Unit 5
Electronic Structure of Matter
Table of Contents
Table of Contents
1
Electronic Structure of Matter
3
Essential Questions
4
Review
4
Lesson 5.1: The Bohr Model and the Quantum Mechanical Model of the Atom 5
Objectives
5
Warm-Up
6
Learn about It
7
Key Points
13
Web Links
14
Check Your Understanding
15
Challenge Yourself
16
Lesson 5.2: Orbitals and Quantum Numbers
Objectives
Warm-Up
Learn about It
Worked Examples
Key Points
Web Links
Check Your Understanding
Challenge Yourself
18
18
19
19
25
27
27
28
29
Lesson 5.3: Electron Configuration
Objectives
Warm-Up
Learn about It
Worked Examples
Key Points
Web Links
Check Your Understanding
30
30
30
31
37
40
41
42
Laboratory Activity
44
Performance Task
46
Self Check
48
Key Words
48
Wrap Up
49
References
49
Answer Key
50
2
GRADE 9 | SCIENCE
Unit 5
Electronic Structure of
Matter
The idea that the world is made up of atoms is not new. It was first formulated by
Democritus in ancient Greece. As scientists learned more about the atom, our
understanding of it changed over time. These discoveries gave rise to atomic
models such as Thomson’s plum pudding model and Rutherford’s nuclear atomic
model. However, these models cannot explain one simple question: Why do metals
produce colors when heated?
This question gave birth to a new field of science known as quantum chemistry. The
development of technologies in this field allowed us to illustrate the most accurate
model of the atom—the quantum mechanical model. This model explains where
the beautiful colors of fireworks come from. In this unit, you will learn about the
development of this atomic model and the importance of the electron as a
component of atoms and matter.
3
Essential Questions
At the end of this unit, you should be able to answer the following questions.
●
●
●
●
How did the Bohr model revolutionize the description of an atom?
How are electrons arranged in the quantum mechanical model of the atom?
Why do metals produce colors when heated?
How are the colors of the fireworks produced?
Review
● The atom is generally made up of three fundamental particles: protons,
neutrons, and electrons.
o Protons are positively-charged particles.
o Neutrons are neutral or uncharged particles.
o Electrons are negatively-charged particles.
● The atomic number (Z) of an atom is equal to its number of protons.
● The periodic table is a systematic and organized way of presenting elements
in order of increasing atomic number.
o The vertical columns of the periodic table are called groups. Elements
belonging to the same group have similar chemical properties.
o The horizontal rows of the periodic table are called periods.
o The elements are grouped into blocks based on their similarities in
properties.
4
Lesson 5.1: The Bohr Model and the
Quantum Mechanical Model of the Atom
Objectives
In this lesson, you should be able to:
● demonstrate an understanding of the development of atomic
models that describe the behavior of electrons within atoms;
● describe Bohr’s model as a refinement of Rutherford’s model;
and
● describe the main features of the quantum mechanical model of
the atom.
Up until the 19th century, scientists believed that the world was made up of four
metaphysical elements. They believed that fire, water, air, and earth constitute all
forms of matter. In contrast, some believed that the world is made up of small
indivisible particles, which they called atoms.
Subsequent discoveries in chemistry led to the acceptance of the atomic theory as
the appropriate theory for explaining chemical phenomena. Scientists collected
evidence that the atom is made up of smaller particles we now know as protons,
electrons, and neutrons. The discovery of these subatomic particles proved that the
atom is divisible. This eventually laid the foundation for the atomic theory. How
was the atomic theory changed and refined as we learned more about the
universe?
5
Warm-Up
Making a Big Atom!
Atoms are so small, yet scientists have already deduced what they look like. The
discovery of the subatomic particles kept scientists busy for almost a century on
figuring out how they are arranged inside the atom.
In this activity, you will use your previous knowledge on atomic models and create a
big, 3D model of a particular element.
Materials:
● 5 pieces each of red, blue, and
green balls
● 1 piece, 5 ft. wire
● glue or adhesives
Procedure:
1. Your teacher will assign you the element you will be working on. He/she will
also assign you the atomic model you will be using to build your 3D model.
Possible element and model combination are as follows:
● Billiard ball model of hydrogen
● Plum pudding model of calcium
● Nuclear model of boron
2. Use the balls to represent the subatomic particles. Red balls represent the
positively-charged protons. Blue balls represent the negatively-charged
electrons. Green balls represent the neutral or uncharged neutrons. Use the
wire to represent paths and connect your balls.
3. After the activity, present your model in front of the class. Show them where
the protons, neutrons, and electrons are found. Let your classmates guess
the type of model you built.
