (ml)
Spin on the electron (ms)

5. Schrodinger & deBroglie
S & deB pictured the electron bound to the atom in a standing wave

6. Schrodinger
Sch.. Proposed that electrons move around the nucleus in standing waves
Each orbit represents some whole number multiple of a wavelength
Schrodinger analyzed the hydrogen data based on the assumption that the electrons behaved as standing waves.

7. Standing Waves

8. Schrodinger Schrodinger’s equation takes into account:
The position of the electron in 3D space (its x,y,z coordinates)
Potential energy of the atom due to the attraction between electrons and protons
Kinetic energy of the electron

9. Schrodinger’s Equation!

10. Schrodinger Schrodinger’s equation has many solutions
Each solution is called a wave function (y) and is correlated to a specific amount of energy
Each wave function is more commonly called an orbital.

11. Orbitals
Each solution to Schrodinger’s equation describes a specific wave function (y) /orbital
The square of a wave function, (y)2, generates a probability distribution for an electron in that orbital
Also called an electron density map for a given orbital
(y)2 describes the shape, size, and orientation of the orbital

12. Orbitals
Orbitals are regions in space where an electron is likely to be found
90% of the time the electron is within the boundaries described by the electron density map
Can describe its energy, shape, and orientation
The exact path of an electron in a given orbital is not known!

13. Heisenberg
Heisenberg uncertainty principle states that we cannot know both the position and the momentum of an electron at the same time.
Therefore, we do not know the exact path of the electron in an orbital.

14. Orbitals
The lowest energy solution to Sch..’s equation for an electron in a hydrogen atom describes what is known as the 1s orbital.

15. Describing Orbitals
Use quantum numbers to describe orbitals. A given orbital can be described by a set of 3 quantum numbers:
Principal quantum number (n)
Angular momentum quantum number (l)
Magnetic quantum number (ml)

16. Principal Quantum Number (n)
(n) describes the size and energy of the oribital
Possible values: whole number integer
1, 2, 3, …
As “n” increases so does the size and energy of the orbital

17. Angular momentum quantum number (l)
(l) is related to the shape of the orbital
Possible values: (l) is an integer between 0 and n-1
Each (l) value is also assigned a letter designation

18. Angular momentum quantum number (l)
(l) Value
Letter Designation s 1 p 2 d 3 f

19. n
Possible
l values
Designation 1 1s 2 2s 2p 3 3s 3p 3d 4 4s 4p 4d 4f

20. Magnetic quantum number (ml)
(ml) is related to the orientation of the orbital in 3-D space
Possible values: - l to + l

21. Magnetic quantum number (ml)
Consider the p orbital…it has an l value of 1 and thus the possible ml values are -1, 0, +1
These 3 ml values correspond to the 3 possible orientations of the p orbital

22. Ml and Orbitals l ml # orbitals 0 (s) 1 1 (p) -1, 0, 1 3 2 (d)1
1 (p)
-1, 0, 1 3
2 (d)
-2, -1, 0, 1, 2 5
3 (f)
-3, -2, -1, 0, 1, 2, 3 7

24. Quantum Number Summary
See page 256 and board.
A set of 3 quantum numbers describes a specific orbital
Energy and size - n
Shape - l
Orientation – ml

25. 4th Quantum Number!
A 4th quantum number was added to describe the spin on a given electron.
Called the electron spin quantum number - ms
Possible values: +1/2 and -1/2

26. More on electron spin.
Each orbital can hold a maximum of 2 electrons of opposite spin.
Pauli exclusion principle states that no two electrons in an atom can have the same set of 4 quantum numbers

27. Summary Three quantum numbers describe a specific orbital
Energy and size, shape, and orientation
Four quantum numbers describe a specific electron in an atom

28. 7.9 Polyelectronic atoms
The Schrodinger model was based on H and works in principle for atoms with more than one electron.
The shapes and possible orientations of the hydrogen based orbitals holds true for polyelectronic atoms.
However, the size and energy of the orbitals in polyelectronic atoms differ from those calculated for hydrogen.

29. Polyelectronic Atoms
In general, find that in a given principal quantum number (n)
S is lower energy than p, which is lower energy than d…..
s < p < d < f
Already know that 1s < 2s < 3s… and 2p < 3p < 4p…. (in terms of size and energy)

30. 7.11 The Aufbau Principle Putting electrons in to orbitals…
Aufbau means “building up” in German
Electrons always enter the lowest energy orbital with room

31. Hund’s Rule
The orbitals of a given sublevel (e.g. p, or d, or f) are degenerate (of the same energy).
The lowest energy state occurs with the maximum number of unpaired electrons.
Meaning…..electrons enter an empty orbital of a given sublevel before pairing up.

