Models of the Atom & Quantum Mechanics

1. Models of the Atom & Quantum Mechanics

2. Previous experiments-White light gives off all wavelengths of energy- all colors.

3. Previous experiments-helium gas only gives off certain colors thus the line emission spectra for helium is produced.

4. Light and Spectra • Every element emits light when its given energy • Atomic Emission Spectrum = passing the light emitted by an element through a prism

5. How Light Relates to Electron Location • Bohr observed that only certain colors were given off • Therefore the electron could only orbit at certain distances from the nucleus

6. Electromagnetic Radiation (EMR) • Electromagnetic Radiation • Energy that is a wave • Electromagnetic Spectrum • All forms of EMR

7. EMR Waves • Parts of an EM wave • Frequency -- v (measured in Hertz or Hz) • Wavelength -- λ (measured in meters or m) • Their relationship is shown in the equation • c = λv • Where c is the speed of light -- 3.00 x 108 m/s • You will need this conversion! • 1 m = 1 x 109 nm wavelength crest amplitude origin

8. Waves long wavelength l Amplitude Low frequency short wavelength l Amplitude High frequency

9. EMR & Light • The previous equation can help us solve for the type of light • But what if we want to know the energy • Max Planck • Said that energy is emitted in certain amounts • Called quantum • Found the equation • E=hv • Where E is energy in joules • h is known as Planck’s constant (6.63 x 10-34 J ∙s) • v is frequency

10. Practice • What is the frequency of green light (~4.86 x 10-7 m)? • 1) We have two equations • 2) Need to rearrange 1 of them to solve for frequency • So let’s rearrange our equation c=λv to solve for the frequency v.

11. Practice Continued • Remember sig figs • 6.17 x 1014 Hz

12. More Practice • Find the energy released by a photon with a frequency of 3.22 x 1024 Hz E = hv • h is Planck’s constant 6.63 x 10-34 J∙s • This is a simple plug and chug because all our units are correct • 2.13 x 10-9Joules

13. One little problem with Rutherford’s idea…

14. Timeline of the Models* *Let’s Recap! ?

15. The Evolution of Atomic Models • In 1913, Neils Bohr came up with a new atomic model • Protons and electrons are oppositely charged…why aren’t the e- attracted to the nucleus? • Proposes that e- are limited to circular paths around the nucleus called “orbits” • Orbits are energy levels • Each electron has a “fixed” amount of energy in an orbit and cannot fall into the nucleus

16. Bohr’s Atomic Model

17. How do electrons move between energy levels? • Think of energy levels like a ladder: • Lowest rung = lowest energy level • Person can climb ladder rung-to-rung • Electrons can “jump” energy levels, BUT only if they have enough energy to get there! • Ex  you can’t stand in the middle of a rung on a ladder

18. A recap: Summary of Bohr’s Rules • RULE 1: Electrons can orbit only at certain allowed distances from the nucleus (energy-levels). • RULE 2: An atom absorbs energy when an electron gets boosted from a low-energy orbit to a high-energy orbit. • Rule 3: Atoms radiate energy (in the form of a photon or light) when an electron falls down from a higher-energy orbit to a lower-energy orbit.

19. Schrödinger • Developed the Quantum Mechanical Model of the atom that we use today. • Electrons DO NOT move in circular pathways like Bohr theorized. We CANNOT pin point the exact location of an electron.

20. We can only predict the location of an electron. • An electron can only be found in the electron cloud surrounding the nucleus 90% of the time.

21. De Broglie Concluded that electrons can act as both waves and particles.

22. Heisenberg • Developed the Heisenberg Uncertainty Principle which states that it is impossible to know both the velocity and the location of an electron at the same time.

23. Today’s Model of the Atom Quantum Mechanical Model • Louis De Broglie • Theorized that electrons can behave like a particle AND a wave • Werner Heisenberg • Found that it is impossible to determine the location and velocity of an electron • This is because the light knocks the electrons around • Called the Heisenberg Uncertainty Principle

24. Today’s Model-Electron Cloud • Erwin Schrodinger • Used an equation that treated electrons like waves • Solutions are the “clouds” • Found that electrons exist in “orbitals” • A 3-D region around the nucleus where the electron probably is. • Today's model says electrons are not confined to fixed orbits. • They occupy volumes of space outside the nucleus.

25. Difference from Bohr • Note: An orbit in the Bohr model is a fixed circular path. An orbital is a cloud like map representing the likelihood of the position of an electron.

26. Quantum Numbers • Specify the properties of atomic orbitals and their properties • Think of a college dorm • No two electrons can have the same set of quantum numbers (THEY ARE UNIQUE)

27. Quantum Numbers & Assigning Electrons • Atom: • Rules must be followed to put electrons in there correct location. • College: • In putting students into their dorms, the college makes rules for assigning rooms: • Fill the bottom floor first (because those are the easiest to move into!) • two students per room

28. Quantum Numbers • Quantum mechanical model designates energy levels in terms of quantum numbers (n) • Assigned numbers in terms of increasing energy n = 1, 2, 3, 4…etc • Average distance from the nucleus increases as n increases When electrons are in their lowest level, they are the most stable!

