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# Quantum Numbers

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### Quantum Numbers

1. 1. QUANTUM NUMBERS CAPE Unit 1
2. 2. SCHROEGINDER WAVE EQUATION <ul><li>Wave-particle duality of electrons </li></ul><ul><li>The position of an electron is described in terms of probability density </li></ul><ul><li>Orbital </li></ul><ul><ul><li>region (volume of space around the nucleus) where there is a high probability of finding an electron of a given energy </li></ul></ul><ul><li>Atomic model </li></ul><ul><ul><li>3-D </li></ul></ul><ul><ul><li>3 quantum numbers (principal, angular, magnetic) </li></ul></ul>
3. 3. QUANTUM NUMBERS <ul><li>Describe the size, shape and orientation in space of the orbitals </li></ul><ul><li>Principal Quantum Number (n) </li></ul><ul><ul><li>Energy level of the electron </li></ul></ul><ul><ul><li>Maximum number of electrons at n level is 2n 2 </li></ul></ul>Energy Level No. of electrons n = 1 2 n = 2 8 n = 3 18 n = 4 32
4. 4. QUANTUM NUMBERS <ul><li>Angular Quantum Number (l) </li></ul><ul><ul><li>Sublevels in n & Shape of the orbitals </li></ul></ul><ul><ul><li>s, p, d, f </li></ul></ul><ul><ul><li>Each energy level has n sublevels </li></ul></ul>Energy Level No. of Sublevels Sublevels n = 1 1 1s n = 2 2 2s, 2p n = 3 3 3s, 3p, 3d n = 4 4 4s, 4p, 4d, 4f
5. 5. QUANTUM NUMBERS <ul><li>Magnetic Quantum Number </li></ul><ul><ul><li>Number of orbitals within a sublevel </li></ul></ul>Sublevel No. of Orbitals Max. Electrons s 1 2 p 3 6 d 5 10 f 7 14
6. 6. QUANTUM NUMBERS <ul><li>Fourth Quantum Number???????? </li></ul><ul><li>Spin Quantum Number </li></ul><ul><ul><li>Each electron has a magnetic field and a spin associated with that electron </li></ul></ul><ul><li>Pauli Exclusion Principle </li></ul><ul><ul><li>No more than two (2) electrons can occupy an orbital </li></ul></ul><ul><ul><li>Two (2) electrons in the same orbital must have opposite spins </li></ul></ul><ul><ul><li>NO TWO ELECTRONS IN AN ATOM HAVE THE SAME FOUR QUANTUM NUMBERS </li></ul></ul>
7. 7. SHAPES OF ORBITALS CAPE Unit 1 Dr. Z. Clarke
8. 8. SHAPES OF ORBITALS <ul><li>s orbital </li></ul><ul><ul><li>Each energy level has one s orbital </li></ul></ul><ul><ul><li>Maximum number of electrons = 2 </li></ul></ul><ul><ul><li>Spherical </li></ul></ul><ul><ul><li>1s and 2s orbitals are similar in shape however electron density is closer to the nucleus for the 1s orbital </li></ul></ul>
9. 9. SHAPES OF ORBITALS <ul><li>p orbitals </li></ul><ul><ul><li>Each energy level has three (3) degenerate p orbitals </li></ul></ul><ul><ul><ul><li>i.e. 3 orbitals of EQUAL ENERGY </li></ul></ul></ul><ul><ul><li>Dumb-bell shape </li></ul></ul>
10. 10. ELECTRONIC CONFIGURATION CAPE Unit 1 Dr. Z. Clarke
11. 11. ELECTRONIC CONFIGURATIONS <ul><li>s orbitals have slightly lower energy than the p orbitals at the same energy level i.e. 2s < 2p </li></ul><ul><li>s orbital will ALWAYS fill before corresponding p orbitals </li></ul><ul><li>s orbital have the lowest energy then p, d, f </li></ul><ul><ul><li>s < p < d < f </li></ul></ul>