6
Learn about It
Earlier Atomic Models
The first idea of the atom was proposed by Democritus, a
Greek philosopher. According to Democritus, the world is
made up of tiny indivisible particles called atomos. This was
later on coined as the atomism theory. The idea was not
very popular in ancient Greece because of Aristotle’s
competing theory that all matter is composed of four
classical elements: earth, water, fire, and air.
In 1803, John Dalton proposed the solid sphere model of
the atom. According to Dalton, the atom is a uniform solid
sphere similar to a billiard ball. Dalton imagined these balls
as indivisible and eternal.
During the Industrial Revolution of the 19th century, atomism saw a resurgence. It
acquired experimental evidence when Sir Joseph John Thomson discovered the
electron in 1897. With the discovery of the electron, Thomson made the plum
pudding model of the atom in 1904. In the plum pudding model, the electrons are
like negatively-charged plums stuck to a positively-charged pudding.
7
In 1911, Lord Ernest Rutherford discovered the nucleus. It is made up of
densely-packed positively-charged particles at the center of the atom, which he
found out through his gold foil experiment. His discovery allowed him to propose a
new model of the atom called the nuclear model. In this model, negatively-charged
electrons surround the positively-charged nucleus at the center of the atom. The
atom can be thought of as a minuscule ‘solar system’ in which electrons revolve
around the nucleus.
Fig. 1. Earlier atomic models.
Bohr’s Model
Later, scientists found out that Rutherford’s model
cannot explain certain physical observations such as the
capacity of atoms to emit light. It cannot explain why
metals release a characteristic color in the form of light
when they are heated. It also cannot explain why
electrons do not fall into the nucleus even though they
are electrically attracted to its positive charge. Hence, it
cannot account for the stability of the atom. If we were to
accept Rutherford’s model, all atoms would be unstable
because electrons will fall to the nucleus and the atom
will collapse. However, this is not the case.
In 1913, Niels Bohr improved Rutherford’s model by
adding the concept of orbits. According to Bohr,
8
electrons only move around the nucleus in fixed circular orbits. Orbits are specific
distances from the nucleus where electrons can be found. These are stable discrete
regions where electrons do not radiate energy. Since electrons move, they are not
pulled towards the nucleus.
Orbits are also known as energy levels (n). Its values are any whole number from 1,
2, 3, 4, and onwards. For example, the first orbit or the first circle from the nucleus
is also known as the first energy level (n = 1). You will learn in the succeeding model
of the atom, that n is also known as the principal quantum number.
Bohr’s model could account for light emissions because the presence of orbits can
explain the absorption of energy of an atom. The energy transformations that
result in the emission of light is due to the movement of an electron from one
atomic orbit to a higher atomic orbit, and back to its original atomic orbit.
Fig. 2. Bohr’s model of the atom.
When an electron absorbs energy, it moves to an atomic orbit with higher energy.
The original atomic orbit of the electron is called the ground state while the higher
atomic orbit is the excited state. The electron in the excited state is unstable. The
excited electron will eventually return to its ground state. It is accompanied by the
release of the absorbed energy in the form of light.
In Bohr’s model, an electron can only jump in a certain orbit. For example, an
electron could only jump from n = 1 to n = 3. An electron cannot jump in between
n = 1 and n = 2, or between n = 2 and n = 3. Instead of having continuous energy
levels, Bohr’s model introduces the concept of quantized energy levels wherein
9
each orbit (or energy level) has a definite amount of energy. As the distance from
the nucleus increases, the amount of quantized energy in an orbit also increases.
The amount of released energy in the form of light is equivalent to a specific
wavelength of light. The specific wavelength is observed as the atom’s resulting
spectrum. The resulting spectrum serves as the atom’s unique fingerprint. It is used
in analytical techniques to detect the presence of an element. Each line in the
atomic spectra corresponds to a definite energy transformation within the atom.
Fig. 3. The emission spectrum of hydrogen. The lines with corresponding wavelengths
indicate release of energy as electrons relax from an excited state to their ground state.
The emission of light due to excitation of electrons is the reason why elements emit
characteristic light. For example, calcium releases orange light, sodium releases
yellow light, and copper releases green light. This is how fireworks get their colors.
sodium
potassium
calcium
copper
lithium
Fig. 4. Elements release characteristic colors when subjected to the flame test.
10
Table 1. Flame color when metals are heated.
Element
Color
Sodium
Yellow
Potassium
Lilac
Calcium
Orange
Copper
Green
Lithium
Red
Bohr’s model is useful in explaining observations on hydrogen and hydrogen-like
atoms but fails to explain phenomena for larger atoms. It cannot account for atoms
with more than one electron that have spectral lines in pairs.
