Ch'4 The Electronic Structure of Atoms

1
The Electronic Structure of Atoms
4.1 The Electromagnetic Spectrum 4.2 Deduction of
Electronic Structure from Ionization
Enthalpies 4.3 The Wave-mechanical Model of the
Atom 4.4 Atomic Orbitals
2
The electronic structure of atoms
Chapter 4 The electronic structure of atoms (SB
p.80)
Niels Bohr
Bohrs model of H atom
3
The electronic structure of atoms
Chapter 4 The electronic structure of atoms (SB
p.80)
Niels Bohr
Bohrs model of H atom
4
The electromagnetic spectrum
4.1 The electromagnetic spectrum (SB p.82)
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Continuous spectrum of white light
4.1 The electromagnetic spectrum (SB p.82)
Fig.4-5(a)
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Line spectrum of hydrogen
4.1 The electromagnetic spectrum (SB p.83)
Fig.4-5(b)
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The emission spectrum of atomic hydrogen
4.1 The electromagnetic spectrum (SB p.83)
UV
Visible
IR
Let's Think 1
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Interpretation of the atomic hydrogen spectrum
4.1 The electromagnetic spectrum (SB p.84)
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Interpretation of the atomic hydrogen spectrum
4.1 The electromagnetic spectrum (SB p.84)
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Interpretation of the atomic hydrogen spectrum
4.1 The electromagnetic spectrum (SB p.84)
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4.1 The electromagnetic spectrum (SB p.85)
Bohr proposed for a hydrogen atom
1. An electron in an atom can only exist in
certain states characterized by definite energy
levels (called quantum).
2. Different orbits have different energy levels.
An orbit with higher energy is further away
from the nucleus.
3. When an electron jumps from a higher energy
level (of energy E1) to a lower energy level (of
energy E2), the energy emitted is related to the
frequency of light recorded in the emission
spectrum by ?E E1 - E2 h?
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4.1 The electromagnetic spectrum (SB p.86)
How can we know the energy levels are getting
closer and closer together?
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4.1 The electromagnetic spectrum (SB p.87)
?E E1 - E2 h?
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4.1 The electromagnetic spectrum (SB p.87)
Emission spectrum of hydrogen
Absorption spectrum of hydrogen
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Production of the absorption spectrum
4.1 The electromagnetic spectrum (SB p.87)
Absorption spectrum of hydrogen
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Convergence limits and ionization
4.1 The electromagnetic spectrum (SB p.87)
What line in the H spectrum corresponds to this
electron transition (n 8 ? n1)?
Last line in the Lyman Series
For n8 ? n1
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4.1 The electromagnetic spectrum (SB p.87)
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The uniqueness of atomic emission spectra
4.1 The electromagnetic spectrum (SB p.89)
No two elements have identical atomic spectra
?atomic spectra can be used to identify unknown
elements.
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Deduction of Electronic Structure from Ionization
Enthalpies
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Ionization enthalpy
4.2 Deduction of electronic structure from
ionization enthalpies (p.91)
Ionization enthalpy (ionization energy) of an
atom is the energy required to remove one mole of
electrons from one mole of its gaseous atoms to
form one mole of gaseous positive ions.
The first ionization enthalpy M(g) ? M(g)
e- ?H 1st I.E.
The second ionization enthalpy M(g) ? M2(g)
e- ?H 2nd I.E.
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Evidence of shells
4.2 Deduction of electronic structure from
ionization enthalpies (p.91)
? shells
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Evidence of sub-shells
4.2 Deduction of electronic structure from
ionization enthalpies (p.91)
? subshells
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The Wave-mechanical Model of the Atom
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Bohrs atomic model and its limitations
4.3 The Wave-mechanical model of the atom (p.94)
Bohr considered the electron in the H atom (a
one-electron system) moves around the nucleus in
circular orbits.
Basing on classical mechanics, Bohr calculated
values of frequencies of light emitted for
electron transitions between such orbits.
The calculated values for the frequencies of
light matched with the data in the emission
spectrum of H.
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4.3 The Wave-mechanical model of the atom (p.94)
Bohr tried to apply similar models to atoms of
other elements (many-electron system), e.g. Na
atom.
Basing on classical mechanics, Bohr calculated
values of frequencies of light emitted for
electron transitions between such orbits.
The calculated values for the frequencies of
light did NOT match with the data in the emission
spectra of the elements.
? The electron orbits in atoms may NOT be simple
circular path.
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Wave nature of electrons
4.3 The Wave-mechanical model of the atom (p.95)
A beam of electrons shows diffraction phenomenon

• Electrons possess wave properties
• (as well as particle properties).

