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Download “Location” of Electrons in the Quantum Mechanical Model
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“Location” of Electrons in the Quantum Mechanical Model Now…where are those electrons again? Uncertainty and Schrödinger's Wave Equations • The work of Heisenberg and Schrodinger lead us to the conclusion that the exact location of an electron can never be known • Schrodinger’s wave equations reveal areas of high “electron density” – Although we don’t know for sure, we have a good idea where we can most likely find an electron • These areas of high electron density (or “probability density” are referred to as orbitals Quantum Numbers “Electron’s Address” • Each orbital has a unique set of quantum numbers • These numbers provide the “address” for an electron – Remember – it’s not the exact location of the electron…just the most probable location • Each orbital has four (4) quantum numbers that are unique to that orbital – Each electron has its own “address” Principal Quantum Number • Symbolized by “n” • The main energy level where the electron is found – n = 1, 2, 3, … • Orbitals closer to the nucleus (lower Principal Quantum Numbers) have electrons with lower energy Energy Sublevels • Within each principal energy level, areas with greater electron density exist – Sublevels • The first sublevel in each PEL is labeled “s” – All PEL’s have an “s” sublevel (l = 0) “s” Sublevel Orbitals Energy Sublevels • The second sublevel is labeled “p” – The first PEL does not have a “p” sublevel – Each PEL from 2 on up has a “p” sublevel (l = 1) “p” Sublevel Orbitals Energy Sublevels • The third sublevel is labeled “d” – “d” sublevels don’t start until third PEL (l = 2) • The fourth sublevel is labeled “f” –l=3 “d” Sublevel Orbitals Comparison of Sublevels Angular momentum Quantum Number • Symbolized by l • Indicates the sublevel (and consequent) shape of the orbital • • • • l = 0 for s orbital l = 1 for p orbital l = 2 for d orbital l = 3 for f orbital Magnetic Quantum Number • Symbolized by ml • Each orbital contains a maximum of two electrons Magnetic Quantum Number • Indicates which orbital the electron is in, within each sublevel – Which of the “p-orbitals” (or “d” orbitals, or “f” orbitals”) does the electron occupy? – x-axis, y-axis, or z-axis? • Indicates the orientation of the orbital around the nucleus • Possible values go from –l to +l – m= -1 for the x-axis p orbital – m = 0 for the y-axis p-orbital – m = 1 for the z-axis p orbital Spin Quantum Number • Symbolized by ms • Each orbital can only hold two electrons – Pauli Exclusion Principle • Electrons have different “spin” to distinguish them – Spin Quantum Number only has two possible values – + ½ or – ½