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Quantum Numbers

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