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Wave nature of electrons
4.3 The Wave-mechanical model of the atom (p.95)
Schrödinger used complex differential
equations/wave fucntions to describe the wave
nature of the electrons inside atoms (wave
mechanic model).
The solutions to the differential equations
describes the orbitals of the electrons inside
the concerned atom.
An orbital is a region of space having a high
probability of finding the electron.
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Quantum numbers
4.3 The Wave-mechanical model of the atom (p.95)
Electrons in orbitals are specified with a set of
numbers called Quantum Numbers 1. Principal
quantum number (n) n 1, 2, 3, 4,
... 2. Subsidiary quantum number (l)
l 0, 1, 2, 3, n-1 s p d
f 3. Magnetic quantum number (m) m
-l, , 0, l 4. Spin quantum number (s)
s ½, -½
The solutions of the wave functions are the
orbitals -- which are themselves equations
describing the electrons.
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4.3 The Wave-mechanical model of the atom (p.96)
8
18
32
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4.3 The Wave-mechanical model of the atom (p.97)
3d
4s
3p
3s
2p
2s
Each orbital can accommodate 2 electrons with
opposite spin.
1s
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Atomic Orbitals
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s Orbitals
4.4 Atomic orbitals (p.98)
Graph of probability of finding an electron
against distance from nucleus
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s Orbitals
4.4 Atomic orbitals (p.98)
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p Orbitals
4.4 Atomic orbitals (p.100)
The shapes and orientations of 2px, 2py and 2pz
orbitals
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d Orbitals
4.4 Atomic orbitals (p.101)
The shapes and orientations of 3dxy, 3dyz,
3dx2-y2 and 3dz2 orbitals
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The END
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4.1 The electromagnetic spectrum (SB p.82)
Let's Think 1
Some insects, such as bees, can see light of
shorter wavelengths than humans can. What kind of
radiation do you think a bee sees?
Answer
Ultraviolet radiation
Back
38
4.1 The electromagnetic spectrum (SB p.87)
Let's Think 2
What does the convergence limit in the Balmer
series correspond to?
Answer
The convergence limit in the Balmer series
corresponds to the energy required for the
transition of an electron from n 2 to n ?.
Back
39
4.1 The electromagnetic spectrum (SB p.88)
Example 4-1A
Given the frequency of the convergence limit of
the Lyman series of hydrogen, find the ionization
enthalpy of hydrogen. Frequency of the
convergence limit 3.29 ? 1015 Hz Planck
constant 6.626 ? 10-34 J s Avogadro constant
6.02 ? 1023 mol-1
Answer
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4.1 The electromagnetic spectrum (SB p.88)
Back
Example 4-1A
For one hydrogen atom, E h? 6.626 ? 10-34
J s ? 3.29 ? 1015 s-1 2.18 ? 10-18 J For
one mole of hydrogen atoms, E 2.18 ? 10-18 J ?
6.02 ? 1023 mol-1 1312360 J mol-1
1312 kJ mol-1 The ionization enthalpy of hydrogen
is 1312 kJ mol-1.
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4.1 The electromagnetic spectrum (SB p.88)
Example 4-1B
The emission spectrum of atomic sodium is
studied. The wavelength of the convergence limit
corresponding to the ionization of a sodium atom
is found. Based on this wavelength, find the
ionization enthalpy of sodium. Wavelength of the
convergence limit 242 nm Planck constant
6.626 ? 10-34 J s Avogadro constant 6.02 ? 1023
mol-1 Speed of light 3 ? 108 m s-1 1 nm 10-9 m
Answer
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4.1 The electromagnetic spectrum (SB p.88)
Back
Example 4-1B
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4.1 The electromagnetic spectrum (SB p.90)
Check Point 4-1