The Quantum Mechanical Model
In 1924, Louis de Broglie developed the wave-particle duality. According to his
theory, subatomic particles, like electrons, can also act as waves, rather than
definite particles with determinate positions. In 1927, his theory was experimentally
confirmed. The wave nature of electrons indicates that it can undergo wave
phenomena such as interference and refraction. The model also indicated that the
exact position of an electron cannot be precisely determined. Just like a wave’s
11
position, the position of an electron could not be exactly determined, but its
momentum can be determined.
The fact that an electron’s position cannot be precisely determined brings the
model in accordance with the uncertainty principle. According to Werner Karl
Heisenberg who proposed the uncertainty principle, two paired variables cannot be
simultaneously determined with precision in a quantum system. In terms of
electrons, the position and momentum of an electron cannot be exactly
determined if one of them is precisely known. Hence, it denies the fact that
electrons are located in “fixed” orbits as stated in Bohr’s model.
Fig. 5. Quantum mechanical model of the atom.
Instead, electrons in the quantum mechanical model are in regions called orbitals,
where electrons can only most probably be found. These orbitals are
mathematically computed using a mathematical equation known as the
Schrödinger equation. The Schrödinger equation uses de Broglie’s hypothesis of
the electron as a wave. It describes the momentum of the electron precisely but not
its location. Electrons in an atom are described by solutions to the Schrödinger
equation called wave functions (ψ).
With the ideas of de Broglie, Heisenberg, and Schrödinger came the idea of the
quantum mechanical model of the atom. In summary, this model of the atom uses
the theoretical approaches in the field of quantum chemistry. The model considers
12
electrons as a wave probably located in certain regions around the nucleus. The
electrons are most likely found near the nucleus. There are greater chances of
locating the electrons in darker areas of the model.
The quantum mechanical model was successful in explaining what Bohr’s model
could not explain.
Key Points
● The principles of quantum chemistry established new concepts that founded
Bohr’s atomic model and the quantum mechanical model of the atom.
● In Bohr’s atomic model, the electrons are positioned in fixed orbits and
revolve around the nucleus. These orbits are also called energy levels
because they have fixed energies.
● The electrons in the allowed orbits do not radiate energy. This prevents the
electrons from being pulled by the nucleus.
● Electrons can move between energy levels. The energy level at which the
electron is normally situated is called the ground state. An electron moves
to a higher energy level, called the excited state, when sufficient energy is
acquired.
● If an electron goes back to its ground state, energy is released in the form of
light. This explains why metals give off characteristic color when heated.
● Bohr’s atomic model cannot explain the spectral characteristics of larger
atoms. It was later replaced by the quantum mechanical model of the atom
where electrons are found in specific regions rather than on fixed orbits.
● In the quantum mechanical model of the atom, the electrons are confined in
a region of space called orbitals. Electrons are most likely to be found in
darker areas near the nucleus.
● The orbitals are mathematical solutions of the Schrödinger equation, which
uses the principles of de Broglie’s wave-particle duality and Heisenberg’s
uncertainty principle.
● De Broglie’s wave-particle duality sees electrons as waves rather than
definite particles.
● Heisenberg’s uncertainty principle states that two paired variables cannot be
simultaneously determined with precision in a quantum system. The position
of the electrons cannot be accurately determined and should be expressed
in terms of probability rather than fixed positions.
13
Web Links
For further readings, you can check the following web links:
● Read the complete history of the atomic theory.
Anon. 2020. ‘A History of Atomic Theory.’
https://chem.libretexts.org/@go/page/98684
● Read about the life story of Niels Bohr, the man who
revolutionized how we should see the atom.
Nobel Media. 2014. ‘Niels Bohr - Biographical.’
https://www.nobelprize.org/nobel_prizes/physics/laureates/
● The probability of finding an electron in an orbital, how do the
orbitals really look like?
kominowskia. 2013. ‘Cassiopeia Project: Quantum Numbers and Electron Probability
Clip.’ https://www.youtube.com/watch?v=drCg4ruJCfA
● What is Heisenberg’s uncertainty principle?
TED-Ed. 2014. ‘What is the Heisenberg Uncertainty Principle? - Chad Orzel.’
https://www.youtube.com/watch?v=TQKELOE9eY4
● An experiment demonstrating how elements produce spectral
lines when heated.
Basement Bob. 2009. ‘Spectrum Analysis Demo - Bohr Model.’
https://www.youtube.com/watch?v=xUX-nmPL9SE
14
Check Your Understanding
A. True or False
Read the following statements carefully. Write true on the blank provided before
each number if the statement is true. Otherwise, write false.
