Quantum Mechanical Model of the Atom

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 • Standing vs. traveling waves • See page 253

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. 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

8. 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.

9. 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

10. 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!

11. 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.

12. Orbitals • The lowest energy solution to Sch..’s equation for an electron in a hydrogen atom describes what is known as the 1s orbital. • See pages 306/307

13. 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)

14. 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

15. 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

16. Angular momentum quantum number (l)

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

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

20. Ml and Orbitals

21. 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

22. 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

23. 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

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

25. 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.

26. 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)

27. 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

28. 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.

29. 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.

30. 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:

31. Periodic Table and Electron Configurations

32. 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s…

33. 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:

34. 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 • Actually…..

35. CH 7: Atomic Structure and Periodicity Sections 7.10 -7.13

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

37. 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

38. 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

39. 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 ……......3s1 • K ………………..4s1

40. 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

41. Atomic Radius Consider the 2nd period…filling n = 2 Li Be B C N O F Ne # p 3 4 5 6 7 8 9 10  decreasing atomic radius

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

43. 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

44. 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.

45. 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.

46. 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.

47. 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 = 4560 kJ/mol

48. 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 = 4560 kj/mol (core e)

49. 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)

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