Quantum Mechanics and the atom

position and velocity are

complementary and kintetic energy is a function of velocity.

therefore, energy and position are complementary

get precise values of energy at the cost of

imprecise values of positions →probability distributions for position

the probability distribution for the location which corresponds to a particular electron energy is called

an orbital

the energies and orbitals are determined from the

The energies and orbitals are determined from the Schrodinger Equation for the atom in question, given as:  HY = EY  where H is the Hamiltonian Operator (Total E of the electron), Y is the wave function which describes the electron, and E which is the actual kinetic energy of the electron. 

Y² represents

the orbital, or probability distribution map of the electron.

Schrodinger Equation → many solutions → Orbitals

principle quantum number

n

angular momentum quantum number

L

magnetic quantum number

ml

spin quantum number

ms

the 1st three quantum numbers define the orbital:

n, l, ml

the 4th, ms, defines

the orientation of the electron

n determines

the size and energy of the orbitals

n can be any positive integer greater than 0

l defines

shape of orbitals

can be any integer from 0 to positive (n-1)

ex. if n=3, l=0,1,2

defines the sublevel and type of orbitals denoted by letters

l=0

s sublevell

=1

p sublevel

l=2

d sublevel

l=3

f sublevel

ml defines

the number and geometry (spatial orientation) of the orbitals in the subshell

can have all possible integers from -l to +l

ms denotes

the spin orientation of the electron in the orbital

= ± ½ only. 2 electrons per orbital one spin up and one spin down