Transcript Quantum numbers

Quantum Mechanical Model of
the Atom
Chapter 6
Part III
Bohr’s model was Imperfect
The model of an electron in a circular
orbit around a nucleus worked only for
Hydrogen, Lithium but by Boron, the
model was ineffective.
Electrons bound to the nucleus
seemed similar to a standing wave.
 See if video works
De Broglie, Heisenberg and
Schrödinger pioneered wave
mechanics, aka Quantum Mechanics.
 http://www.colorado.edu/UCB/AcademicAffairs/
ArtsSciences/physics/PhysicsInitiative/Physics2
000/quantumzone/debroglie.html
 This site shows how a particle such as an
electron can have wave-like functions.
 http://www.chemtopics.com/lectures/unit04/lectu
re3/l3u4.htm
 This site demonstrates wave like qualities of
orbitals.
Schrödinger & de Broglie
 Both felt the electron acted like a standing
wave. (see slinky)
 Theorizing that the electron acts like a wave,
and has a wave function  That represents
the x, y and z coordinates of the electron.
 A specific wave function is often called an
orbital.
By treating the electron as a wave:
Schrödinger
mathematically
described a series of
wave functions each
having discrete
energy levels.
Heisenberg’s Uncertainty Principle
∆x * ∆ (mv) > h/4
x= the uncertainty of the particle’s position
mv = the uncertainty of the particle’s
momentum
h = Planck’s constant
Stating that we cannot know both the
speed and position of an electron
Heisenberg’s big idea
 http://www.chemtopics.com/lectures/unit04/lec
ture3/l3u4.htm
 This url demonstrates how the model of a
circular orbit (Bohr) morphs into a model
demonstrating the Uncertainty Principle.
 Electron clouds as orbitals.
Wave Functions
 [(X1, Y1, Z1)]2 = N1
[(X2, Y2, Z2)]2
N2
 N1/N2 gives the ratio of the probability of
finding the electron at position 1 relative to
position 2. If the number is 100, the electron
is 100 times more likely to be in position 1
than 2.
Probability
Distribution
This square of the
wave function is
represented as a
probability
distribution.
AKA electron
density map.
When the electron density map is divided into equal
spheres, the plot of finding the electron in each
successive sphere gives the following curve
The size of an atom
The definition of the size of a
hydrogen atom 1s orbital is the
radius of the sphere that encloses
90% of the total electron probability.
Quantum numbers
When solving Schrödinger's equation for
the hydrogen model we find wave
functions / orbitals.
Each orbital is characterized by a series
of numbers called Quantum
Numbers.
Principle Quantum number
n has intergral values 1, 2, 3…
n is related to the size an energy
level of the orbital.
Or n= energy level
Angular quantum number
 l has integral values of 0 to n-1 for each
value of n.
Each value of l has a shape associated
with it.
0= s
1=p
2=d
3=f
Magnetic quantum number
m is related to the orientation of the
orbital and may equal any integral
value between l and – l. This
includes zero.
It relates to the orientation of the
orbital in space relative to other
orbitals in the atom.
Spin
Each orbital may hold two electrons.
Quantum number are +1/2 and -1/2
Nodes
 See handout