Chapter Seven

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Chapter Seven

• Atomic Structure

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Contents
1. Classical View of Atomic Structure (1) The
Electron Experiments by Thomson and
Millikan (2) Atomic Models Thomson and
Rutherford (3) Protons and Neutrons (4) Positive
Ions and Mass Spectrometry 2. Light (1) The
Wave Nature of Light (2) Photons Energy by the
Quantum 3. Quantum View of Atomic
Structure (1) Bohrs Hydrogen Atom A Planetary
Model (2) Wave Mechanics Matter as
Waves (3) Quantum Numbers and Atomic Orbitals
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• Classical View of Atomic Structure
• (1) The Electron Experiments by Thomson and
  Millikan

1) Cathode Rays A beam of negatively charged
particles (now called electrons) that travels
from the cathode to the anode, an electric
current passed through a vacuum tube.
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• More about Cathode Rays
• The properties of cathode rays do not depend on
  the composition of the cathode. For example, the
  cathode rays from an Al cathode are the same as
  those from a Ag cathode.
• The rays cause glass and other materials to
  fluoresce, cathode ray tubes (CRT) are applied in
  TV and monitor.
• The rays are deflected by a magnet.

• Classical physics
• Matter is a particle
• Light is a wave

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3) me/e of Cathode Rays by J.J. Thomson
Ratio of cathode ray particles mass (me) to the
charge (e)
me /e 5.686 1012 kg C1
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4) Electron Charge Millikans Oil-Drop Experiment
Read p. 263, text and Figure 7.3
Animation
The electrons charge e 1.602 1019 C

• Mass of an Electron (me)
• J.J. Thomson me /e 5.686 x 1012 kg/C
• Robert Millikan e 1.602 x 1019 C
• Therefore,
• me 9.109 x 1031 kg/electron

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(2) Atomic Models Thomson and Rutherford

• Thomsons Raisin Pudding Model

Thompson's raisin pudding model was disproved
by Rutherford's gold-foil experiment
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2) Rutherford's Nuclear Model of Atom
Animation

• a (He2) scattering experiment
• Discovered the positive charge of an atom is
  concentrated in the center of an atom (now called
  nucleus)

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(3) Protons and Neutrons 1) Proton

• The positive charge particles in the nucleus
  called protons
• The nucleus of a hydrogen atom consisted of a
  single proton
• Atomic number represents the number of protons in
  the nucleus of an atom
• The mass of a proton is 1.67252x1027 kg
• The charge of proton is 1.602 x 1019 C

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2) Neutron

• Except for hydrogen, an atom does not have enough
  protons to account for the mass of the atom
• James Chadwick discovered neutrons in the
  nucleus, which have mass as 1.67495x1027 kg and
  no charge

Mass Charge Electron 9.109 x 1031 kg 1.602 x
1019 C Proton 1.67252x1027 kg 1.602 x 1019
C Neutron 1.67495x1027 kg 0
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• Positive Ions and Mass Spectrometry
• 1) Mass Spectrometry

• A cathode-ray tube also produced positive
  particles, metal of the cathode for example
• M ? e M

Positive particles
Cathode rays

• A stream of positive ions having equal velocities
  is brought into a magnetic field.
• The lightest ions are deflected the most, the
  heaviest ions are deflected the least.
• Mass spectrometer is designed so that most
  particles attain a 1 charge.
• The ions are thus separated by mass, actually, by
  (m/e) ratio

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2) Mass Spectrometer
3) Mass Spectrum for Hg

• How many isotopes does Hg have?
• Ans 7
• What is the most abundant isotope of Hg?
• Ans

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• Light
• (1) The Wave Nature of Light (also called
  Electromagnetic Waves or Radiation)

• Definition
• A wave that has an electric field component and a
  mutually perpendicular magnetic field component
• Electromagnetic waves require no medium for their
  propagation

Amplitude
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2) Wavelength And Frequency

• Wavelength (?, lambda) The distance between any
  two identical points in consecutive cycles.
• Frequency (?, nu) The number of cycles of the
  wave that pass through a point in a unit of time.
• Unit waves/s or s1 (Hz, hertz).
• The relationship between wavelength and
  frequency
• c ?v
• c 2.99792458 108 m/s (speed of light)
• (often rounded to 3.00 108 m/s)

• Classical physics
• Matter is a particle
• Light is a wave

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3) The Electromagnetic Spectrum

• The electromagnetic spectrum is largely invisible
  to the eye
• Sunburned skin is a sign of too much ultraviolet
  radiation
• Our bodies absorb visible light, but transmit
  most X rays
• Window glass transmits visible light, but absorbs
  ultraviolet radiation

