Atomic Structure chapter 6 written by JoAnne L' Swanson University of Central Florida

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Atomic Structurechapter 6written byJoAnne L.
SwansonUniversity of Central Florida
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The properties of light, the way that energy
travels through space, are referred to as
________________________ _________________________
_
Light has properties of both matter and waves.
It is described as particles that travel through
space in waves. These particles of light are
called ______________.
Light has 3 main characteristics. These are
____________, l, ___________, n, and _________,
c. Definitions follow
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WAVELENGTH l - The distance between two,
consecutive, corresponding points on a wave. The
units are_____________ __________________________
__________________ FREQUENCY n The number of
waves that pass a given point per second. The
units for frequency are s-1 or Hz. SPEED OF
LIGHT c The speed of light (measured in a
vacuum to negate the effect of friction) is 2.998
x 108 m/s.
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RELATIONSHIPS BETWEEN l, n, and c Small
wavelength large wavelength A small wavelength
will have a ______________ than a large
wavelength because more waves can pass a given
point per second. THEREFORE, WAVELENGTH AND
FREQUENCY ARE INVERSELY PROPORTIONAL. A small
wavelength also has _________________.
THEREFORE, WAVELENGTH AND ENERGY ARE INVERSELY
PROPORTIONAL AND ENERGY AND FREQUENCY
ARE DIRECTLY PROPORTIONAL.
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There were some phenomena that could not be
explained by assuming light had only wave
properties Black body radiation Photo
electric effect Emission spectra from excited
atoms
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Black body radiation ___________________________
____ The higher the temperature, the more
intense the glow and the glow can be different
colors (or wavelengths) Physicists tried to
explain the relationship of the wavelengths of
light (color) to the intensity of the heat. Max
Planck made the assumption that the atoms were
giving off and absorbing heat ___________________
(he called __________). His equation shows the
relationship of this fixed amount of energy being
proportional to the frequency of the radiation.
Multiplying the frequency by a proportionality
constant (called Plancks constant), gives the
equation E hn. Where h6.63 x 10-34 Js
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• In Summary -
• Planck energy can only be absorbed or released
  from atoms in certain amounts called quanta.
• The relationship between energy and frequency is
• E hn
• where h is Plancks constant (6.626 ? 10-34 J.s).

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Photoelectric Effect

• light can strike the surface of some metals and
  ________________________________
• Albert Einstein explained this effect
• 1921 Nobel Prize in Physics
• light has particle-like behavior

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• The Photoelectric Effect and Photons
• The photoelectric effect provides evidence for
  the particle nature of light -- quantization.
• If light shines on the surface of a metal, there
  is a point at which electrons are ejected from
  the metal.
• The electrons will only be ejected when
  ___________
• _______________________________________
• Below that frequency, _______________________.
• Above that frequency, the number of electrons
  ejected depend on the intensity of the light.

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• The Photoelectric Effect and Photons
• Einstein assumed that light traveled in energy
  packets called photons.
• The energy of one photon
• E hn

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• Emission Spectra of Excited Atoms
• Radiation composed of only one wavelength is
  called _______________.
• Radiation that spans a whole array of different
  wavelengths is called ______________.
• White light can be separated into a continuous
  spectrum of colors.
• Note that there are no dark spots on the
  continuous spectrum. That would correspond to
  different lines.
• When atoms are excited by electricity or heat,
  they emit only _________________________ (that
  is, not a continuous spectra of light).

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• Colors from excited gases arise because electrons
  move between energy states in the atom.

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• Modern atomic theory arose out of studies of the
  interaction of radiation with matter.
• Electromagnetic waves have characteristic
  wavelengths and frequencies.
• Example visible radiation has wavelengths
  between ____________________________________.

