Download “Location” of Electrons in the Quantum Mechanical Model

“Location” of Electrons in the
Quantum Mechanical Model
Now…where are those electrons again?
Uncertainty and Schrödinger's Wave
Equations
• The work of Heisenberg and Schrodinger lead us
to the conclusion that the exact location of an
electron can never be known
• Schrodinger’s wave equations reveal areas of high
“electron density”
– Although we don’t know for sure, we have a good idea
where we can most likely find an electron
• These areas of high electron density (or
“probability density” are referred to as orbitals
Quantum Numbers
“Electron’s Address”
• Each orbital has a unique set of quantum
numbers
• These numbers provide the “address” for an
electron
– Remember – it’s not the exact location of the
electron…just the most probable location
• Each orbital has four (4) quantum numbers
that are unique to that orbital
– Each electron has its own “address”
Principal Quantum Number
• Symbolized by “n”
• The main energy level where the
electron is found
– n = 1, 2, 3, …
• Orbitals closer to the nucleus
(lower Principal Quantum
Numbers) have electrons with
lower energy
Energy Sublevels
• Within each principal energy level, areas with
greater electron density exist
– Sublevels
• The first sublevel in each PEL is labeled “s”
– All PEL’s have an “s” sublevel (l = 0)
“s” Sublevel Orbitals
Energy Sublevels
• The second sublevel is labeled “p”
– The first PEL does not have a “p” sublevel
– Each PEL from 2 on up has a “p” sublevel (l = 1)
“p” Sublevel Orbitals
Energy Sublevels
• The third sublevel is labeled “d”
– “d” sublevels don’t start until third PEL (l = 2)
• The fourth sublevel is labeled “f”
–l=3
“d” Sublevel Orbitals
Comparison of Sublevels
Angular momentum Quantum Number
• Symbolized by l
• Indicates the sublevel (and consequent) shape
of the orbital
•
•
•
•
l = 0 for s orbital
l = 1 for p orbital
l = 2 for d orbital
l = 3 for f orbital
Magnetic Quantum Number
• Symbolized by ml
• Each orbital contains a maximum of two
electrons
Magnetic Quantum Number
• Indicates which orbital the electron is in,
within each sublevel
– Which of the “p-orbitals” (or “d” orbitals, or “f”
orbitals”) does the electron occupy?
– x-axis, y-axis, or z-axis?
• Indicates the orientation of the orbital around
the nucleus
• Possible values go from –l to +l
– m= -1 for the x-axis p orbital
– m = 0 for the y-axis p-orbital
– m = 1 for the z-axis p orbital
Spin Quantum Number
• Symbolized by ms
• Each orbital can only hold two electrons
– Pauli Exclusion Principle
• Electrons have different “spin” to distinguish
them
– Spin Quantum Number only has two possible
values
– + ½ or – ½