Chapter 7: Atomic Structure
Chapter 7 Problem Set
Pages 326-329
21, 23, 25, 29, 31, 34, 43, 45, 49, 54, 55, 57, 64, 65, 76, 78
7.1
ELECTROMAGNETIC RADIATION
What is the wavelength of a wave?
What is the frequency  of a wave?
Units for frequency are….
What is the amplitude of a wave?
What are nodes?
What is the velocity of a wave?
In electromagnetic radiation, the product of wavelength and frequency is equal to the speed of
light, c. c = 2.998 x 108 m/s
c = 
EXAMPLE 7L.1
The wavelength of the radiation which produces the yellow color of a sodium vapor light is
589.0 nm. What is frequency of radiation?
Figure 7.3, page 295 Electromagnetic spectrum. Know which types of waves have higher
energies
EXERCISE 7L.1
Orange light has a ________________ frequency and a __________________ wavelength than
blue light.
What are standing or stationary waves?
For standing waves, only certain wavelengths are possible
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7.2
PLANCK, EINSTEIN, ENERGY, AND PHOTONS
Planck’s Equation
Electromagnetic spectrum page 295
Energy increases as frequency increases
Energy increases as wavelength decreases
E  h  or E  h
Planck’s constant
c

h = 6.6261 x 10-34 J ·s
Einstein and the Photoelectric Effect
Photoelectric effect occurs when….
EXAMPLE 7L.2 Calculating Photon Energies
Compare the energy of a mole of photons of blue light (4.00 x 102 nm) with the energy of a
mole of photons of microwave radiation having a frequency of 2.45 GHz. Which has the
greater energy?
7.3
ATOMIC LINE SPECTRA AND NIELS BOHR
What is the continuous spectrum?
What is a line emission spectrum?
Every element has a unique line spectrum
Why do excited gaseous atoms emit light of only certain energies?
What is the Rydberg equation?
1

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R(
1
2
2

1
n
2
)
n 2
Page 2
Rydberg constant R = 1.0974 x 10-7 m-1
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The Bohr Model of the Hydrogen Atom
Bohr introduced notion that energy of the atom was “quantized” (Page 305)
Bohr showed that the potential energy possessed by the single electron in the nth orbit of the
hydrogen atom is given by the simple equation. n = principal quantum number
En  
Rhc
n
2
Rhc = 2.179 x 10-18 J/atom or 1312 kJ/mol
What is the ground state?
What is the excited state?
EXAMPLE 7.3 Page 306 Energies of the Ground States of the H atom
Use Equation 7.4 to calculate the energies of the n = 1 and n = 2 states of the hydrogen atom in
joules per atom and in kilojoules per mole. The values needed to use this equation are
R = 1.0974 x 10-7 m-1 h = 6.6261 x 10-34 J ·s
c = 2.998 x 108 m/s
Rhc = 2.179 x 10-18 J/atom or 1312 kJ/mol
En  
Rhc
n2
EXERCISE 7.4 Page 307 Electron Energies
Calculate the energies of the n = 3 state of the hydrogen atom in:
a. joules per atom
b. kilojoules per mole.
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A major assumption of Bohr’s theory was that an electron in an atom would remain in its
lowest energy level unless disturbed.
The closer the electron is to the nucleus, the greater the force of attraction.
As a result the value of E is more negative as the distance becomes smaller.
Chemists and physicists say that the energy is therefore lower (meaning more negative)
When H has n = 1, which is its ground state, E is a large negative value
To move up to a higher energy level, energy must be absorbed, endothermic, +
Can calculate amount of energy required to carry the H atom from n = 1 to n = 2
 E  E final state  E initialstate
 E  E 2  E1
or
 E  (
Rhc
2
)  (
Rhc
) or E   Rhc (
n 2initial
n final
where Rhc = 1312 kJ/mol
1
2
n final

1
n 2initial
EXAMPLE 7.4 Page 310 Energies of Emission Lines for Excited Atoms
Calculate the wavelength of the green line in the visible spectrum of excited H atoms using
Bohr’s theory. The green line is the second most energetic line in the visible spectrum of
hydrogen (Figure 7.12) and arises from electrons moving from n = 4 to n = 2.
7.4
THE WAVE PROPERTIES OF THE ELECTRON
De Broglie proposed that a free electron of mass m moving with a velocity v should have an
associated wavelength given by the equation:

h
mv
which linked the particle properties of the electron mass and velocity with a wave property.
EXERCISE 7.6 Page 312 De Broglie’s Equation
Calculate the wavelength associated with a neutron having a mass of 1.674 x 10-24g and a
kinetic energy of 6.21 x 10-21J. (KE of a moving particle is E = ½ mv2)
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)
7.5
THE WAVE MECHANICAL VIEW OF THE ATOM
The comprehensive modern day theory about electron behavior comes from Schrödinger and is
known as quantum mechanics or wave mechanics.
The Uncertainty Principle
How can an electron be both a particle and a wave?
What is Heisenberg’s uncertainty principle?
In practical terms the only thing we can do is calculate the probability of finding an electron
with a given energy within a given space.
Schrödinger’s Model of the Hydrogen Atom and Wave Functions
Solutions to the Schrödinger equation called wave functions are chemically important. Page
314. Add as much or as little as you choose.
1. Only certain wave functions are allowed.
2. Each wave function  corresponds to an allowed energy for the electron
3. The energy of the electron is quantized.
4. 2 related to probability of the electron within a given region of space. Scientists refer to
this as the electron density in a given region.
Theory does not predict exact position of the electron. Can only describe the probability of the
electron being at a certain point in space when in a given energy state.
5. The matter waves are called orbitals?
6. To solve Schrödinger,s equation for an electron in 3-d space, three integer numbersquantum numbers n ,  , and m -must be introduced.
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Quantum numbers
Page 316 In a 3-d space, three numbers are required to ……
For the wave description of the electron in an atom, ……
It is important to say:

The quantum numbers n,  , and m are all integers…

The 3 quantum numbers…
n principal quantum # = 1, 2, 3, 4, ….electron shell
the greater the value of n, the…….
 angular quantum # = 0, 1, 2, 3, …n-1
subshells, orbital shapes
Value of 
0
1
2
3
Corresponding Subshell Label
s - sharp
p - principle
d - diffuse
f - fundamental
m , the magnetic quantum # = 0 , 1, 2 , 3 ,...  
orbitals in a given subshell differ only in their orientation in space, not in their shape.
Useful Information About Quantum Numbers is Summarized in Table 7.1 Page 318
EXERCISE 7.7 Page 318 Using Quantum Numbers
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7.6
THE SHAPES OF ATOMIC ORBITALS
What are valance electrons?
s Orbitals
What does 2 represent?
What is the shape of an s orbital?
What is the difference between s orbitals of different n values?
p Orbitals
What is the nodal plane?
d Orbitals
The value of  is equal to the number of nodal planes that slice through the nucleus.
f Orbitals
Orbital Shapes and Chemistry
When an element is part of a molecule, are the orbitals the same?
Do they have the same shapes?
What does the shape of orbitals have to do with the chemistry of an element?
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