Download Quantum Lecture _08

Quantum Mechanics
Chapter 4
CPS Chemistry
Objectives
Discuss the wave-particle nature of light
Describe the photoelectric effect
Discuss how electrons act as waves
Discuss the development of the quantum
model of the atom
What is Heisenberg Uncertainly principle
Who was Schrodinger?
Light as a Particle
 Visible light is a kind of electromagnetic
radiation that exhibits wave like behavior
as it moves through space.
All electromagnetic radiation moves at the
same speed in a vacuum
3.0x108m/s(speed of light)
Photoelectric Effect
 Albert Einstein found that if you shined light on a
piece of metal with the correct frequency that
electrons would be knocked off, creating an
electric current. Which could be detected like
voltage flowing from a battery
 This is called the Photoelectric Effect, which
Albert Einstein won the Nobel Prize for in 1921*
*Note Nobel Prizes can be awarded years or decades after important discoveries have been made
Quantum
 Max Plank found in the early 1900’s that the
release of light by hot objects (think filament in a
light bulb) does not release energy in a stream
(think water from a hose), but in small packets of
energy (think the energy to throw a tennis ball)
called Quanta (plural)
 A quantum is the minimum quantity of energy
that can be lost or gained by an atom(energy
needed to throw 1 tennis ball)
Quantum II
The vehicle for this energy is called a
Photon, a mass-less particle of
electromagnetic radiation (Think, tennis
ball)
Ground & Excited states
 Electrons exist at certain levels outside the
nucleus of the atom, the further away from the
nucleus the higher the energy
 When a electron goes from an excited state
(higher level) to a lower level, it releases energy
in form of a photon, or light, each element has its
own “signature” or frequency of light. It is this
color(s) of light that allow us to identify different
elements
 To get an electron to leave a ground state to go
to a higher state you must add energy
Electrons as Waves
 So far we have discussed how light can act as a
particle, but conversely particles can act as
waves
 Work by deBroglie found that electrons around
the nucleus of an atom exhibited wave behavior,
acting at certain frequencies around the nucleus
 Further experiments proved more wavelike
behavior such as a stream of electrons can be
bent (diffracted), or that two electron beams can
interfere with each other, just like water waves.
Heisenburg’s Experiment
The idea that electrons sometimes acted like
particles and other times acted like waves was
very confusing for scientists.
Werner Heisenburg had an experiment where he
tried to detect the exact location of an electron
by hitting them with photons (about the same
energy as an electron) like pool balls on a pool
table. But with this method it was hard to
pinpoint the location of any particular electron,
Heisenburg Uncertainty Principle
Through his experiment Heisenburg found
that it was impossible to know both the
location AND the speed of any particular
electron simultaneously
Schrödinger Wave Equation
Schrödinger found that only specific
energies for electrons made them act like
waves, not ALL energies.
Schrodinger & Heisenburg’s work laid the
foundation for modern quantum theory
Atomic Orbitals & Quantum Numbers
First, you must think of an atom 3dimensionally, that electrons live in not
only an x-y space but also in a z direction
Quantum numbers are the “address” of an
electron in relation to the nucleus
Each electron has an “address” of a
unique combination of 4 quantum numbers
Principle Quantum number - N
 N is the principle quantum number, it represents
the energy level of the electron, or how far away
it is from the nucleus
 N can be a positive integer, 1, 2, 3, etc.
 The bigger the number, the higher the energy
and the further it is from the nucleus
 More than one electron can have the same N
quantum number, if they are in the same “Shell”
or level. The total number of orbitals in a shell is
equal to N2
Angular Momentum QN
 Angular Momentum describes the shape of the
sublevels of the orbital
 L value tells you the shape of the orbital, the
number of shapes possible is equal the principle
QN
Example
 When n = 1, there is one shape (sphere)
 When n = 2 there are two shapes (sphere & dumbbell)
 When n = 3 there are three shapes (sphere, dumbbell,
and flower)
Values of L
 L can be zero or any positive integer, example
0,1,2,3, up to n-1
 So if n = 2 than the possible values for L are 0
and 1, since the highest value is n-1
 What if n=4 what are the values of L?
0,1,2,3 since 3 = N-1= 4-1(=3)
Understand that quantum numbers explain where the
likelihood of an electron to be, but due to Heisnburg’s
uncertainty principle we can not know exactly where a
particular electron is at any given time.
Shapes of L
 Each value of L corresponds to a different shape
of the orbital, and each shape has its own
identifying letter
 0 is the s orbital and has a sphere shape
 1 is the p orbital and has a dumbbell shape
(three orientations: x,y,z)
 2 is the d orbital and has a flower shape and has
many different orientations
 3 is the f orbital and has a bizarre shapes that
can not easily be described.
Orientation of L
 The magnetic quantum number explains the
orientation or the orbital around the nucleus
 For the s orbital there is only one orientation
M = 0
 For the p orbital there are 3 orientations
M = -1,0,1
 For the d orbital there are 5 orientations
M= -2,-1,0,1,2
 For the f orbital there are 7 orientations
M= -3,-2,-1,0,1,2,3
Spin Quantum Number
Lastly, electrons in their orbitals also spin,
and the spin of the electron can be
described in two ways +1/2 and –1/2
An orbital can have at most 2 electrons,
therefore they must have opposite spins
Review of Quantum numbers
 N: Principle, describing how far from nucleus.
N=1,2,3,4,etc.
 L: Angular Momentum, describing the shape of
the orbital. L = 0,1,2,3…n-1
S,p,d,f
 M: Magnetic, describing the orientation around
the nucleus
 Sp: Spin, either +½ or - ½
 Each electron needs a UNIQUE set of Quantum
Numbers