Matter and Measurement

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CHAPTER 7 Atomic Structure

• Road Map
• Test 2 Extra credit Collection

2
Equations

• speed of light wavelength x frequency
• c ? X ? 3.00 x 108 m/s
• E nh? nh(c/?) n positive integer
• Plancks constant(h) 6.626 x 1034 J s
• ?Eatom Eemitted (or absorbed) radiation ?nh?
• Rydberg equation R
• n2 gt n1
• R 1.096776 x 107 m-1
• ?E Efinal Einitial 2.18 x 1018 J
• Ephoton Estate A Estate B h?

3
Old Dead Dudes

• Planck blackbody radiation hot glowing object
  emit or absorb certain discrete quanta of energy
• Bohr one electron model spectral lines
  explained e- motion restricted to fixed orbits
• Einstein explained photoelectric effect - flow
  of current when monochromatic light of sufficient
  energy hits an object
• Rydberg predicted energy levels

4
Practice Problem 21-1

• The frequency of electromagnetic radiation of
  wavelength 5.6 mm is
• A) 5.4 x 107 Hz
• B) 1.9 x 10-11 Hz
• C) 5.4 x 1010 Hz
• D) 1.1 x 108 Hz
• E) none of the above

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Practice Problem 21-1 Answer

• The frequency of electromagnetic radiation of
  wavelength 5.6 mm is
• A) 5.4 x 107 Hz
• B) 1.9 x 10-11 Hz
• C) 5.4 x 1010 Hz
• D) 1.1 x 108 Hz
• E) none of the above

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Practice Problem 21-2 (7.12) Answer

• 7.12 540 nm (10-9m/1nm) 5.4 ? 107 m
• E
• 3.7 ? 1019 J/photon
• This radiation does not have enough energy(6.7
  x 10-19 J/atom) to activate the switch. This is
  also true for radiation with wavelengths greater
  than 540 nm.

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Bohr Model

• Energy of atoms quantized photon emitted when e-
  decreases in orbit
• Spectral line from emission
• Emission - higher to lower energy state
• Absorption lower to higher energy state
• n quantum number
• Lower n smaller radius
• of orbit (space e- circling in)
• Ground state n1
• Excited state ngt1

Quantum staircase
8

• 7.20 Which of these electron transitions
  correspond to absorption of energy and which to
  emission?
• n 2 to n 4
• n 3 to n 1
• n 5 to n 2
• n 3 to n 4

Absorption Emission Emission Absorbtion
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The Bohr explanation of the three series of
spectral lines.
n2 visible
n3 infrared
n1 ultraviolet
Numerous atoms with different excitation states
(n) and subsequent ? of emission
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Practice Problem 21.3

• How much energy is absorbed when an electron is
  excited from the first level to the fourth?

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Practice Problem 21.3 Answer

• How much energy is absorbed when an electron is
  excited from the first level to the fourth?
• 2.04 x 10-18 J

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Practice Problem 21.4

• Calculate the frequency of the light emitted by a
  hydrogen atom during a transition of its electron
  from the n 3 to n 1 energy level, based on
  the Bohr theory.
• A) 2.92 x 1015 s-1 B) 1.94 x 10-18 s-1
• C) 3.21 x 1015 s-1 D) 3.05 x 10-15 s-1
• E) Not enough information given to calculate
  answer.

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Practice Problem 21.4 Answer

• Calculate the frequency of the light emitted by a
  hydrogen atom during a transition of its electron
  from the n 3 to n 1 energy level, based on
  the Bohr theory.
• A) 2.92 x 1015 s-1 B) 1.94 x 10-18 s-1
• C) 3.21 x 1015 s-1 D) 3.05 x 10-15 s-1
• E) Not enough information given to calculate
  answer.

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The Quantum-Mechanical Model of the Atom

• Acceptance of the dual nature of matter and
  energy and of the uncertainty principle
  culminated in the field of quantum mechanics,
  which examines the wave motion of objects on the
  atomic scale. In 1926, Erwin Schrödinger derived
  an equation that is the basis for the
  quantum-mechanical model of the hydrogen atom.

