The quantum mechanical model of the atom

Chemistry

1. The Quantum Mechanical Model of the Atom

2. What is the chance of finding an electron in the nucleus?

3. QUANTUM MECHANICAL MODEL OF ATOM STATES THAT: Electrons are NOT in circular orbits around nucleus. Electrons are in a 3-D region around the nucleus called atomic orbitals. The atomic orbital describes the probable location of the electron.

4. Where does this model come from? A quick history. Louis de Broglie: Electrons behave with wave and particle properties at the same time .

5. Werner Heisenberg: It is impossible to know both the position and velocity of an electron simultaneously. * Heisenberg's Uncertainty Principle

6. Erwin Schrodinger : Refined the wave-particle theory proposed by de Broglie. Developed an equation that treated an electron like a wave and predicted the probable location of an electron around the nucleus called the atomic orbital.

7. The quantum mechanical model of the atom treats an electron like a wave.

8. The Quantum Mechanical Model The quantum model determines the allowed energies an electron can have and how likely it is to find the electron in various locations around the nucleus. 5.1

9. The Quantum Mechanical Model The probability of finding an electron within a certain volume of space surrounding the nucleus can be represented as a fuzzy cloud. The cloud is more dense where the probability of finding the electron is high.

10. Atomic Orbitals (fuzzy cloud) = An atomic orbital is often thought of as a region of space in which there is a high probability of finding an electron . 5.1

11. Quantum Mechanics Radial Distribution Curve Orbital Orbital (“electron cloud”) Region in space where there is 90% probability of finding an e -

12. .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 13 Scanning Tunneling Microscope Electron Clouds

13. ATOMIC ORBITALS 14

14. Smaller atom Smaller atom— Fewer electrons take up less space. Larger atom— More electrons take up more space. s-orbitals are spherically shaped.

15. p-orbitals are “dumbell” shaped. z-axis

16. p-orbitals are “dumbell” shaped. x-axis

17. p-orbitals are “dumbell” shaped. y-axis

18. p-orbitals together x, y, & z axes.

19. Shells and Orbitals and Atomic Structure Shells of an atom contain a number of stacked orbitals 1 2 3 4 s p d f

20. 1 st and 2 nd level s-orbitals and the p-orbitals all together.

21. Atomic Orbitals 5.1 Different atomic orbitals are denoted by letters. The s orbitals are spherical, and p orbitals are dumbbell-shaped. Four of the five d orbitals have the same shape but different orientations in space.

22. .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 24 1s 3s 2s 2px 3pz 3d 2py 2pz 3py 3px

23. Atomic Orbitals The numbers and kinds of atomic orbitals depend on the energy sublevel. 5.1 Energy Level, n # of sublevels Letter of sublevels # of orbitals per sublevel # of electrons in each orbital Total electrons in energy level

24. Atomic Orbitals The numbers and kinds of atomic orbitals depend on the energy sublevel. 5.1 Energy Level, n # of sublevels Letter of sublevels # of orbitals per sublevel # of electrons in each orbital Total electrons in energy level 1 1 s 1 2 2 2 2 s p 1 3 2 6 8 3 3 s p d 1 3 5 2 6 10 18 4 4 s p d f 1 3 5 7 2 6 10 14 32

25. The quantum mechanical model describes the probable location of electrons in atoms by describing: -Principal energy level/Principal quantum number (n ) -Energy sublevel/ Angular momentum quantum number (l ) -Orbital (in each sublevel)/Magnetic quantum number (ml ) -Spin/Spin quantum number ( ms )

26. .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 28 The principal quantum number(n) represents the “shell number” in which an electron “resides .” n = 1, 2, 3, 4…

27. .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 29 The angular momentum quantum number ( l ) distinguishes “sub shells” within a given shell that have different shapes. Each main “shell” is subdivided into “sub shells.” Within each shell of quantum number n, there are n sub shells, each with a distinctive shape. l can have any integer value from 0 to (n - 1) The different subshells are denoted by letters. Letter s p d f g … l 0 1 2 3 4 ….

28. .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 30 The magnetic quantum number (m l ) distinguishes orbitals within a given sub-shell that have different shapes and orientations in space. Each sub shell is subdivided into “orbitals,” each capable of holding a pair of electrons. m l can have any integer value from - l to + l . Each orbital within a given sub shell has the same energy.

29. The spin quantum number ( m s ) refers to the two possible spin orientations of the electrons residing within a given orbital. Each orbital can hold only two electrons whose spins must oppose one another. The possible values of m s are +1/2 and –1/2. .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 31

30. .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 32

31. .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 33 Tell how many electrons in a given atom can have the following sets of quantum numbers: n=2 n=2, l = 1 n=2, l =1, m l = -1 n=2, l =1, m s = +1/2

32. Eight electrons Six electrons Two electrons 1 electron

33. how is it likely to find the electron in an atom by probability? .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 35

34. ASSESSMENT .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 36

35. Write “true” if the statement is correct and change the underlined word with the correct answer if the statement is false. .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 37 1. in quantum model, the nucleus is very small compared to the region where electrons are likely to be found . 2. the orientation describes the probability of finding an electron at different angles about the nucleus. 3 . there are four different kinds of p orbitals . 4 . in the quantum model of the atom, electrons do not accelerate in their orbits around the nucleus as they do in the Bohr model . 5. two electrons within the same orbital my have the same spin.

36. Identification .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 38 The spin quantum number describes what? The fourth quantum number is called what? The magnetic quantum number describes what? Scientist accept that an electron spends how much time inside an atomic orbital? Each orbital holds how many electrons? 6 – 7. probabilities are used because of Heseinberg’s Uncertainty Principle. This principle states that the ___ and ___ of an electron can be measured but not simultaneously.

37. Identification .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 39 Why are electrons assigned quantum numbers? Electrons are assigned how many quantum numbers? The first quantum number is called what? The principal quantum number describes what? Which principal quantum number describes the ground state? The second quantu m number is called what? The azimuthal quantum number describes what?

38. Identification .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 40 15. The third quantum number is called what? 16. The magnetic quantum number describes what? 17. It is a region in space in which the electrons are most likely to be found. 18. What is the shape of the p orbitals?

39. .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 41 Direction: tell what type of orbital (such as 1s, 3d, and so on) is described by each of the following sets of quantum numbers: 1. n=2, l=0 2. n=4, l=2 3. n=3, l=1 4. n=4, l=0 5. n=5, l=3

40. .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 42 Direction: tell how many electrons there can be in a given atom, with the following sets of quantum numbers. n=4 n=3, l =2 n=4, l=2,m 1 = -1,0 n=8 (3 pts .) n=3, l =2, m1=1, ms =+ 1/2

41. .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 43 Direction: tell how many orbitals there are in each of the following sets. s d g i p

42. Answer .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 44 Part A: True Orbital shape Three True Opposite Part B: Electron spin Spin Orbital orientation 90% 2 6 – 7. position, velocity 8. To find the probable location of electrons 9. 4 10. Principal 11. Energy level

43. Answer .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 45 Part B: 12. 1 13. Angular momentum/azimuthal quantum number 14. Orbital shape 15. Magnetic quantum number 16. Orbital orientation 17. Atomic orbital 18. Dumbbell shape

44. Answer .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 46 Part C 2s 4d 3p 4s 5f Part D 32 e- 10 e- 4 e- 1 e- 128 e- Part E 1 5 9 13 3

45. ASSIGNMENT .Copyright © Houghton Mifflin Company.All rights reserved. Presentation of Lecture Outlines, 7 – 47 Define the following: 1. electronic configuration 2. aufbau principle 3. hund’s rule