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• Neils Bohr, a Danish physicist, assumed the
  electrons orbited the nucleus analogous to
  _________
• _________________________________________.
• However, a charged particle moving in a circular
  path should lose energy.
• This means that the atom should be unstable and
  get pulled into the nucleus according to Bohrs
  theory.
• Bohr noted the line spectra of certain elements
  and _____________________________________________
  ______________________. These were called orbits.

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• emission spectrum
• ____________________________
• ______________________________
• ___________________________
• emission or bright line spectrum

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• Bohr theorized why excited Hydrogen atoms emitted
  line spectra.
• Electrons have energies __________________________
  _____ ___________________________________________
  ________
• They will not lose energy in this allowed energy
  state (orbit).
• Energy is only emitted or absorbed when an
  ______________ ____________________. (like one
  step on a ladder to another). The lowest energy
  state, n1, is the _________, like the bottom
  rung of a ladder and the higher energy states
  from n2 and greater are the _______________.

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• spectra are fingerprints of elements
• use spectra to identify elements
• can even identify elements in stars

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• Since the energy states are quantized, the light
  emitted from excited atoms must be quantized and
  appear as line spectra.
• Bohr showed that
• where n is the principal quantum number (i.e., n
  1, 2, 3,). 2.18 x 10 18 is the ground state
  energy for H.
• __________________________________________________
  ___ ______________________________________________
  _

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• Balmer discovered that the wavelengths in the
  visible line spectrum of hydrogen fit a simple
  equation.
• The Rydberg equation generalizes Balmers
  equation to
• where RH is the Rydberg constant (1.096776 ? 107
  m-1), h is Plancks constant (6.626 ? 10-34
  Js), n1 and n2 are integers (n2 gt n1).

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• Bohr Model
• The first orbit in the Bohr model has n 1, is
  ________ ___________________.
• The furthest orbit in the Bohr model has n close
  to infinity and corresponds to zero energy.
• Electrons in the Bohr model can only move between
  orbits by absorbing and emitting energy in quanta
  (hn).
• The amount of energy absorbed or emitted on
  movement between states is given by

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• The change in energy between orbits correspond
  to
• When ni gt nf, energy is emitted.
• When nf gt ni, energy is absorbed
• PLEASE SEE PAGE 264-268 IN YOUR TEXT FOR
  DERIVATIONS OF THESE EQUATAIONS.

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• Limitations of the Bohr Model
• Can only explain the line spectrum of _________
  ________________________.

• considers only the particle nature of the
  electron. ___________________________.
• Electrons travel in circular paths like planets

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Bohr Model
e
e
e
e
P
n
e
e
e
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• light has a particle nature, matter has a wave
  nature.
• Using Einsteins and Plancks equations, de
  Broglie showed
• l h / mv (v velocity)
• The momentum, mv, is a particle property, whereas
  ____________________.
• de Broglie summarized the concepts of waves and
  particles, with noticeable effects if the objects
  are small.

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• To determine the mass of a photon of light
  derivation -
• If Ehn and cln Then Ehc/l and if Emc2
  Then
• mE/c2 and so m hc / lc2
  h / lc h / l2 n
• so, m h / lc and
  m h / l2 n
• If the particle is not moving at the speed of
  light but instead at some velocity, v, m h /
  lv (where v velocity)
• de Broglies equation shows the dual nature of
  light, in that it allows the wavelength of a
  particle to be calculated. l h / mv

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EINSTEIN, PLANCK, AND DE BROGLIES EXPERIMENTS
CONCLUDED THAT MATTER AND ENERGY ARE NOT
DISTINCT. MATTER EXHIBITS BOTH PARTICULATE AND
WAVE PROPERTIES. ____________ ___________________
__________________
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• The Uncertainty Principle
• Heisenbergs Uncertainty Principle
• For electrons we cannot determine their momentum
  and position simultaneously.