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The Quantum-Mechanical Model of the Atom The
Atomic Orbital and the Probable Location of the
Electron

• Each solution to the equation is associated with
  a given wave function, also called an atomic
  orbital. Its important to keep in mind that an
  orbital in the quantum-mechanical model bears
  no resemblance to an orbit in the Bohr model
  an orbit was an electrons path around the
  nucleus, whereas an orbital is a mathematical
  function with no direct physical meaning.

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Quantum Numbers and Atomic Orbitals

• An atomic orbital is specified by three quantum
  numbers.
• n the principal quantum number distance from
  nucleus (size) n 1,2,3
• l the angular momentum quantum number shape l
  0 to n-1
• ml the magnetic moment quantum number orbital
  orientation ml -l to l

.
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• n LEVELS
• Smaller n, the lower the energy level the greater
  the probability of the electron being closer to
  the nucleus
• l orbital shape
• l 0 s spherical
• l 1 p dumb bell crash and burn, Fig 7.18
• l 2 d cloverleaf, Fig 7.19
• l 3 f too complicated

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The Quantum-Mechanical Model of the Atom
Quantum Numbers of an Atomic Orbital

• Sublevel (subshell) designate the orbital
  shape. Each sublevel has a letter designation
• l 0 is an s sublevel
• l 1 is a p sublevel.
• l 2 is a d sublevel.
• l 3 is an f sublevel.
• Orbital. Each allowed combination of n, l, and
  ml values specifies one of the atoms orbitals.
  Thus, the three quantum numbers that describe an
  orbital express its size (energy), shape, and
  spatial orientation .
• The total number of orbitals for a given n value
  is n2.

Smart People Dont Fail
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The Quantum-Mechanical Model of the Atom Shapes
of Atomic Orbitals

• Orbitals with Higher l Values
• Orbitals with l 3 are f orbitals and must have
  a principle quantum number of at least n 4.
  There are seven f orbitals (2l 1 7), each
  with a complex, multi-lobed shape.

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The Quantum-Mechanical Model of the Atom Energy
Levels of the Hydrogen Atom

• The energy state of the H atoms depends on the
  principal quantum number n only.

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CLASSICAL THEORY
Matter particulate, massive
Energy continuous, wavelike
Summary of the major observations and theories
leading from classical theory to quantum theory.
Observation
Theory
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Practice Problem 21.5 Determining Quantum Numbers
for an Energy Level
PLAN
Follow the rules for allowable quantum numbers
found in the text.
l values can be integers from 0 to n-1 ml can
be integers from -l through 0 to l.
SOLUTION
For n 3, l 0, 1, 2
For l 0 ml 0
For l 1 ml -1, 0, or 1
For l 2 ml -2, -1, 0, 1, or 2
There are 9 ml values and therefore 9 orbitals
with n 3.
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Practice Problem 21.6 Determining Sublevel Names
and Orbital Quantum Numbers
Give the name, magnetic quantum numbers, and
number of orbitals for each sublevel with the
following quantum numbers
PROBLEM
(a) n 3, l 2
(b) n 2, l 0
(c) n 5, l 1
(d) n 4, l 3
PLAN
Combine the n value and l designation to name the
sublevel. Knowing l, we can find ml and the
number of orbitals.
SOLUTION
n
l
sublevel name
possible ml values
of orbitals
(a)
2
3d
-2, -1, 0, 1, 2
3
5
(b)
2
0
2s
0
1
(c)
5
1
5p
-1, 0, 1
3
(d)
4
3
4f
-3, -2, -1, 0, 1, 2, 3
7
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Practice Problem 21.7 What is wrong with this
picture, or complete the name.

• n l ml name
• 1 1 0 1p
• 4 3 1 4d
• 3 2 -2 ?
• ? ? ? 2s
• 2 1 0 ?
• 3 1 -2 3p

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The Quantum-Mechanical Model of the Atom
Quantum Numbers of an Atomic Orbital

• The energy states and orbitals of the atom are
  described with specific terms and associated with
  one or more quantum numbers.
• Level (n). The atoms energy levels, or shells,
  are given by the n value the smaller the n
  value, the lower the energy level and the greater
  the probability of the electron being closer to
  the nucleus.

