Download Quantum Mechanical Model of the Atom - stpats-sch4u-sem1-2013

Quantum Mechanical Model
of the Atom
Name This Element
Building on Bohr
• The simple Bohr model
was unable to explain
properties of complex
atoms
• Only worked for
hydrogen
• A more complex model
was needed…
Quantum Mechanics
• Uses mathematical equations to describe the
wave properties of subatomic particles
• It’s impossible to know the exact position,
speed and direction of an electron
(Heisenberg Uncertainty Principle)
• So Bohr’s “orbits” were replaced by orbitals
– A wave function that predicts an electron’s
energy and location within an atom
– A probability cloud in which an electron is most
likely to be found
Orbits
Orbitals
- Bohr
- Quantum Mechanics
- 2-dimensional ring
- 3-dimensional space
- Electron is a fixed
- Electrons are a variable
distance from nucleus
distance from nucleus
- 2, 8, or 18 electrons per - 2 electrons per orbital
orbit
Wave Particle Duality
• Experimentally, DeBroglie found
that light had both wave and
particle properties
• Therefore DeBroglie assumed
that any particle (including
electrons) traveled in waves
• Wavelengths must be quantized
or they would cancel out
Heisenberg’s Uncertainty
Principle
• Due to the wave and particle nature of matter,
it is impossible to precisely predict the
position and momentum of an electron
• SchrÖdinger’s equation can be used to
determine a region of probability for finding
an electron (orbital)
• Substitute in a series of quantum numbers to
solve the wave function
Quantum Numbers
• Four numbers used to describe a
specific electron in an atom
• Each electron has its own specific set of
quantum numbers
• Recall: Describes orbitals (probability
clouds)
The Principal Quantum Number
“n”
• Indicates the average distance (size) of the
orbital from the nucleus (same as Bohr’s
energy levels)
• Higher n = greater distance from nucleus =
greater energy
• n = integers > 1 (1,2,3…)
• The greatest number of electrons possible in
each energy level is 2n2
The Secondary Quantum
Number “l”
• Describes the shape of the orbital
• Atoms with many electrons showed spectrum
with many lines, some close together and
others spaced apart
• Subshells within the main energy levels
• Each subshell has a different shape with the
highest probability of finding an electron
The Secondary Quantum
Number “l”
• Positive integers ranging from 0-3
• Maximum value of n-1
– l = 0 (s orbital)
– l = 1 (p orbital)
– l = 2 (d orbital)
– l = 3 (f orbital)
• Total number of sublevels = n
The Magnetic Quantum Number
“ml”
• Describes orientation of the orbital
• ml = integers from -l to +l
• Maximum number of orientations = n2
The First Three Quantum
Numbers
The Spin Quantum Number
“ms”
• Describes the direction an electron is
spinning in a magnetic field (up or down)
• Only two electrons per orbital
• ms = + 1/2 or - 1/2
Letter Analogy
Miss Smith
4 The Parkway
Kanata
ON
n= 3
l=1
ml = -1
ms = +1/2
Quantum Numbers Summary Chart
Name
Symbol Allowed Values
Property
Principal
n
positive integers
1,2,3…
Orbital size and
energy level
Secondary
l
Integers from
0 to (n-1)
Orbital shape
(sublevels/subshells)
Magnetic
ml
Integers –l to +l
Orbital orientation
+½ or –½
Electron spin
Direction
Spin
ms
Practice!
• Quantum number handout
• p. 182 #3-5
• p. 184 #3-7