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• Some important mathematical relationships
• c l n
• E h n Max Plancks equation showing energy is
  quantized
• E m c2 Einsteins theory of relativity,
  shows energy has mass
• E h c
• l
• h / mv de Broglies relationship of matter
  with wavelength
• c 2.998 x 108 m/s (speed of light in
  vacuum)
• h is Planks constant. h6.626 x 10-34 Js or kg
  m2/s
• Units of E are Joules which equal, (kg m2 /
  s2) Jkg m2 / s2

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• OTHER EQUATIONS TO KNOW
• (derived from Bohrs model for the hydrogen
  atom.)
• E -2.178 x 10-18 J (z2 / n2) where z is the
  nuclear charge,and for H 1,
• and n is the energy level. Ground state, n 1.
  Ionized e-, n infinity
• and 2.178 x 10-18 is the ground state energy for
  H. So, since z21 for H, then
• E -2.178 x 10-18J / n2 for the energy levels
  available in the H atom
• And.. Calculating Energy Difference Between 2
  Levels
• DE Efinal - Einitial Ehi Elow h c / l
• So,
• DE -2.178 x 10-18 J / n2final (-2.178 x
  10-18J /n2initial) hc / l

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• Examples
• The color of Sodium atoms, when excited by a
  flame, are yellow and have the wavelength 589.0
  nm. Calculate a. the frequency of this
  wavelength and b. the energy associated with
  this photon?
• a. n c 5.090 x 1014 s-1
• l
• b. E h n 6.626 x 10-34 Js x
  3.37 x 10-19 J for this photon

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• example
• It takes 382 kJ of energy to remove one mole of
  electrons from gaseous cesium. What is the
  wavelength associated with this energy?
• To convert between energy and wavelength,
  requires the energy to be per photon, not moles
  of photons, therefore,
• 382 kJ x _________________ 6.343 x 10-19
  J (per photon)
• 1 mol
• E h c so, l hc
• l E
• 3.13 x 10-7 m

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• example
• What is the wavelength of an electron with mass
  9.11 x 10-31kg, traveling at 5.31 x 106m/s ?
• m h / lv therefore, l h / m v
• 6.626 x 10-34 Js 6.626 x 10-34 kg m2s-1
• 1.37 x 10-10 m

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• Quantum Mechanical Model
• Schrödinger proposed an equation that contains
  both wave and particle terms. Considers the wave
  and particle nature of light.
• Solving the equation leads to wave functions.
• The wave function gives the shape of the
  electronic orbital.
• wave equation is written for each electron
• The square of the wave function, gives the
  probability of finding the electron, (a 3-D area
  of finding an electron)
• that is, gives the electron density for the atom.

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POLYELECTRONIC ATOMS _________________________
_________________________________________________
Electron Correlation Problem electrons repel
and since the exact pathways of electrons are not
known, the electron repulsions cannot be
calculated. The repulsions can be approximated
by the number of electrons between the electron
in question and the other electrons in the
atom. An electron would have a very strong
attraction for the nucleus, but since there are
other electrons in an atom which repel each
other, the electron is ___________from the
nucleus from these other electrons. Now we will
look at how the energies of the orbitals of many
electron atoms
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Atomic Orbitals
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• Orbitals and Quantum Numbers
• If we solve the Schrödinger equation, we get wave
  functions and energies for the wave functions.
• We call wave functions ___________.
• Schrödingers equation requires 3 quantum
  numbers
• Principal Quantum Number, n. This is the same as
  Bohrs n. As n becomes larger, the atom becomes
  larger and the electron is further from the
  nucleus. _________________________________

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• Azimuthal Quantum Number, l. This quantum number
  depends on the value of n. The values of l begin
  at 0 and increase to (n - 1). We usually use
  letters for l (s, p, d and f for l 0, 1, 2, and
  3). Usually we refer to the s, p, d and
  f-orbitals. s0, p1, d2, f3.
  Ex._______________
• Magnetic Quantum Number, ml. This quantum number
  depends on l. The magnetic quantum number has
  integer values between -l and l. Magnetic
  quantum numbers give the 3D orientation of each
  orbital. For instance, px, py, pz
• ex.______________________________