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4) Continuous Spectrum

• l 650 nm
• 575 nm
• l 500 nm
• l 480 nm
• l 450 nm

• White light passed through a prism produces a
  spectrum of rainbow colors in continuous spectra.
• The different colors of light correspond to
  different wavelengths (also frequencies)

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5) Line Spectrum
Emission spectrum of H

• A discontinuous spectrum, the light emitted from
  excited atoms of an element is call a line
  spectrum.
• Line spectra cant be explained using classical
  physics

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6) Line Spectra of Some Elements

• The pattern of lines emitted by excited atoms of
  an specific element is unique.
• The line emission spectrum of an element is a
  fingerprint for that element, and can be used
  to identify the element

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Example 7.1 Calculate the frequency of an X ray
that has a wavelength of 8.21 nm.
Solution
Ans
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• Photons Energy by the Quantum
• 1) Plancks Quantum Hypothesis

• Max Planck proposed that the vibrating atoms in a
  heated solid (black body) could emit
  electromagnetic energy only in discrete amounts.
• The smallest amount of energy, a quantum, is
• E h?
• h 6.626 1034 J s (Plancks constant)
• Energy can be absorbed or emitted only as a
  quantum or as whole multiples of a quantum, that
  is, 1 hv, 2 hv, 3 hv etc

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2) Photoelectric Effect by Albert Einstein
Animation

• Einstein proved electromagnetic energy to be
  bundled in to little packets called photons
• E hv
• The energy of one mole of photons
• E NA hv
• The minimum value of the frequency to eject the
  electron called threshold frequency

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3) Wave-Particle Duality of Light

• Wave like behavior light is dispersed into
  spectrum by a prism
• Particle like behavior photons displace
  electrons from a metal in the photoelectric effect

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Example 7.3 Calculate the energy, in joules, of a
photon of violet light that has a frequency of
6.15 x 1014 s1.
Solution
Ans
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Example 7.4 A laser produces red light of
wavelength 632.8 nm. Calculate the energy, in
kilojoules, of 1 mol of photons of this red light.
Solution
Ans
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• Quantum View of Atomic Structure
• (1) Bohrs Hydrogen Atom A Planetary Model
• 1) Bohrs Proposal

• Niels Bohr proposed the electron energy of
  hydrogen atom is quantized
• Each specified electron energy value, called an
  energy level (En), of the atom

n an integer, RH 2.179 x 1018 J (Rydberg
constant)

• When the electron is located infinitely far from
  nucleus En 0
• The sign represents attraction forces

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2) The Bohr Model of Hydrogen
Keywords Absorption Emission Ground
state Excited state Transition
e
Line Spectra Arise
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3) Bohrs Explanation of H atom Line Spectra

• Bohrs Equation

?E energy change of an electron from initial
energy level to final energy level Ef final
energy level Ei initial energy level RH 2.179
x 1018 J

• Energy of H(g) from n 1 to n 8, ?E 2.179 x
  1018 J/atom, It is the ionization energy of the
  H(g)
• Also, ?E h? (h 6.626 1034 Js)
• Bohrs theory is limited for one-electron
  species, such as H, He, and Li2

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4) Energy Levels and Spectral Lines for H Atom
Visible and ultraviolet
Infrared
Ultraviolet

• The larger ?E, the higher ?, the shorter ?

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Example 7.6 Calculate the energy change, in
joules, that occurs when an electron falls from
the ni 5 to the nf 3 energy level in a
hydrogen atom.
Solution
Ans
Example 7.7 Calculate the frequency of the
radiation released by the transition of an
electron in a hydrogen atom from the n 5 level
to the n 3 level.
Solution
Ans
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• Wave Mechanics Matter as Waves
• 1) Wave-Particle Duality of Electron

• Particle like behavior photoelectric effect, and
  Bohrs model of quantized electron energy level
• Wave like behavior De Broglies prediction and
  the diffraction phenomenon of electron

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2) De Broglies Equation

• Louis de Broglie proposed that matter can behave
  as both particles and waves, just like light
• The wavelength of a particle (such as an
  electron) given by

? wavelength h Plancks constant m mass of
the particle v moving speed of the particle
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3) Heisenbergs Uncertainty Principle

• We cant know exactly position and motion of a
  particle simultaneously

?x uncertainty of position ?p uncertainty of
momentum (p mv)

• Bohrs H model violated uncertainty principle
  Bohrs model trying to specify both the position
  and energy of a electron, simultaneously
• Uncertainty is better expressed by probability

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• Quantum Mechanics (Wave Mechanics)
• Schrödinger (wave) equation

• A fundamental equation developed by Erwin
  Schrödinger that established the mathematics of
  quantum mechanics.
• The equation describes the wavelike properties of
  a subatomic particle, such as an electron in
  hydrogen atom

• Wave Functions (?)