12. 12. ELECTRONIC CONFIGURATIONS <ul><li>Anomaly </li></ul><ul><ul><li>Irregularity in the position of the 3d and 4s orbitals </li></ul></ul><ul><ul><li>3d has slightly more energy than 4s </li></ul></ul><ul><ul><li>4s fills first then 3d orbitals followed by 4p orbitals </li></ul></ul>
13. 13. ELECTRONIC CONFIGURATIONS <ul><li>Describes the arrangement of electrons in the orbitals of an atom </li></ul><ul><li>How are electronic configurations worked out? </li></ul><ul><ul><li>Electrons are added one at a time, starting with the lowest energy orbital ( Aufbau Principle ) </li></ul></ul><ul><ul><li>No more than two electrons can occupy an orbital ( Pauli Exclusion Principle ) </li></ul></ul><ul><ul><li>Electrons fill degenerate orbitals one at a time with parallel spin before a second electron is added with opposite spin ( Hund’s Rule ) </li></ul></ul>
14. 14. ELECTRONIC CONFIGURATIONS <ul><li>How do we write electronic configurations? </li></ul><ul><ul><li>Principal Quantum number (1, 2, 3 etc) </li></ul></ul><ul><ul><li>Symbol for the orbital (s, p, d, f) </li></ul></ul><ul><ul><li>Superscript that shows the number of electrons in the sublevel </li></ul></ul><ul><ul><ul><ul><ul><li>number of electrons in orbital </li></ul></ul></ul></ul></ul><ul><ul><li>energy level 1s 2 </li></ul></ul><ul><ul><li>type of orbital </li></ul></ul>
15. 15. ELECTRONIC CONFIGURATIONS Atomic Number Symbol Electronic Configuration 1 H 1s 1 2 He 1s 2 or [He] 3 Li [He] 2s 1 4 Be [He] 2s 2 5 B [He] 2s 2 2p 1 6 C [He] 2s 2 2p 2 7 N [He] 2s 2 2p 3 8 O [He] 2s 2 2p 4 9 F [He] 2s 2 2p 5 10 Ne [He] 2s 2 2p 6 or [Ne]
16. 16. ELECTRONIC CONFIGURATIONS Atomic Number Symbol Electronic Configuration 11 Na [Ne] 3s 1 12 Mg [Ne] 3s 2 13 Al [Ne] 3s 2 3p 1 14 Si [Ne] 3s 2 3p 2 15 P [Ne] 3s 2 3p 3 16 S [Ne] 3s 2 3p 4 17 Cl [Ne] 3s 2 3p 5 18 Ar [Ne] 3s 2 3p 6 or [Ar] 19 K [Ar] 4s 1 20 Ca [Ar] 4s 2
17. 17. ELECTRONIC CONFIGURATIONS Atomic Number Symbol Electronic Configuration 21 Sc [Ar] 4s 2 3d 1 22 Ti [Ar] 4s 2 3d 2 23 V [Ar] 4s 2 3d 3 24 Cr [Ar] 4s 1 3d 5 25 Mn [Ar] 4s 2 3d 5 26 Fe [Ar] 4s 2 3d 6 27 Co [Ar] 4s 2 3d 7 28 Ni [Ar] 4s 2 3d 8 29 Cu [Ar] 4s 1 3d 10 30 Zn [Ar] 4s 2 3d 10
18. 18. ELECTRONIC CONFIGURATIONS – ABBREVIATED <ul><li>He, Ne and Ar have electronic configurations with filled shells of orbitals </li></ul><ul><ul><li>Abbreviated electronic configurations </li></ul></ul><ul><ul><li>He = 1s 2 or [He] </li></ul></ul><ul><ul><li>Ne = 1s 2 2s 2 2p 6 or [Ne] </li></ul></ul><ul><ul><li>Ar = 1s 2 2s 2 2p 6 3s 2 3p 6 or [Ar] </li></ul></ul>
19. 19. ELECTRONIC CONFIGURATIONS - SPECIAL <ul><li>After 3p orbitals are filled, 4s orbital is filled before the 3d orbital </li></ul><ul><ul><li>4s orbital is at a slightly lower energy than the 3d </li></ul></ul><ul><ul><li>K is [Ar] 4s 1 </li></ul></ul><ul><ul><li>Ca is [Ar] 4s 2 </li></ul></ul><ul><ul><li>Sc is [Ar] 4s 2 3d 1 </li></ul></ul>
20. 20. ELECTRONIC CONFIGURATIONS - SPECIAL <ul><li>After Sc, the 3d orbitals are filled </li></ul><ul><li>Irregularity is seen in the electronic configuration of Cr and Cu </li></ul><ul><ul><li>Cr is [Ar] 4s 1 3d 5 </li></ul></ul><ul><ul><li>Cu is [Ar] 4s 1 3d 10 </li></ul></ul>
