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Quantum Numbers Chemistry March 3, 2011 Bohr Model of the Atom • Last time we saw Hydrogen… • Atom had a small, positive nucleus with electrons orbiting around it. • Hydrogen model with quantized energy levels. • BUT….Bohr’s model of quantized energy levels only worked for Hydrogen, no other atoms. Wave Mechanical Model • Erwin Schrodinger • No EXACT location for the electron--”wave- like” behavior • Instead, Schrodinger’s mathematical equation was able to predict the probabilities of finding the electron at given points in space around the nucleus. • High probability of finding an electron in a 3-D region called an orbital. Energy Levels Principal Sublevels • An atom has discrete energy level available energy levels called: 1 1s • Principal Energy Levels 2 2s2p • Each principal energy 3 3s 3p 3d level is divided into sublevels 4 4s 4p 4d 4f • Each sublevel has a specific amount of orbitals Orbitals • Describes the direction in space of the electron cloud • Each orbital can have a maximum of 2 electrons • S:1 orbital p:3 orbitals d:5 orbitals f: ? orbitals • Orbital visuals Orbitals Number of Number of Total Maximum sublevels orbitals number of number of (s,p,d,f) orbitals electrons 1 (1) 1 2 2 (1,3) 4 8 3 (1,3,5) 9 18 4 (1,3,5,7) 16 32 Quantum Numbers • Three dimensions Three quantum numbers • Principal quantum number: n= 1,2,3,… • Designates the size of the electron cloud • Orbital quantum number: l = 0,1,2,…(n-1) • Designates the shape of the orbital (sublevel) • l=0(s) l=1(p) l=2(d) l=3(f) • Magnetic quantum number: ml = 0,±1 ,±2, …,±l • Designates the possible direction in space of the electron cloud Pauli’s Exclusion Principle • Wolfgang Pauli • Scientist (physicist) from Vienna • Proposed 4 quantum numbers are needed to characterize the atomic electron • ms quantum number describes clockwise and counterclockwise rotations of electrons in an orbital • The electrons in the same orbital must have opposite spin • ms can have values of +1/2 and -1/2 (arbitrary) Pauli’s Exclusion Principle • This 4th quantum number showed that: • No two electrons in an atom can exist in the same quantum state • Each electron must have a different set of quantum numbers n, l, ml, ms. One more thing… • Hund’s rule: electrons in an orbit shall remain unpaired whenever possible. • Electrons with parallel spin are more separated in space than those that are paired off. • The farther the electrons are from one another, the lower the energy of the atom. • Less energy more stable arrangement! • That is why we fill in orbitals one electron at a time!
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