# The Quantum Mechanical Picture of the Atom

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The Quantum Mechanical Picture of the Atom
The allowed energy states of atoms and molecules can be described by sets of numbers called quantum numbers n  m ms

Quantum Numbers  - the angular momentum quantum number
n - the principal quantum number n = 1, 2, 3, 4, “shells”  - the angular momentum quantum number  = 0, 1, 2, 3, … , n – 1 “subshells”  = s, p, d, f, m - the magnetic quantum number m = –, – + 1, … ,  – 1,  ms - the spin quantum number ms = –½, +½

Quantum Numbers and Orbitals
Define the energy of the electron Defines the shape of the orbital Orbital The volume around the nucleus where the electron appears 90-95% of the time The Pauli principle No two electrons in an atom may have identical sets of four quantum numbers

s orbital ( = 0) There is only one s orbital per n level

p orbital ( = 1) There are 3 p orbitals per n level
They are named px , py , and pz

d orbital ( = 2) There are 5 d orbitals per n level

f orbital ( = 3) There are 7 f orbitals per n level

Order of Orbital Energy

Building Atoms Build the nucleus by adding the required # of protons and neutrons according to the atomic # and mass # of the atom Fill energy levels (orbitals) with the required # of electrons starting from the lowest available energy level and following Pauli and Hund rules (this is called Aufbau principle)

Building Atoms - Period 1
n  m ms H He

Building Atoms - Period 2
n  m ms Li Be

Building Atoms - Period 2
n  m ms B C

Hund’s Rule Electrons occupy all the orbitals of a given subshell (with the same ) singly before pairing begins. These unpaired electrons have parallel spins (the same sign of ms). n  m ms C

Building Atoms - Period 2
F Ne

Building Atoms - Period 3
Na P Mg S Al Cl Si Ar

Building Atoms - Period 4
K Ca Sc – 4p or 3d ?

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