21. 21. ELECTRONIC CONFIGURATIONS - SPECIAL <ul><li>One electron has been transferred from the 4s orbital to the 3d orbital </li></ul><ul><ul><li>Half-filled and filled sublevels of 3d orbitals decreases </li></ul></ul><ul><ul><ul><li>Energy </li></ul></ul></ul><ul><ul><li>Spin pairing of the 4s orbital increases </li></ul></ul><ul><ul><ul><li>Energy </li></ul></ul></ul>
22. 22. IONIZATION ENERGY CAPE Unit 1 Dr. Z. Clarke
23. 23. IONIZATION ENERGY <ul><li>1 st Ionization Energy of an element </li></ul><ul><ul><li>Energy needed to convert 1 mole of its gaseous atoms into gaseous ions with a single positive charge </li></ul></ul><ul><li>M (g) M + (g) + e - </li></ul><ul><li>Energy required to remove each successive electron is called the 2 nd , 3 rd , 4 th , etc. ionization energy </li></ul><ul><li>Ionization energies are positive because it requires energy to remove an electron </li></ul>
24. 24. IONIZATION ENERGY – INFLUENCING FACTORS <ul><li>Magnitude of ionization energy </li></ul><ul><ul><li>how strongly the electron to be lost is attracted to the nucleus </li></ul></ul><ul><li>Factors that influence ionization energy </li></ul><ul><ul><li>Atomic Radii </li></ul></ul><ul><ul><li>Nuclear Charge </li></ul></ul><ul><ul><li>Shielding (Screening) </li></ul></ul>
25. 25. IONIZATION ENERGY – ATOMIC RADII <ul><li>Atomic Radii </li></ul><ul><ul><li>Distance of the outer electron is from the nucleus </li></ul></ul><ul><ul><li>As distance increases ( ), nuclear attraction for the outer electron decreases ( ), ionization energy decreases( ) </li></ul></ul>
26. 26. IONIZATION ENERGY – ATOMIC RADII <ul><li>Successive Ionization Energies of Sodium (Na) </li></ul>Ionization Energy Energy Orbital Electron Lost From 1 st 496 3s 2 nd 4562 2p 3 rd 6912 2p 4 th 9543 2p 5 th 13353 2p 6 th 16610 2p 7 th 20114 2p
27. 27. IONIZATION ENERGY – NUCLEAR CHARGE <ul><li>Nuclear Charge </li></ul><ul><ul><li>As nuclear charge increases, attraction of the nucleus for the outer electron increases, ionization energy increases </li></ul></ul><ul><ul><li>Atomic Radii and Electron Shielding (Screening) can outweigh the effect of nuclear charge </li></ul></ul><ul><ul><ul><li>Cs has a larger nuclear charge than Na, loses electron more readily than Na </li></ul></ul></ul>
28. 28. IONIZATION ENERGY – SHIELDING (SCREENING) <ul><li>Screening Effect of Inner Electrons </li></ul><ul><ul><li>Electrons experience repulsion by other electrons </li></ul></ul><ul><ul><li>Outer electrons are shielded from the attraction of the nucleus by repelling effect of inner electrons </li></ul></ul><ul><ul><li>Screening effect of electrons in lower energy levels is more effective than electrons in higher energy levels </li></ul></ul>
29. 29. IONIZATION ENERGY – SHIELDING (SCREENING) <ul><li>Screening Effect of Inner Electrons </li></ul><ul><ul><li>Electrons in same energy level has negligible screening effect on each other </li></ul></ul><ul><ul><li>As screening effect becomes more effective, ionization energy decreases </li></ul></ul>