Guide to Chapter 5. Periodicity and Atomic Structure ... - Mattson

Guide to Chapter 5. Periodicity and Atomic Structure
Answers to problem club questions in orange.
We will spend 2 - 3 lecture days on this chapter. In this chapter we will learn more about the structure of the
atom. We will start with a review of electromagnetic radiation. We will discuss the nature of matter, the
deBroglie relationship, and the hydrogen spectrum. The most important concept of the first part of this chapter is
the introduction to the postulates of quantum mechanics, use of the quantum numbers n and l, ml and ms. We
will learn the shapes of orbitals, energy diagrams, electronic configurations, ground states, excited states, orbital
box diagrams, dia- and paramagnetism, Pauli exclusion principle, electronic configuration and the periodic
table. Following that, we will shift to some very practical results of quantum mechanics: periodic trends. In this
chapter we will discuss shielding, effective nuclear charge, and atomic radii (size). More periodic trends will be
introduced in Chapter 6.
This is a chapter study guide, given section-by-section. Work problems on separate sheets of paper and keep them
with this guide. When working problems, use plenty of space and when appropriate, show all work.
The following useful formulas, equations and constants will be given to you on the exam:
c = lu DE = hc/l
E = -2.178 x 10 -18 J(1/n 2 ) DE = Ef – Ei = -2.178 x 10 -18 J(1/nf 2 - 1/ni 2 )
1/l = 1.097 x 10 -2 nm -1 (1/nf 2 - 1/ni 2 )
Read the introductory paragraph to Chapter 5. Periodicity and Atomic Structure and
then read Section 5.1 Development of the Periodic Table.
Read Section 5.2 Light and Electromagnetic Spectrum.
Learning Objective 1: Know how to use the equations for electromagnetic radiation: E = hn, ln = c.
Learning Objective 2: Use the Planck equation to determine the energy of light per photon or per mol of
photons.
Learning Objective 3: Use the equation, ln = c, to determine frequency, energy, or the wavelength of
light.
Learning Objective 4: Given a list of types of electromagnetic radiation (UV, IR, radio waves, etc.).
Rank them in order of increasing/decreasing energy, wavelength, or frequency.
Do Problem 1-3 at the end of the section.
Do the following end-of-chapter problems: 30, 32, 34, 36
Problem Club Question A. Consider these two electromagnetic waves, shown superimposed on the same
axis. Note that one is a solid line and the other is dashed.
(a) Which one represents the higher
energy? Circle: SOLID or DASHED
(b) If these waves represented GREEN
and VIOLET, which would be GREEN?
Circle: SOLID or DASHED
(c) Suppose that one of these waves had a
wavelength of 600 nm. Would it be in
the VISIBLE spectrum,
ULTRAVIOLET spectrum or
INFRARED spectrum? Circle your
answer.
(d) Suppose that one of these waves had a wavelength of 440 nm. Calculate the frequency of the wave.
Dr. Mattson, General Chemistry, Chm 203, Guide to Chapter 5. Periodicity and Atomic Structure 1

Answer: 6.8 x 10 14 s -1
(e) Convert 440 nm into units of kJ/mol
Answer: 272 kJ/mol
Advice from a former student:
My only advice would be to read the chapters before the material is covered in class. Since the class
covers material quickly, it sometimes becomes difficult to spend much time on a topic in class, whereas if a person
has read the material prior, the student will have refined his or her questions
Problem Club Question B (ACS-Style). Answer: A
Problem Club Question C (ACS-Style). Answer: C
Read Section 5.3 Electromagnetic Radiation and Atomic Spectra.
Learning Objective 5: For the hydrogen atom, determine the energy required (a positive amount) to
excite an electron from a lower energy shell (more stability) to a higher energy shell (less stable). Also
perform the same calculation but the electron drops from a higher energy shell to a lower energy shell.
The signs of DE should make sense.
Learning Objective 6: Determine the energy required to make the hydrogen atom into the hydrogen ion
(H + ). This is the ionization energy for hydrogen.
Do Problem 4 - 6 at the end of the section.
Do the following end-of-chapter problems: 44, 46, 48
Problem Club Question D. Calculate the wavelength (in nm) for the electronic transition n = 7 æ Æ n = 3
for hydrogen atoms.
Answer: 1005 nm
Problem Club Question E. In the Pfund series, excited electrons relax to level n = 5. (a) What transition (n
= ? to n=5) would result in the longest wavelength? The shortest wavelength? (b) Calculate the longest
wavelength possible for a transition of this series.