32. Goals To be able to write for any atom:
Electron configuration
Box/energy diagram
Lewis dot symbol
State the quantum numbers for each electron in an atom.
To relate the electron configuration of an atom to its location on the periodic table and its properties.

33. Goals Elaborated
Electron configuration – shows the number of electrons in each sublevel
Format: 1s22s22p4 or [He] 2s22p4
Box/energy diagram – shows electrons as arrows and each orbital as a box. Electrons of opposite spin are indicated by up and down arrows.
Format:

34. Periodic Table and Electron Configurations

35. 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s…

36. Goals Elaborated
Lewis Dot Symbol – shows valence electrons as dots around the symbol for the atom
Maximum of 2 electrons per side of the symbol
Valence electrons are all of the electrons in the highest occupied principle quantum level (n)
Format:

37. The fun part - practice! Representative elements – IA – 8A
Ions formed by above
Transition metals
Iron
Ion formation
Exceptions
Cr – expect ___ electrons in 3d
Actually…..
Cu – expect ___ electrons in 3d

38. CH 7: Atomic Structure and Periodicity
Sections

39. Periodic Trends Models explain observed behavior.
The better the model the fewer the exceptions
Consider computer weather models vs. kinetic molecular theory

40. Periodic Trends
The quantum mechanical model of the atom explains many trends in the properties observed for the elements.
Trends in physical properties
Atomic radius
Size of the ion vs. the “parent” atom
Trends in reactivity:
Charge on the ion formed
Ease of removing or adding an electron to an atom

41. Atomic Radius Measuring/defining atomic radius
Metals: atomic radius is half the distance between nuclei in a solid
Nonmetals; atomic radius is half the distance between the nuclei of atoms in a diatomic molecule Cu H H

42. Atomic radius trends (pg 276)
Atomic radius increases down a group
Valence electrons are in higher (larger) principal quantum levels with increased shielding.
H 1s1
Li …..2s1
Na …… s1
K ………………..4s1

43. Atomic radius trends
Atomic radius decreases across a period of representative elements
Valence shell (PEL) remains the same across a period, same shielding across the period……however…
The # protons increases across a period
The increased nuclear charge “pulls” shells closer to the nucleus

44. Atomic Radius Consider the 2nd period…filling n = 2 Li Be B C N O F Ne
 decreasing atomic radius

45. Atomic radius
Atomic radius remains ~same across a row of transition metals
Why?

46. Ionization Energy
Ionization Energy – energy needed to remove the highest energy electron from an atom in its gaseous state.
See page 272/273, IE > 0
Na(g)  Na+ (g) e IE1 = 495 kJ/mole

47. IE Trends
First IE (IE1 ) becomes less endothermic (less +) down a group
See table 7.5 on page 272
Why?
As you go down a group, the electron being removed is farther from the nucleus and shielded by more core electrons from the attractive forces of the nucleus.
Therefore, it’s easier to remove.

48. IE Trends In general, first IE (IE1 )increases across a period.
See figure 7.31 on page 273
Why?
Atoms become smaller across a period and the # core electrons (shielding) remains the same while nuclear charge increases.
Electron to be removed is held more tightly to the nucleus across a period.

49. Exceptions to IE Trends
A dip in IE1 is observed for elements in group 3A and 6A.
3A elements are all ns2p1
Hypothesized that the s2 electrons shield the first p electron
6A elements are all ns2p4
Hypothesized that the first pairing of p electrons increases repulsions and thus this electron is easier to remove.

50. Trends in Successive IE
IE increases as additional electrons are removed from a given element
see table 7.5 on page 272
Na(g)  Na+ (g) e IE1 = 495 kJ/mole
Na+ (g)  ____ e IE2 = kJ/mol

51. Trends in Successive IE
IE jumps when the first core electron is removed.
Why?
Na(g)  Na+ (g) e IE1 = 495 kJ/mole (val. e)
Na+ (g)  ____ e IE2 = kj/mol (core e)

52. Electron Affinity
EA – energy change associated with the addition of an electron to a gaseous atom.
In this text, EA < 0 (convention varies)
See page 275
X (g) + e  X-(g)

53. EA Trends MANY EXCEPTIONS!
In general, EA becomes less negative down a group.
In general, EA becomes more negative across a period.

54. Periodic Trends Atomic radius Ionization Energy (>0)
First IE and successive IE
3A and 6A exceptions
Electron Affinity (<0)