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 p- suborbitals in each shell beyond the first. p-suborbitals are barbell- shaped 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 d- suborbitals. 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 d- suborbitals 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 f- suborbitals. f-suborbitals have complex shapes No known element has more than one shell with f- suborbitals.