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Quantum Mechanics Bohr’s Model • Bohr’s model was better, but there were still wholes in it. • It didn’t do a very good job of explaining how ions formed. • Bohr was able to improve on his 1913 model, but he needed Wolfgang Pauli to really make sense of it. Pauli’s Exclusion Principle • Two objects can not be in the same place at the same time. • This is more or less what the exclusion principle says. • Stated a little more precisely, no two fermions (e.g. electrons) can have the same quantum numbers. • A set of quantum numbers is a set of numbers that can describe a quantum mechanical system. Quantum Numbers • Principle quantum number (n)—this tells which electron shell • Angular momentum quantum number (l)—this tells the type of sub-shell • Azimuthal quantum number (m)—this tells which sub-shell • Spin quantum number (s)—this tells whether the electron spins clockwise or counter-clockwise • n = 1, 2, 3… • l = n-1 (0, 1, 2…) • m = ±l (-1, 0, 1) • s = ±½ (-½, ½) Suborbitals • If n = 1, then the only possible value for m and l is 0. • Thus, the first shell contains only one suborbital which holds 2 electrons. • The suborbital is given the symbol “s” and is spherical. • Each additional shell begins with an s-suborbital. • These are shaped as nested spheres. Suborbitals • For n = 2, m can equal 0 or 1. • So, there are two types of suborbital in the second shell: “s” and “p”. • For m = 1, l can equal -1, 0, or 1—this means there are 3 psuborbitals in each shell beyond the first. • p-suborbitals are barbellshaped and each holds 2 electrons. • Additional p-suborbitals form beyond those in lower shells. Suborbitals • For n = 3, l can equal 0, 1, or 2. • This allows three types of suborbital: “s”, “p”, and “d”. • For l = 2, m can equal -2, -1, 0, 1, or 2. • This means there are 5 dsuborbitals. • The first 4 are shaped like the letter “x”. • The fifth is shape like a barbell with a ring around it. • In higher shells, additional dsuborbitals form outside lower ones. Suborbitals • For n = 4, l can equal 0, 1, 2, or 3. • Shells 4 and up can support “f” suborbitals. • For l = 3, m can equal -3, -2, -1, 0, 1, 2, or 3, meaning each shell can hold 7 fsuborbitals. • f-suborbitals have complex shapes • No known element has more than one shell with fsuborbitals.