Answer: (a) n = 6 to 5; (b) n = • to 5; l = 7460 nm
Problem Club Question F. (a) What is the maximum number of emission lines for
atomic hydrogen that you would expect to see in a spectroscope if the only electronic
energy levels involved are those shown at right? [hint there are more than 5] (b)
Which transition would have the least energy? (c) Which one would emit a photon of
shortest wavelength?
Answer: (a) 15; (b) n = 6 to n = 5; (c) n = 6 to n = 1
Problem Club Question G. (ACS-Style) Answer: A
Problem Club Question H. (ACS-Style) Answer: D
Problem Club Question I. (ACS-Style) Answer: A
These three sections can be grouped together:
Read Section 5.4 Particlelike Properties of Electromagnetic Radiation: The Planck
Equation.
Read Section 5.5 Wavelike Properties of Matter: The de Broglie Equation.
Read Section 5.6 Quantum Mechanics and the Heisenberg Uncertainty Principle.
Do Problem 7 and 8 at the end of Section 4.
Dr. Mattson, General Chemistry, Chm 203, Guide to Chapter 5. Periodicity and Atomic Structure 2
n = 6
n = 5
n = 4
n = 3
n = 2
n = 1

Problem Club Question J. Carbon dioxide absorbs energy at a frequency of 2.001 x 10 13 s -1 . (a) Calculate
the wavelength, l of this absorption in nanometers. (b) In what spectral range does this occur? (c) What
is the energy difference in kJ/mol? (Note: "per mole" requires you to use Avogadro's number.)
Answer: (a) l = 1.5 x 104 nm (b) infrared (c) 8.0 kJ/mol
Read Section 5.7 Wave Functions and Quantum Numbers.
Learning Objective 7: Be able to define each quantum number and determine its value. For example,
Given a value for n, what are all the possible values for l? Given a value for l, what are all the possible
values for ml? Given a value for ml, what are all the possible values for ms?
Learning Objective 8: Given a set of quantum numbers n, l, ml, and ms, decide whether the values are
valid.
Learning Objective 9: Using a 2-D axis, draw the shapes of the 1s, 2p (all three), and 3d (all five) atomic
orbitals.
Learning Objective 10: Define the term node and determine the number of nodes that are possible for
a given atomic orbital.
Learning Objective 11: For a given value of n, determine the possible subshells or the number of orbitals
possible (and type, s, p, d, etc.) and the total number of electrons that are possible.
Learning Objective 12: For a given value of l, determine the possible orbitals, and the total number of
electrons that are possible.
Learning Objective 13: For any given set of quantum numbers (just n or n and l, or n, l, and ml, etc.)
determine the maximum number of electrons that can have the designated quantum numbers.
Do Problem 11 - 13 at the end of the section.
Do the following end-of-chapter problems: 50, 56, 58, 60
Problem Club Question K. What are the possible values of l for (a) n = 4; (b) n = 6; (c) n = 2
Answer: (a) l = 0 - 3 (b) l = 0 - 5 (c) l = 0, 1
Problem Club Question L. Which member of each pair of orbitals is lower in energy? (a) 3s or 3p; (b) 1s or
2s; (c) 4p or 4d
Problem Club Question M. Which of the following combinations is not allowed: (a) n = 2 and l = 2; (b) n =
4 and l = 0; (c) n = 3 and l = 2
Answer: (a)
Problem Club Question N. What is (a) the minimum value of n for which l = 4? (b) the maximum value of l
for n = 4? (c) the minimum value of l for n = 4? (d) the maximum value of n for l = 4?
Answer: (a) n = 5 (b) l = 3 (c) l = 0 (d) n = infinity
Problem Club Question O. Give the orbital designation of an electron with each of the following quantum
numbers. The first one is done for you.
electron n l ml ms
7s 7 0 0
4p 4 1 -1
6s 6 0 0
5f 5 3 0
+ 1 /2
Dr. Mattson, General Chemistry, Chm 203, Guide to Chapter 5. Periodicity and Atomic Structure 3
- 1 /2
- 1 /2
+ 1 /2
Problem Club Question P. How many orbitals can have these quantum numbers? (a) n = 3, l = 2; (b) n = 4
and l = 1 and ml = -1; (c) n = 4

Answer: (a) five: m l = 2, 1, 0, -1, -2
(b) just one; these three quantum numbers designate one orbital
(c) max l = 3: therefore m l = 3, 2, 1, 0, -1, -2, -3 for seven orbitals. BUT l could also equal 2, 1 or 0 when
n = 4. This adds 5 + 3 + 1 orbitals for a grand total of 16 orbitals that could have n = 4.