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The Quantum-Mechanical Model of the Atom
Quantum Numbers of an Atomic Orbital

• Sublevel (l). The atoms levels contain
  sublevels, or subshells, which designate the
  orbital shape. Each sublevel has a letter
  designation
• l 0 is an s sublevel
• l 1 is a p sublevel.
• l 2 is a d sublevel.
• l 3 is an f sublevel.

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The Quantum-Mechanical Model of the Atom
Quantum Numbers of an Atomic Orbital

• Orbital (ml ). Each allowed combination of n, l,
  and ml values specifies one of the atoms
  orbitals. Thus, the three quantum numbers that
  describe an orbital express its size (energy),
  shape, and spatial orientation .

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Practice Problem 21-8

• What value or values of ml are allowable for an
  orbital with l 2?
• A) 0
• B) 2
• C) -1
• D) none of the above
• E) all of the above

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Practice Problem 21-8 Answer

• What value or values of ml are allowable for an
  orbital with l 2?
• A) 0
• B) 2
• C) -1
• D) none of the above
• E) all of the above

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The Quantum-Mechanical Model of the Atom Shapes
of Atomic Orbitals

• The s Orbital
• An orbital with l 0 has a spherical shape with
  the nucleus at its center and is called an s
  orbital.
• The 2s orbital (Figure 7.17B) has two regions of
  higher electron density. Between the two regions
  is a spherical node, a shell-like region where
  the probability drops to zero.

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Practice Problem 21-9

• The nodes for a 3s atomic orbital are
• A) two points near the nucleus and another point
  at an infinite distance from the nucleus.
• B) three spherical solids.
• C) one plane and two spheres.
• D) two concentric circles.
• E) two concentric spheres.

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Practice Problem 21-9 Answer

• The nodes for a 3s atomic orbital are
• A) two points near the nucleus and another point
  at an infinite distance from the nucleus.
• B) three spherical solids.
• C) one plane and two spheres.
• D) two concentric circles.
• E) two concentric spheres.

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The Quantum-Mechanical Model of the Atom Shapes
of Atomic Orbitals

• The p Orbital
• An orbital with l 1 has two regions (lobes) of
  high probability, one on either side of the
  nucleus, and is called a p orbital. In Figure
  7.18, the nucleus lies at the nodal plane of this
  dumbbell-shaped orbital. Keep in mind that one
  p orbital consists of both lobes and that the
  electron spends equal time in both.

34
The Quantum-Mechanical Model of the Atom Shapes
of Atomic Orbitals

• The p Orbital
• Since there are three ml values, these describe
  the three mutually perpendicular orientations in
  space. Unlike an s orbital, each p orbital does
  have a specific orientation in space. The l 1
  value has three possible ml values 1, 0, and
  1, which refer to three mutually perpendicular p
  orbitals. They are identical in size, shape, and
  energy, differing only in orientation.

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The Quantum-Mechanical Model of the Atom Shapes
of Atomic Orbitals

• The d Orbital
• An orbital with l 2 is called a d orbital.
  There are five possible ml values for the l 2
  value 2, 1, 0, 1, 2.
• Thus, a d orbital can have any one of five
  orientations, as shown in Figure 7.19.

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The Quantum-Mechanical Model of the Atom Shapes
of Atomic Orbitals

• Orbitals with Higher l Values
• Orbitals with l 3 are f orbitals and must have
  a principle quantum number of at least n 4.
  There are seven f orbitals (2l 1 7), each
  with a complex, multilobed shape Figure 7.20
  shows one of them.

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Practice Problem 21-10

• According to the quantum-mechanical model, how
  many orbitals in a given atom have n 3?
• A) 4
• B) 7
• C) 9
• D) 10
• E) 18

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Practice Problem 21-10 Answer

• According to the quantum-mechanical model, how
  many orbitals in a given atom have n 3?
• A) 4
• B) 7
• C) 9
• D) 10
• E) 18

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Next Lesson

• Chapter 8