Transcript Quantum theory

Quantum theory
Electron Clouds and
Probability
• Bohr’s model of the atom is unable to describe
electron (e-) behavior in an atom
• Problem: multiple spectral lines closely spaced
• deBroglie Hypothesis
• Believed e- had a Dual-nature
• Acted as particles with mass and waves of energy
with no mass, simultaneously
• Combined Einstein’s Relativity equation (E=mc2)
with Plank’s quantum equation (E= hv) (Plank’s
constant, frequency of a wave)
• mc2 = hv substitute c with v ( general velocity)
• v(frequency of wave)= v/l velocity/wavelength)
• Final equation l = h
mv
• Enabled de Broglie to predict the
wavelength of a particle of mass m and
velocity v
• Showed that an e- stream acted as a group
of particles and in some ways as a ray of
light
• Waves can act as particles and particles can
act as waves
• Wave-particle duality of nature
• Momentum (p) is the product of mass and
velocity (speed and direction of motion
l = h/p
 Wavelength inversely proportional to
momentum
 Only worth studying for particles of small
mass
 Quantum mechanic: small particles
traveling near speed of light
• Heisenberg studied e- as particles
• Noted it was impossible to determine both
the exact position and exact momentum of
an e- at the same time
• Due to the fact that you interacted with the
particle to “see” it and changed one of the
two properties
• There is always uncertainty
• Proposed Heisenberg Uncertainty Principle
• Impossible to know the exact position and
momentum of an e- at the same time
• Scientists are unable to describe the exact
structure of an atom due to this
• But it can be determined with probability
• Can determine with high probability where
an e- is most likely to be found in the
energy levels of an atom at any one given
time
• Schrodenger
• Studied e- as waves
• Found amplitude of wave was related to
distance or point in space an e- was from the
nucleus
• Developed an equation using e- energies and
amplitude along with quantum levels to
describe wave function
• Included e- total and P.E. in equation
• Max Born found that the square of the
amplitude gave the probability of finding
the e- at that same point in space around the
nucleus for which the equation is solved
• Probability
• Is the ratio between the number of times the
e- is in that current position and the total
number of times it is at all positions
• The higher the probability, the more likely
the e- will be found in a given position
• The probability plots give a three
dimensional shape to a region of space an eis most likely to be found
• Since the e- is traveling at the speed of light
and appearing at all these positions, the eappears to be everywhere
• The area the e- occupies appears to be a
region of negative charge with a specific
shape
• This is referred to as an Electron cloud
• Now lets put this into the Bohr Model
• Electrons are assumed to have a circular path and
to always be found at a specific distance from the
nucleus dependent on their P.E.(ground state)
• But there is the probability of any e- at trillions if
not more points in space
• Many of these points have high probability
• Connect all these points together and you obtain a
3D shape
• The most probable place to find the e- is on the
surface of this shape
• Remember that e- move near speed of light
• The e- random movement causes it to
appear as a cloud
• The e- occupies all the volume of this cloud
• Does not normally go beyond the outer
volume area(ground state)
• Now in order to describe an e- behavior we
need to represent different energy states
• Do this by use of quantum numbers
• The differences correspond to the lines
observed in the spectrum of atoms
• Easily described using H
• When an e- moves from ground to excited
state, energy emitted as a form of light
• Represented by a line in the H
spectrumhttp://www.colorado.edu/physics/2
000/applets/a2.html
• Atoms with more than one e• Interactions of the other e- cause other problems
as well as the increased nuclear pull
• It is assumed that the various e- in a multielectron
atom occupy the same energy states without
affecting each other
• To describe an e- in an atom, four quantum
numbers are required
• Quantum numbers are ID’ed by the letters n, l, m,
s
• Each e- has its own unique set of these four
numbers
• Any one e- can occupy only a specific
energy level based on its total and P.E.
• These energy levels are represented by
whole integers starting with 1
• The number of the energy level, represented
by the letter n, is called the Principle
Quantum Number 1,2,3….n
• Electrons can be found in each energy level
of an atom
• Greatest number of e- in a level is 2n2
• Second Quantum number is l
• Represents the energy sublevels and orbitals
• Each energy level is a group of energy
states
• Represented by the number of spectral lines
we saw of the same color
• These are closely grouped together
• States called sublevels
• # sublevels in an energy level is equal to the
principle quantum number
•
•
•
•
•
Principle quantum level 1 has 1 sublevel
Principle quantum level 2 has 2 sublevels
Principle quantum level 3 has 3 sublevels
And so on…
The lowest sublevel of energy in any
principle energy is always designated by the
letter s
• 2nd sublevel is p so 2nd level has an s and p
• 3rd sublevel is d so 3rd has a s,p,d
• 4th sublevel is f so 4th has s,p,d,f
• Each sublevel holds a maximum number of
e• Every s can contain 2e- (one pair)
• Every p can contain 6e- (three pair)
• Every d can contain 10e- (five pair)
• Every f can contain 14e- (seven pair)
• Each pair in a sublevel has a different place
in space
• Due to the interactions of the e- within a
sublevel on each other
• Try to be as far from each other as possible
due to the fact they are all same charge
• The space occupied by one pair of e- is
called an orbital
• Designated by quantum number m
• Defines each orbital by indicating its
direction in space
• Ex. Sublevel s is simply spherical in nature
• Sublevel p with three orbitals (6e-, 3 pairs)
has e- in 3D along the x,y,z axis
• Orbitals of the same sublevel are alike in
size and shape and have same energy
• Orbitals of the same energy are called
DEGENERATE
• Shapes:
•
•
•
•
Electrons in the same orbital must coexist together
How if they are repulsive
Fourth quantum number is spin s
Electrons in the same orbital spin in opposite
directions
• Sets up opposite magnetic fields, so e- become
slightly attractive to each other
• Up and down arrows E used to show spin
direction
• Pauli Exclusion Principle: no two e- in the same
atom can have the exact same four quantum values
• So lets see how e- would start to occupy
positions in an atom
• Aufbau principle states that e- will always
occupy lowest available energy levels first
• So lets see how this might look:
• .
• As more e- are added to the atom and
occupy higher energy levels, the
interactions become greater between e- of
different energy levels and sublevels
• Also remember that the nucleus is also
gaining protons and its overall charge is
increasing causing it to pull harder
• All these interactions force sublevels to
begin to overlap each other
• It changes the filling pattern of e- in atoms
• Note: starting with energy level three, 4s
fills before 3d
• Thus have a new filling pattern for e• Can use an ARROW DIAGRAM to
determine the pattern
• .
• One more e- filling fact
• Hund’s Rule:
• The most stable atoms are those which have
the most parallel (same direction) spinning
e• Designated by using boxes and the arrows
for e- spin
• .