• The first line of the Balmer series of the
  emission spectrum of atomic hydrogen corresponds
  to the energy emitted in the transition of an
  electron from the third energy level to the
  second energy level. It has a wavelength of 656.3
  nm. What is the energy difference between the
  second and the third energy levels?
• (Planck constant 6.626 ? 10-34 Js, Avogadro
  constant 6.02 ? 1023 mol-1)

Answer
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4.1 The electromagnetic spectrum (SB p.90)
Check Point 4-1
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4.1 The electromagnetic spectrum (SB p.90)
Check Point 4-1
(b) Given that the frequency of the convergence
limit corresponding to the ionization of helium
is 5.29 ? 1015 Hz, calculate the ionization
enthalpy of helium. (Planck constant 6.626 ?
10-34 Js, Avogadro constant 6.02 ? 1023
mol-1)
Answer

• For 1 mole of helium atoms,
• I.E. hvL
• 6.626 ? 10-34 J s ? 5.29 ? 1015
  s-1 ? 6.02 ? 1023 mol-1
• 2.11 ? 106 J mol-1
• 2110 kJ mol-1

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4.1 The electromagnetic spectrum (SB p.90)
Check Point 4-1
(c) The blue colour in fireworks is often
achieved by heating copper(I) chloride (CuCl) to
about 1200 oC. The compound then emits blue light
with a wavelength of 450 nm. What is the energy
released per copper(I) ion at the specified
condition?
Answer
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4.1 The electromagnetic spectrum (SB p.90)
Check Point 4-1

• Name the element present in the sample when the
  following flame colours are observed in flame
  tests.
• (i) Golden yellow
• (ii) Lilac
• (iii) Brick-red
• (iv) Bluish green

(d) (i) Sodium (ii) Potassium (iii)
Calcium (iv) Copper
Answer
Back
48
4.2 Deduction of electronic structure from
ionization enthalpies (p.94)
Check Point 4-2

• Given the successive ionization enthalpies of
  boron, plot a graph of the logarithm of
  successive ionization enthalpies of boron against
  the number of electrons removed. Comment on the
  graph obtained.
• Successive I.E. (in kJ mol-1) 800, 2400, 3700,
  25000, 32800

Answer
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4.2 Deduction of electronic structure from
ionization enthalpies (p.94)
Check Point 4-2
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4.2 Deduction of electronic structure from
ionization enthalpies (p.94)
Check Point 4-2
(b) Give a rough a sketch of the logarithm of
successive ionization enthalpies of potassium.
Explain your sketch.
Answer
51
4.2 Deduction of electronic structure from
ionization enthalpies (p.94)
Check Point 4-2
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4.2 Deduction of electronic structure from
ionization enthalpies (p.94)
Check Point 4-2

• There is always a drastic increase in ionization
  enthalpy whenever electrons are removed from a
  completely filled electron shell. Explain
  briefly.

Answer
(c) A completely filled electron shell has extra
stability. Once an electron is removed, the
stable electronic configuration will be
destroyed. Therefore, a larger amount of energy
is required to remove an electron from such a
stable electronic configuration.
Back
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4.3 The Wave-mechanical model of the atom (p.97)
Back
Check Point 4-3

• What are the limitations of Bohrs atomic model?
• Explain the term dual nature of electrons.
• (c) For principal quantum number 4, how many
  sub-shells are present? What are their symbols?

Answer
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4.4 Atomic orbitals (p.101)
Check Point 4-4

• Distinguish between the terms orbit and orbital.
• Sketch the pictorial representations of an s
  orbital and a p orbital. What shapes are they?

Answer
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4.4 Atomic orbitals (p.101)
Back
Check Point 4-4

• How do the 1s and 2s orbitals differ from each
  other?
• How do the 2p orbitals differ from each other?

Answer