Chapter. 5: Electrons in Atoms

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Chapter. 5 Electrons in Atoms

• Section 5.1 Light Quantized Energy
• Section 5.2 Quantum Theory the Atom

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Objectives

• Identify the inadequacies in the Rutherford
  atomic model.
• Identify the new assumption in the Bohr model of
  the atom.
• Describe the energies and positions of electrons
  according to the quantum mechanical model.
• Describe how the shapes of orbitals at different
  sublevels differ.

3
Recall . . .

• Rutherfords nuclear atomic model
• The atom is mostly empty space.
• All of an atoms positive charge and almost all
  of its mass are concentrated in a central
  structure called the nucleus.
• Fast-moving electrons are found in the space
  surrounding the nucleus.

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Unanswered Questions

• Rutherfords atomic model was incomplete.
• Why werent the negatively charged electrons
  pulled into the positively charged nucleus?
• How were electrons arranged around the nucleus?
  
• How does the model explain differences in
  chemical behavior between elements?

5
More Unanswered Questions

• In the early 1900s, scientists found that
  certain elements emitted visible light when
  heated in a flame. Different elements emitted
  different colors of light.
• Rutherfords model could not explain this either!

Fluorine
Copper
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The Development of Atomic Models

• In 1913, Neils Bohr (who was working for
  Rutherford) believed Rutherfords model needed
  improvement.

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Bohrs Atomic Model

• Bohr proposed that an electron is found only in
  specific circular paths, or orbits, around the
  nucleus.

Bohrs model came to be known as the planetary
model.
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Bohrs Atomic Model

• Each possible electron orbit had a fixed amount
  of energy that was called the electrons energy
  level.
• The closer the orbit
• was to the nucleus,
• the smaller the orbit
• was AND the lower
• the electrons
• energy level.

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The Planetary Model

• In Bohrs model, the lowest allowable energy
  state is called the ground state.
• When an atom gains energy, it is said to be in an
  excited state. Many excited states are
  possible.

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Bohrs Atomic Model

• To become excited and move from one energy
  level to another, an electron had to gain or lose
  just the right amount of energy.
• A quantum of energy is the amount of energy
  required to move an electron from one energy
  level to another energy level.

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An Analogy

• Think of each quantum of energy as a step in a
  staircase.
• To walk up the staircase, you move up one step at
  a time. You do not move up a 1/2 step or 1 1/2
  steps.
• When an electron increases in energy, it
  increases 1 quantum (or 1 energy level) at a time.

Quanta
4 3 2 1 0
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Bohrs Atomic Model

• The Bohr model gave results in agreement with
  experimental data for the hydrogen atom.
• But it still failed to explain the energies
  absorbed and emitted by atoms with more than one
  electron.

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The Development of Atomic Models

• Erwin Shrödinger (1887-1961) devised and solved a
  mathematical equation to describe the motion of
  electrons.
• The modern description of the electrons in atoms,
  the quantum mechanical model, comes from the
  mathematical solutions of Schrödingers equation.

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The Quantum Mechanical Model

• The energy levels of electrons in the quantum
  mechanical model are labeled by principal quantum
  numbers (n).
• These are assigned the values n1,2,3,4,5,6

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The Quantum Mechanical Model

• An electrons path around the nucleus is not
  circular but is described in terms of
  probability. The probability of finding an
  electron in various locations around the nucleus
  can be pictured in terms of a blurry cloud of
  negative charge.

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Quantum Mechanical Model

• The cloud is most dense where the probability of
  finding the electron is highest.
• An imaginary boundary of the electron cloud
  encloses the area that has a 90 probability of
  containing electrons.

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Quantum Mechanical Model

• Because electrons have different energies, they
  are found in different probable locations around
  the nucleus.
• An atomic orbital is a 3-d region around the
  nucleus of an atom where an electron with a given
  energy is likely to be found.
• For each principal energy level, there are
  several orbitals with different shapes, sizes,
  and energies.

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Quantum Mechanical Model

• Each principal energy level consists of one or
  more sublevels . . .
• As n increases, the of sublevels increases as
  does their distance from the nucleus.

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Quantum Mechanical Model
Sublevels are labeled s, p, d, or f, according to
the shapes of their orbitals. For n1, there is
one sublevel. It is called s. For n2, there
are 2 sublevels. They are called s and
p. For n3, there are 3 sublevels. They are
called . . . .?
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Quantum Mechanical Model
Each type of sublevel consists of one or more
orbitals.

• There is 1 s orbital
• There are 3 p orbitals
• There are 5 d orbitals
• There are 7 f orbitals

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Quantum Mechanical Model

• All s orbitals are spherical.
• Each energy level has a s orbital. They will
  differ in size.

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Atomic Orbitals

• p orbitals have a dumbbell shape.
• There are 3 p orbitals in each energy level
  that contains p orbitals. This is because
  there are 3 orientations that the p orbital can
  have in space.

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Atomic Orbitals

• d and f orbitals have very complex shapes
  with many different orientations.
• There are 5 possible d orbitals and 7
  possible f orbitals.

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Quantum Mechanical Model

• Review
• The principal energy level or principal quantum
  number is designated by n.
• The number of sublevels in a principal energy
  level is always equals the quantum number n.
• Sublevels have letter designations (s, p, d, or
  f), depending on the shapes of the orbitals found
  there.

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Review of Sublevels

• The lowest principal energy level (n1) has 1
  sublevel and it is called 1s. The second
  principal energy level (n2) has 2 sublevels, 2s
  and 2p.
• The 2p sublevel is of higher energy than the 2s.
• 2p consists of 3 p orbitals of equal energy.
• The 2nd principal energy level, therefore, has 4
  orbitals, 1 2s and 3 2ps.

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Review of Sublevels

• The third principal energy level (n3) has 3
  sublevels - 3s, 3p, and 3d.
• The 3d orbitals are of higher energy than the 3p.
• 3d consists of 5 equal energy orbitals.
• The 3rd principal energy level, therefore, has a
  total of 9 orbitals (1 3s, 3 3ps, and 5 3ds)

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Review of Sublevels

• The fourth principal energy level (n4) has 4
  sublevels - 4s, 4p, 4d, and 4f.
• The 4f orbitals are of higher energy than the 4d.
• 4f consists of 7 equal energy orbitals.
• The 4th principal energy level, therefore, has a
  total of 16 orbitals (1 4s, 3 4ps, 5 4ds and 7
  4fs).

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Orbitals and Energy
An orbital diagram
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Quantum Mechanical Model

• The number of sublevels always equals the quantum
  number n.
• The number of orbitals in each sublevel is always
  an odd number s has 1 orbital p has 3 orbitals
  d has 5 orbitals f has 7 orbitals.
• The total number of orbitals in each energy level
  n2 (In n 3, there are 9 orbitals 1 s, 3 ps
  , and 5 ds.)
• Each orbital may contain at most 2 electrons.
• Therefore, the maximum number of electrons in
  each energy level 2n2.

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Orbitals and Energy
Maximum Electron Numbers for Principal Maximum Electron Numbers for Principal
Energy Level n Max. of electrons
1 2
2 8
3 18
4 32