• An acceptable solution to Schrödinger equation
  that states the location of an electron at a
  given point in space and each wave function ? is
  associated with a particular energy E.
• The square of a wave function (?2) gives the
  probability of finding an electron at a given
  point in space.
• Quantum mechanics is applied to explain the
  wave-particle duality behavior for many-electron
  atoms

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(3) Quantum Numbers and Atomic Orbitals

• Quantum Numbers
• Solving a Schrödinger equation, in other words, a
  wave function contain three parameters that have
  specific integral values called quantum numbers
  (n, l, and ml).
• A wave function with a given set of three quantum
  numbers is called an atomic orbital.
• These orbitals allow us to visualize a
  three-dimension region which describe the
  probability of finding an electron.
• A fourth quantum number, called electron spin
  quantum number (ms), describe the magnetic moment
  of the orbitals
• Each electron in a atom is described by its
  unique set of four quantum number.

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• The Principal Quantum Number (n)
• n 1, 2, 3, .....(positive integer)
• Determines the size and the energy level of the
  atomic orbital
• All orbitals with same value of n constitute a
  (principal) shell

• 3) The Angular Momentum Quantum Number (?)
• ? 0, 1, 2,...., n1
• Determines the shape of the orbital
• All orbitals with the same value of n and the
  same value of ? constitute a subshell
• Value of ? 0 1 2 3
• Orbital (subshell) designation s p d f

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• 4) The Magnetic Quantum Number (m? )
• m? ? , ?1, ..., 0, ..., ?2, ?1, ?
• Determines the orientation in space of the
  orbitals of any given type in a subshell

5) Quantum Number Summary
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Example 7.10 Considering the limitations on
values for the various quantum numbers, state
whether an electron can be described by each of
the following sets. If a set is not possible,
state why not. (a) n 2, l 1, ml 1 (c) n
7, l 3, ml 3 (b) n 1, l 1, ml 1 (d) n
3, l 1, ml 3
Solution
(a) All the quantum numbers are allowed
values. (b) Not possible. The value of l must be
less than the value of n. (c) All the quantum
numbers are allowed values. (d) Not possible. The
value of ml must be in the range l to l (in
this case, 1, 0, or 1).
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6) Electron Probabilities and the Shapes of
Orbitals
(A) 1s Orbital (n 1, l 0, m? 0)

• Boundary surface diagram (encloses 90
  probability of the total electron)
• Two-dimensional cross-section dots plot
• Plot of an electron probability (?2) versus
  distance from the nucleus (r), at a given point
• Plot of total electron probability (4pr2?2)
  versus distance from the nucleus (r), the peak
  corresponds to the most probable radius for the
  electron.

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(B) 2s Orbital (n 2, l 0, m? 0)

• Two regions of high electron probability, both
  being spherical
• Node the region of zero electron probability

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(C) The Three p Orbitals (l 1, m? 1, 0, 1)
Three values of m? gives three p orbitals in the
p subshell
m? 1
m? 1
m? 0

• First principal shell to have p subshell
  correspond to n 2.

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(D) The Five d Orbitals (l 2, m? 2, 1, 0,
1, 2)
Five values of m? gives five d orbitals in the d
subshell

• First principal shell to have d subshell
  correspond to n 3.

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Example 7.11 Consider the relationship among
quantum numbers and orbitals, subshells, and
principal shells to answer the following. (a) How
many orbitals are there in the 4d subshell? (b)
What is the first principal shell in which f
orbitals can be found? (c) Can an atom have a 2d
subshell? (d) Can a hydrogen atom have a 3p
subshell?
Solution
(a) Five. (b) n 4 (c) No (d) Yes, 3p is an
excited state orbital of hydrogen
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• The Electron Spin Quantum Number (ms)

• Refers to a magnetic field induced by the moving
  electric charge of the electron as it spins
• Applied to explain the finer features of atomic
  emission spectra
• Two possible values 1/2(?) and 1/2(?)
• The magnetic fields of two electrons with
  opposite spins cancel one another

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• The Stern-Gerlach Experiment Demonstrates
  Electron Spin

Beam of Ag atoms 24 ½-spin electrons and 23
½-spin electrons
Beam of Ag atoms 23 ½-spin electrons and 24
½-spin electrons.
Ag has 47 electrons (odd number),
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End of Chapter 07