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Orbitals and Quantum Numbers
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In Summary, the Quantum Numbers
Electron orbitals are characterized by a series
of numbers called quantum numbers. They describe
the properties of the orbital. PRINCIPLE QUANTUM
NUMBER (n) represents the energy level of the
orbital. It has values of 1,2,3,4 ANGULAR
MOMENTUM NUMBER (aka subshells) (l) represents
the shape of the orbital. It has values of 0 to
n-1. For l 0, the orbital is an s orbital,
for l 1, the orbital is a p orbital, for l
2, the orbital is a d orbital and for l 3, an
f orbital. MAGNETIC QUANTUM NUMBER (ml)
represents the orientation of the orbital in
space (on the x,y,z axis). It has values of l to
l. Example follows fourth quantum number
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The fourth quantum number is the electron spin
number (ms). It can have values of 1/2 and
1/2. A simple interpretation is that an electron
can spin in a clockwise or counterclockwise
direction. The Pauli Exclusion Principle states
that no two electrons in the same atom can have
the same 4 quantum numbers and ______________
__________________________________________________
____ ____________________________________________
_________. The Aufbau Principle states that as
protons are added one by one to the nucleus of an
atom, so are electrons added to orbitals, from
____________________.All orbitals with the same
value of n have the same energy and are said to
be degenerate. Hunds Rule states that electrons
add so that orbitals of the same energy each
contain one electron before a second electron, of
opposite spin is added.
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Sample 7.6 from text Determine the number of
allowed subshells in principle quantum level
n5. Solution subshells are the angular
quantum number, l, which is equal to (0 to n-1),
so for l 0 is s, l 1 is p, l 2 is d, l 3
is f, l 4 (which is n-1) is g, are allowed in
energy level 5, the subshells 5s, 5p, 5d, 5f,
and 5g (theoretically) are allowed.
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EXAMPLES OF QUANTUM NUMBERS
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• The s-Orbitals
• All s-orbitals are spherical.
• As n increases, the s-orbitals get larger.
• As n increases, the number of nodes increase.
• A node is a region in space where the probability
  of finding an electron is zero.(see your text for
  plots of nodes and read about it).
• For an s-orbital, the number of nodes is (n - 1).

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• The p-Orbitals
• There are three p-orbitals px, py, and pz.
• The three p-orbitals lie along the x-, y- and z-
  axes of a Cartesian system.
• The letters correspond to allowed values of ml of
  -1, 0, and 1.
• The orbitals are dumbbell shaped.
• As n increases, the p-orbitals get larger.
• All p-orbitals have a node at the nucleus.

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• The d and f-Orbitals
• There are five d and seven f-orbitals.
• Three of the d-orbitals lie in a plane bisecting
  the x-, y- and z-axes.
• Two of the d-orbitals lie in a plane aligned
  along the x-, y- and z-axes.
• Four of the d-orbitals have four lobes each.
• One d-orbital has two lobes and a collar.

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• Orbitals and Their Energies
• Orbitals of the same energy are said to be
  degenerate.
• For n ? 2, the s- and p-orbitals are no longer
  degenerate because the electrons interact with
  each other.
• Therefore, the Aufbau diagram looks slightly
  different for many-electron systems.

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Orbitals and Their Energies
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• Line spectra of many electron atoms show each
  line as a closely spaced pair of lines.
• An experiment was done to find out why.
• Two spots were found one with the electrons
  spinning in one direction and one with the
  electrons spinning in the opposite direction.

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Electron Spin and the Pauli Exclusion Principle
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• Electron Spin and the Pauli Exclusion Principle
• Since electron spin is quantized, we define ms
  spin quantum number ? ½.
• Paulis Exclusions Principle no two electrons
  can have the same set of 4 quantum numbers.
• Therefore, two electrons in the same orbital must
  have opposite spins.