Problem Club Question Q. (ACS-Style) Answer: B
Problem Club Question R. (ACS-Style) Answer: C
Problem Club Question S. (ACS-Style) Answer: A
Problem Club Question T. (ACS-Style) Answer: A
Read Section 5.8 The Shape of Orbitals.
Learning Objective 14: Using a 2-D axis, draw the shapes of the 2s, 3s, 4s, etc., or for any of the three
3p, 4p, 5p, etc., atomic orbitals.
Problem Club Question U. What shape type of orbital ( s, p, d, etc) is designates by: (a) n = 2 and l = 1; (b) n
= 4 and l = 3; (c) n =1 and l = 0
Answer: (a) p; (b) f; (c) s
Problem Club Question V. (ACS-Style) Answer: C
Advice from a former student:
Read the book! It helps reinforce the lecture and problem solving techniques. Don't expect to do well
unless you are willing to work one-two hours on chemistry on the week nights. (and you gotta catch up on
weekends if you were bombarded with other homework during the week, or else it's difficult when you fall
behind!) Have a clear understanding that Tests/Quizzes are the only compilation of your final grade, so I
thought it necessary to study extra hard for them. In order to study well, do all of the assigned book problems and
the problem clubs; you get better with practice. Go in early to class to ask questions of the previous night's
homework or just to listen to others' questions. It's not necessary, but helpful. Don't let the learning objectives fool
you; they were intimidating at first with all the information, but just take them day by day and you'll eventually
come to understand that everything is tied together.
Read Section 5.9 Quantum Mechanics and Atomic Spectra.
Do Problem 16 at the end of this section.
These five sections can be grouped together:
Read Section 5.10 Electron Spin and the Pauli Exclusion Principle.
Read Section 5.11 Orbital Energy Levels in Multielectron Atoms.
Read Section 5.12 Electron Configurations of Multielectron Atoms.
Read Section 5.13 Electron Configurations and the Periodic Table.
Read Section 5.14 Some Anomalous Electron Configurations
Learning Objective 15: Use the periodic table and write the ground-state electron configuration
(complete or abbreviated) for a given element and then draw the orbital-filling diagram for the valence
electrons..
Learning Objective 16: Use your orbital-filling diagram and count the number of unpaired electrons and
then. to determine the magnetism (paramagnetic or diamagnetic) of an element.
Learning Objective 17: For a given element, recognize the difference between its ground-state electron
configuration and an excited state electron configuration.
Learning Objective 18: For a given quantum number, n (shell), or find the elements in the periodic table
that have this quantum number.
Learning Objective 19: For a given quantum number, l (subshell), find the groups in the periodic table
that have this quantum number.
Dr. Mattson, General Chemistry, Chm 203, Guide to Chapter 5. Periodicity and Atomic Structure 4

Learning Objective 20: When both n and l are given (a particular subshell), list all the possible elements
that have these two quantum numbers.
Learning Objective 21: For a given atom or ion, write a set of four quantum numbers for each of the
valence electrons.
Learning Objective 22: Identify the element that begins filling a particular subshell (n and l are known)
or completes a given subshell.
Learning Objective 23: Given a generalized electron configuration, for example, ns 2 np 1 , identify the
family of elements with this electron configuration or identify the element with a specifically given
electron configuration, for example, 1s 2 2s 2 2p 4 .
Do Problems 17 – 19 at the end of Section 13.
