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Chapter 7 Quantum Theory and Atomic Structure
This chapter overlaps physics and is crucial to the understanding of electrons and,
in essence, the behavior of atoms. It is important students understand all the concepts,
although they are not usually tested on all of them. When doing wavelength problems,
students need to be careful about units—meters to nanometers usually need to be
converted.
Major Concepts to Know:
 Students should know the inverse relationship between the wavelength and frequency
of the wave. When the wavelength is long the frequency is short, and when the
wavelength is short the frequency is high. Students should know the higher energy
waves are the shorter waves and include ultraviolet and x-rays, whereas the lower
energy waves include the infrared and radio waves.
Regions of the Electromagnetic Spectrum

In recognizing ground state and an excited state, a student should be able to look at a
configuration and indicate which it is. Also, for emission and absorption spectra, a
student should be able to look at an electron and indicate if it is jumping up
(absorbing energy) or falling down (emitting energy). For instance, 4s to 5s is
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absorbing while 6s to 2s is emitting energy. They also need to be able to calculate the
energy of a jump using the equation given on the formula pages on the AP exam, En =
RH(1/n2)

Students do not need to have memorized names associated with spectral lines, but
they need to know every element has its own unique spectra that can be used to
identify it.
The Line Spectra of Several Elements

Other concepts students should be able to explain include the photoelectric effect and
wave particle duality.

Students should have some background in the history of the development of quantum
theory including the Bohr model of the atom.
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Summary of Major Observations and Theories Leading from
Classical Theory to Quantum Theory

Students should be able to explain the general wave principle of Schrödinger and that
although the exact location of an electron cannot be pinpointed, electron density
determined by the square of the wave function can give us a probability distribution.
It is important in this regard that students distinguish the concept of orbital from an
“orbit.”

Students should know how to explain the difference between the principal quantum
number (n), the angular momentum number (l), and the magnetic number (ml).
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
There are a few useful criteria students should recognize about quantum states of
orbitals. For example:
1. For a s spherically symmetric cloud the middle two numbers are always 0.
2. In any set of numbers, the second number—(l)—can never be larger than the first
number (n).
3. The third number—(ml) —can never be larger than the second number—(l).
A practice question might be to look at a set of quantum numbers and identify which
is impossible, which is ground state, and which is an excited state for an atom.
Students might write these to test one another.

Students should know the basic shapes of s and p clouds.
The 1s, 2s, and 3s Orbitals and the 2p Orbitals
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
Students often ask about d and f shapes but as of yet they have not been tested. The d
shapes are in the following diagram.
3d Orbitals
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
Understanding the shape of s and p orbital will help students as they delve into
bonding. However, it should be stressed that these shapes are the result of theoretical
calculations and do not really represent the shape of the atom itself. They should also
clearly distinguish between comparisons of a single electron in an atom such as
hydrogen, moving from orbital to orbital, with the attractive energy getting smaller as
the principal quantum number increases (from comparisons among multi-element
atoms where more complex relationships are found). There is in-depth discussion on
this issue in Chapters 8 and 9.
Vocabulary to Know:
 Atomic orbital
 Electromagnetic radiation
 Electromagnetic spectrum
 Electron density and electron cloud
 Emission spectrum
 Frequency (v)
 Ground level (or state)
 Heisenberg uncertainty principle
 Line spectrum
 Photon
 Photoelectric effect
 Quantum numbers (principal, angular momentum, and magnetic)
 Wavelength (λ)
 Wave-particle duality
Math Skills Students Must Know:
 Wavelength using c = λv
 ∆E = hv
 En = RH(1/n2)
 ΔE = RH(1/n2i  1/n2f); Note this equation is NOT given to the students on the AP test
but they are given En (above). They can calculate each level and subtract to get ΔE.
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Suggested Problems:
 The Nature of Light: 2, 3, 9, 10, 11
 Atomic Spectra: 20, 23, 24, 86, 95, 101
 Wave-Particle Duality of Matter and Energy: 40, 41, 42
 The Quantum Mechanical Model of the Atom: 48, 49, 51, 55, 56, 57, 58
Suggested Demonstrations or Labs:
Cooper, Melanie M. “Project 13: Analysis of Colas,” Cooperative Chemistry Lab Manual
(McGraw-Hill, 2006).
Questions
1. What is electromagnetic radiation?
2. For each of the following give the symbol and definition, and indicate on a sketch
how to locate each.
a. Wavelength
b. Amplitude
3. What are the units of wavelength?
4. What is frequency?
a. What are the units of wave frequency?
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5. What is an electromagnetic wave?
6. What is an electromagnetic spectrum?
a. What is the relationship between wavelength and frequency for high energy
gamma rays?
b. What is the relationship between wavelength and frequency for low energy radio
waves?
c. What is the difference between IR and UV?
7. What is Planck’s constant?
8. What is a quantum?
9. Explain the basics of quantum theory.
10. What is the photoelectric effect?
a. What are photons?
11. What is the Rydberg equation and what does it solve for?
12. Explain the postulates of the Bohr model of the atom.
13. What is the difference between a ground-state electron and an
excited-state electron?
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14. Explain the limitations of the Bohr model.
15. What is an emission spectra?
a. What can an emission spectra be used for and why?
16. What are the flame test colors for copper and strontium?
17. What is wave-particle duality?
18. Explain the Heisenberg uncertainty principle.
19. Explain the concept of electron density.
a. What is a radial probability distribution plot?
20. Explain how each of the quantum numbers indicate electron location? Also give the
symbol and possible numbers for each.
a. Principal quantum number
b. Angular momentum quantum number
c. Magnetic quantum number
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