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Quantum Mechanical Model of the Atom

Quantum Mechanical Model of the Atom. Many scientists contributed to the development of the quantum mechanical model of the atom. Bohr Planck DeBroglie Heisenberg Schrodinger Pauli. What was already known. Early 1900’s…believed that Energy is quantized

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Quantum Mechanical Model of the Atom

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  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)

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

  18. 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

  19. Ml and Orbitals

  20. 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

  21. 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

  22. 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

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

  24. 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.

  25. 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)

  26. 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

  27. 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.

  28. 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.

  29. 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:

  30. Periodic Table and Electron Configurations

  31. 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s…

  32. 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:

  33. 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…..

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

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

  36. 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

  37. 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

  38. 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

  39. 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

  40. 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

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

  42. 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

  43. 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.

  44. 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.

  45. 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.

  46. 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

  47. 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)

  48. 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)

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

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