Do the following end-of-chapter problems: 24, 26, 66, 68, 70, 76, 78
Problem Club Question W. What are the possible values for ml for: (a) l = 2; (b) l = 4; (c) n = 4; (d) n = 1
Answer: (a) –2, -1. 0. +1. +2; (b) –4, –3, –2, -1. 0. +1. +2, +3, +4; (c) –3, –2, -1. 0. +1. +2, +3; (d) 0
Problem Club Question X. Write the ground state electronic configuration for: (a) Cl; (b) Fe; (c) Se; and (d)
Si
Answer: a. Cl 1s 2 2s 2 2p 6 3s 2 3p 5
b. Fe 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 6
c. Se 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 4
d. Si 1s 2 2s 2 2p 6 3s 2 3p 2
Problem Club Question Y. Give the symbol of the element of lowest atomic number whose ground state has
(a) completed d sub-level; (b) three 4d electrons; (c) five 3p electrons; (d) one s electron
Answer:
(a) Cu does if you remember the exception - otherwise the rules predict Zn
(b) Nb
(c) Cl
(d) H
Problem Club Question Z. Classify each as ground state, excited state, or forbidden state: (a) 1s 1 1p 1 ; (b)
1s 2 2s 1 2p 1 ; (c) 1s 1 2s 2 2p 6 ; (d) [Ne] 3s 2 3p 6 4s 2 3d 8 ; (e) [Ne] 3s 2 3p 6 3d 10 ; (f) 1s 2 2s 2 2p 6 2d 8
Answer:
(a) forbidden
(b) excited
(c) excited
(d) ground
(e) excited
(f) forbidden
Problem Club Question AA. Use the box diagrams (orbital diagrams) to predict the number of unpaired
electrons are present for each of the following species. Label each as diamagnetic or paramagnetic. (a)
C; (b) Fe; (c) P; (d) Zn; (e) Sb
Answer:
(a) two unpaired electrons - paramagnetic
(b) four unpaired electrons - paramagnetic
(c) three unpaired electrons - paramagnetic
(d) zero unpaired electrons - diamagnetic
(e) three unpaired electrons - paramagnetic
Dr. Mattson, General Chemistry, Chm 203, Guide to Chapter 5. Periodicity and Atomic Structure 5

Problem Club Question BB. Assign a set of four quantum numbers to (a) the 5s e - in Rb; (b) the 3d e - s in
Ti; (c) all the p-e - s in P
Answer:
(a) n = 5; l = 0; m l = 0; m s = +1/2
(b) two electrons with these quantum numbers (but not the same m l : n = 3; l = 2; m l = -2, -1, 0, +1, +2;
m s = + 1/2
(c) first the SIX 2p electrons: All six have n = 2 and l = 1; two have m l = -1 (one with m s = +1/2 and one
with m s = -1/2) two have m l = 0 (one with m s = +1/2 and one with m s = -1/2) and two have m l = +1 (one
with m s = +1/2 and one with m s = -1/2). Next, the THREE 3p electrons: All three have n = 3 and l = 1;
one has m l = -1 and m s = +1/2, one has m l = 0 and m s = +1/2 and one has m l = +1 and m s = +1/2.
Problem Club Question CC. Identify the element with the smallest atomic number that has (a) three delectrons;
(b) a filled p-subshell; (c) n = 3 electrons and is diamagnetic
Answer: (a) V; (b) Ne; (c) Mg
Problem Club Question DD. Using “core notation”, give the electron configuration for: (a) Ge and (b) Ru
Answer: (a) [Ar] 4s 2 3d 10 4p 2 ; (b) [Kr] 5s 2 4d 6
Problem Club Question EE. Classify each of the following as a ground state, excited state, or an impossible
electron configuration. Circle G, E or I.
(a) 1s 2 2s 2 2p 6 3s 1 G E I (b) 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 12 G E I
(c) 1s 2 2s 2 2p 6 3d 1 G E I
Problem Club Question FF. Which of the following is/are paramagnetic? (a) Mn; (b) Zn; (c) Sn
Problem Club Question GG. (ACS-Style) Answer: A
Problem Club Question HH. (ACS-Style) Answer: D
Problem Club Question II. (ACS-Style) Answer: B
Problem Club Question JJ. (ACS-Style) Answer: D
Problem Club Question KK. (ACS-Style) Answer: C
Problem Club Question LL. (ACS-Style) Answer: D
Read Section 5.15 Electron Configurations and Periodic Properties: Atomic Radii
Learning Objective 24: Discuss/describe the trends found in the periodic table with respect to atomic
radii (size).
Learning Objective 25: Draw circles to represent the relative sizes of two (or more) atoms.
Do Problem 21 at the end of this section.
Do the following end-of-chapter problems: 28, 54, 84
Problem Club Question MM. Which element of those listed has the largest atomic radius: Ge, As, Se, Sn,
Sb, Te
Dr. Mattson, General Chemistry, Chm 203, Guide to Chapter 5. Periodicity and Atomic Structure 6