29. Maximum number of electrons that can occupy a energy level = 2n2 • n = the quantum number Increasing Energy (Increasing Distance From the Nucleus) Energy level (n) 1 2 3 4 Max. # of e- 2 8 18 32 allowed Think of it as you can only fit 2 people on the first floor, 8 people on the 2nd floor, 18 on the 3rd floor, etc…

30. Energy Sublevels • Within each energy level, there are sublevels: • n = 1; 1 sublevel ‘s’ • n = 2; 2 sublevels ‘s’, and ‘p’ • n = 3; 3 sublevels ‘s’, ‘p’, and ‘d’ • n = 4; 4 sublevels ‘s’, ‘p’, ‘d’, and ‘f’ Principal energy level = principal quantum number Energy sublevel Think of it as floors (energy levels) and wings on a floor (sublevels)

31. Types of sublevel (wings on a floor) • s • Sphere • p • Dumbbell • d • Double-dumbbell • f • Complex (don’t worry about it)

32. Quantum Numbers • Principal Quantum Number • Indicates main energy level the electron is on • Angular Momentum Number • The shape of the orbital • Magnetic Quantum Number • Orientation of the orbital • Spin • Direction of spin of the electron (+1/2 or -1/2)

33. Remember • We can rotate the orbitals to add more areas for the electrons to occupy • Each orbital can hold 2 electrons • S-sublevel • Only has one orientation • Means it can only hold a max of 2 electrons • P-sublevel • Has 3 different orientations (aka orbitals, aka rooms) • Means it can hold a max of 6 electrons • D-sublevel • Has 5 different orientations • Means it can hold max of 10 electrons • F-sublevel • Has 7 different orientations • Means it can hold a max of 14 electrons

34. How do we place electrons? • Aufbau Principle • Electrons occupy the lowest energy orbital that can receive it • Pauli Exlusion Principle • No two electrons can have the same set of four quantum numbers • Hund’s Rule • Orbitals of equal energy are occupied by one electron before any are occupied by another, plus they have opposite spins

35. Electron Configurations • In the atom, electrons arrange themselves around the nucleus in the most stable way possible • Called electron configurations • Three rules that explain electron configurations: • Aufbau principle • Pauli exclusion principle • Hund’s rule

36. Electron Configurations • Aufbau Principle: • Electrons enter orbitals of lowest energy first • s is ALWAYS the lowest energy level within a principle energy level Similar to college: put kids in the rooms on the lowest floor of the dorms because they are the easiest to move into!

37. Electron Configurations • Pauli exclusion principle: • An atomic orbital may describe AT MOST two electrons • s = 1 orbital • p = 3 orbitals • d = 5 orbitals • f = 7 orbitals • Each box ( ) denotes an orbital • For an orbital to be “filled” with electrons, they must have opposite spins Similar to college: we put two students into each dorm room

38. Electron Configurations • Hund’s Rule: • “When electrons occupy orbitals of equal energy, one electron enters each orbital until all the orbitals contain one electron with parallel spins” • Example  Oxygen (8 electrons) Similar to college: fill all the rooms on the bottom level first and then start doubling students up!

39. Let’s apply the 3 rules with examples of Electron Configurations

40. Write out all the orbitals for each level through 7p. • Draw diagonal lines to show filling order. Maximum Number of e- in each orbital: s = 2 p = 6 d = 10 f = 14 7s 7p 7d 7f 6s 6p 6d 6f 5s 5p 5d 5f 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s

41. Shorthand Configuration A neon's electron configuration (1s22s22p6) B third energy level [Ne] 3s1 one electron in the s orbital C D orbital shape Na = [1s22s22p6] 3s1 electron configuration

42. Shorthand Configuration Element symbol Electron configuration Ca [Ar] 4s2 V [Ar] 4s2 3d3 F [He] 2s2 2p5 Ag [Kr] 5s2 4d9 I [Kr] 5s2 4d10 5p5 Xe [Kr] 5s2 4d10 5p6 Fe [He] 2s22p63s23p64s23d6 [Ar] 4s23d6 Sg [Rn] 7s2 5f14 6d4

43. 8 O 15.9994 2s 2p 1s Notation • Orbital Diagram O 8e- • Electron Configuration 1s22s22p4 Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

44. 16 S 32.066 Core Electrons Valence Electrons Notation • Longhand Configuration S 16e- 2p6 2s2 1s2 3s2 3p4 • Shorthand Configuration S 16e- [Ne]3s2 3p4 Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem