# Quantum Theory of the Atom (HL #2)(4).doc

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## Solid State Engineering

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Quantum Theory of the Atom Newton’s laws of motion DO NOT apply to particles of very small mass(like eˉ ’s)  very small particles obey a new set of laws. Quantum Mechanicsstudies these laws. Bohr’s Theory – Bohr’s model only described the energy level of electrons in the atom.Correct: ã Electrons may only exist at allowed E-LevelsIncorrect: ã An eˉ’s position and motion can be specified exactly at a giventime ã Electrons move in an orbit at a fixed radius, changing only whenthe eˉ jumps E-levelsProblem: ã Agrees with experimental evidence only with the case of H atomsor any other 1 eˉ atom (He + ) Erwin Schrodinger (1924) - described an atomic model withelectrons in three dimensions. This model required three coordinates(three quantum numbers) to describe where electrons could be found. ã Developed wave mechanics (a type of math) to describe motionthat has both particle and wave properties ã Wave mechanics involves the use of wave functions. These aremathematical expressions describing a 3-D space around anucleus where there is a high probability of finding an eˉ  these regions are called orbitals  eˉ may be found here 95% of the time Quantum theory provides 4 quantum numbers which describeelectrons in atoms:1.Principle Quantum Number ( n ) Identifies the energy level upon which an electron exists. 2.Secondary Quantum Number ( l  ) Identifies the type (shape) of the orbital in which the electronexists. 3.Magnetic Quantum Number ( m l  )  Identifies the orientation of the orbital in which the electronexists. 4.Spin Quantum Number (m s ) Identifies the direction the electron is spinning on its own axis. In keeping with Bohr’s theory that electrons can exist only on specific energy levels,quantum theory takes this theory and expands each energy level (described by Bohr) intoseveral energy sub-levels. NOTE: Energy levels may also be referred to as shells, and sublevels as sub-shells. Energy Level Diagram for a Many-eˉ AtomFilling Orbitals with Electrons 3 RULES: Aufbau Principle ã When assigning eˉ ’s to orbitals, the eˉ’s must be placed in the lowest E-level for which there is space available. Pauli Exclusion Principle ã An orbital may have 0, 1 or 2 eˉ ‘s occupying it Hund’s Rule ã Electrons at the same E-level will not pair-up in an orbital until all the orbitals atthat sub-level are at least half full  the distribution of eˉ’s among the various orbitals of an atom is called it’s electronconfiguration E-level  Aluminum: 13 Al :1s 2 2s 2 2p 6 3s 2 3p 1 # of eˉ’s occupying the subshelltype of orbitalSulfur: 16 S :1s 2 2s 2 2p 6 3s 2 3p 4 Magnesium: 12 Mg1s 2 2s 2 2p 6 3s 2  Note: Noble Gases… 10  Ne1s 2 2s 2 2p 6  Short cut: Use the noble gas to represent the “core” electron configuration 16 S :1s 2 2s 2 2p 6 3s 2 3p 410  Ne :1s 2 2s 2 2p 6 S becomes….. 16 S :[Ne] 3s 2 3p 4 NOTE: The 4s orbital is lower energy than the 3d orbitals and there for is filledfirst. There is strong evidence for this in the similarities in the chemistry of elements likesodium (1s 2 2s 2 2p 6 3s 1 ) and potassium (1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 )The outer electron governs their properties and that electron is in the same sort of orbitalin both of the elements. That wouldn't be true if the outer electron in potassium was 3d 1 . EXCEPTIONS – Cr (   4s 1 3d 5 ) and Cu (   4s 1 3d 10 )Some configurations appear to “break” the rules  elements in the same group aschromium and elements in the same group as copper.Cu has 29 electrons. Following the rules would lead to a configuration of :1s 2 2s 2 2p 6 3s 2 3p 6 3d 9 4s 2 ....the actual configuration is 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 1 … what happened ?The unusual configurations of chromium and copper may be explained by consideringenergetic stability. The 4s and 3d subshells are very similar in energy and therefore it iseasy to promote electrons from the 4s into the 3d orbitals. In chromium the 4s 1 3d 5 structure is adopted because the repulsion between two pairedelectrons in the 4s orbital is more than the energy difference between the 4s and 3dsubshells. It is thus more stable to have unpaired electrons in the higher energy 3d orbitalthan paired electrons in the lower energy 4s orbital.  In copper , the  full  3d subshell is actually lower in energy than the 4s subshell. The 3dorbitals are thus filled before the 4s orbital. Thus copper adopts a 4s 1 3d 10 configuration. Greater stability is conferred to an atom with either a full sublevel or half full sublevel,than to an atom that has empty orbital(s) in its valence subshell. In all ions of d-block elements, the 4s electrons are always removed first. 3d electrons areonly removed after all 4s electrons have been removed.Exceptions – Cr and Cu Orbitals, Electrons, And The Quantum Numbers The  Principle Quantum Number  (n) – identifies the energy level possessed by an eˉ** For every value of n, there are n types of orbitals and n 2 actual orbitals **Possible Types of Orbitals – these types are described by the secondary quantum number s orbitals  spherical shape p orbitals  peanut shaped ã There are 3 different kinds of p-orbitals; differentonly because they are oriented along differentaxes…d orbitals  complicated shapes
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