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• Electron configurations tells us in which
  orbitals the electrons for an element are
  located.
• Three rules
• electrons fill orbitals starting with lowest n
  and moving upwards
• no two electrons can fill one orbital with the
  same spin (Pauli)
• for degenerate orbitals, electrons fill each
  orbital singly before any orbital gets a second
  electron (Hunds rule).

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• Condensed Electron Configurations(the core
  designation)
• Neon completes the 2p subshell.
• Sodium marks the beginning of a new period.
• So, we write the condensed electron configuration
  for sodium as
• Na Ne 3s1
• Ne represents the electron configuration of
  neon.
• Core electrons electrons in Noble Gas.

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• Transition Metals
• After Ar the d orbitals begin to fill.
• After the 3d orbitals are full, the 4p orbitals
  being to fill.
• Transition metals elements in which the d
  electrons are the valence electrons.

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• Lanthanides and Actinides
• From Ce onwards the 4f orbitals begin to fill.
• Note La Xe6s25d14f0
• Elements Ce - Lu have the 4f orbitals filling and
  are called lanthanides or rare earth elements.
• Elements Th - Lr have the 5f orbitals filling and
  are called actinides.
• Most actinides are not found in nature.

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• The periodic table can be used as a guide for
  electron configurations.
• The period number is the value of n.
• Groups 1A and 2A have the s-orbital filled.
• Groups 3A - 8A have the p-orbital filled.
• Groups 3B - 2B have the d-orbital filled.
• The lanthanides and actinides have the f-orbital
  filled.

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Electron configuration and Orbital
diagrams examples done on doc cam.
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For review THE ATOMIC SPECTRUM OF HYDROGEN AN
ATOM WILL EMIT ONLY CERTAIN WAVELENGTHS OF LIGHT.
THIS IS BECAUSE THERE ARE ONLY CERTAIN ENERGY
LEVELS IN WHICH THE ELECTRONS IN THE ATOM CAN
SHIFT. WHEN ENERGY IS ADDED TO A SUBSTANCE BY
HEAT OR ELECTRICITY, ITS ELECTRONS WILL GAIN
QUANTA OF THIS ENERGY AND WILL JUMP FROM THE
GROUND STATE (UNEXCITED STATE) TO A HIGHER ENERGY
LEVEL (THE EXCITED STATE). THE ENERGY THAT HAD
BEEN GAINED WILL THEN BE LOST AS THE ELECTRONS
FALL BACK DOWN TO THE GROUND STATE, EMITTING
QUANTA OF ENERGY (OR LIGHT) WITH THE WAVELENGTHS
ASSOCIATED WITH ONLY THOSE ENERGIES.
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When visible light (called white light) is passed
through a prism, a continuous spectrum of colors
is seen. The colors of the rainbow. When the
light from hydrogen is passed through a prism,
only a few lines are seen. Each line corresponds
to a particular wavelength. This is called the
atomic emission spectrum or the line spectrum for
hydrogen. This indicates that only certain energy
transitions are allowed from the hydrogen atom.
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The atomic emission spectrum for Hydrogen
H
H
excited state
ground state
H
h?
h?
hydrogen gas
?
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When visible light is passed through a prism, all
of the colors of the rainbow are seen R O Y G
B I V low E.high E long l
.short l When light emitted from different
elements is passed through a prism, only certain
colored lines are seen (this is the emission
spectrum for that element ), meaning that only
certain energies are allowed for different
elements. This means the energy is quantized,
that is, if an electron gains just the needed
amount (quantity, called quantum) of energy to
jump to a higher energy level, it will emit that
exact amount (quantum) of energy when it falls
back down.
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CLASSIFICATION OF ELECTROMAGNETIC
RADIATION SMALL l LARGE l l(nm) 10-2
10-1 101 400-700 105 107
109 1012 1013 Gamma rays X-ray
Ultraviolet visible light Infrared
Microwaves Radio waves High
Energy Low Energy High
Frequency Low Frequency