___________
___________
___________
___________
1.
2.
3.
4.
___________
5.
___________
___________
___________
6.
7.
8.
___________
9.
___________ 10.
Bohr’s model of the atom
Electrons move about the positive nucleus in discrete energy levels.
Electrons move randomly throughout empty space around the nucleus.
Electrons emit energy as it falls to the positive nucleus.
Electrons emit energy in the form of light as it relaxes from an excited
state to its ground state.
Electron energy levels are continuous.
Quantum mechanical model of the atom
Electrons move about in fixed orbits.
Electrons exist as probability clouds that revolve around the nucleus.
The exact position and momentum of an electron can be determined at
the same time.
Orbitals are regions of high probability where electrons can be found.
Electrons move about a fixed, positive nucleus.
B. Short Answers
Answer the following comprehensively.
11. Give one everyday example that demonstrates the concept of quantization.
12. Explain the process of absorption and emission using Bohr’s atomic model.
13. What is an energy level? What is the difference between an electron in the
ground state and an electron in the excited state?
14. Electrons are attracted to protons because of their opposite charges. Why
don’t electrons fall to the nucleus of an atom?
15. What is an atomic orbital? How does it differ from an atomic orbit?
15
C. Venn Diagram
Using a Venn diagram, enumerate at least two characteristics which are contrasting
to Bohr’s atomic model and quantum mechanical model of the atom. Similarly,
identify at least one characteristic that serves as commonality to both atomic
models.
Challenge Yourself
Answer the questions that follow.
1. Explain why elements produce their own characteristic color when heated.
2. Orbitals are merely regions of high probability of finding an electron. Does
this mean electrons can be found outside of orbitals?
For the next items, consider the figure below. Then, answer the following questions.
16
3. Write the letter of the process which corresponds to the absorption of the
largest energy.
4. Write the letter of the process which corresponds to the release of the
largest energy.
5. The released energy from any emission process is in the form of
electromagnetic radiation. Visible light is an example. Why do they emit this
type of radiation and not other types?
17
Lesson 5.2: Orbitals and Quantum
Numbers
Objectives
In this lesson, you should be able to:
● describe the four quantum numbers and their significance; and
● recognize orbital shapes based on the given quantum numbers.
In the quantum mechanical model of the atom, momentum is chosen to be
precisely defined over the location of the electron. Hence, an electron’s position is
based only on probabilities. This allows us to visualize the position of an electron
around the nucleus of the atom in a three-dimensional space. These regions of
space with a high probability of finding electrons are called atomic orbitals.
You had your first look of these orbitals when you
learned about the quantum mechanical model of
the atom in the previous section. The model
shows an electron density map (also known as
electron probability diagram). The simplest way
to interpret this type of diagram is that there is a
greater probability of finding electrons in a darker
area than in a lighter area. There are also other
ways of representing orbitals, which will be
explored in this lesson.
Atomic orbitals have different shapes and
orientations in space, depending on their set of
quantum numbers. What are quantum numbers
and how do they affect the shapes and
orientations of these orbitals?
18
Warm-Up
Where’s the Map?
Help! Your classmate can’t go on to her adventure because
her map is lost! Your Science teacher hid it in one of the
trees in your school’s backyard. But your classmate does
not know how to go to your school. Can you draw a map
for your classmate? Ask your teacher where your
classmate lives. Draw nearby landmarks. You can also label
the streets or put arrow signs on the road. Roughly
estimate the scale and sketch the map. Encircle the spot
where your Science teacher hid the map.
Learn about It
In the quantum mechanical model, an electron orbiting the nucleus will have a
unique set of four quantum numbers. The set of quantum numbers acts as a sort
of address for each electron.
Principal Quantum Number
The principal quantum number ( ) refers to the distance of the electron from the
nucleus. It is also known as the shell. The values of
are 1, 2, 3, 4, and so on. It is
also equal to the period where the element belongs. For example, since the
electron of hydrogen belongs to period 1, the value of is 1.
Fig. 6. As the value of n increases, the electron becomes farther away from the
nucleus.
19
The set of orbitals shown above represents the boundary surface diagrams. It
encloses a region of space where electrons are usually found 90 percent of the
time. The probability suggests that the electrons can also be found outside the
surface, although its likelihood is just approximately 10 percent of the time.
The principal quantum number is also directly related to the main energy level of
an orbital. It represents the energy needed to maintain the attraction of an electron
in an orbital and the proton in the nucleus. Hence, the value of
increases with
distance.
The maximum number of electrons a shell can contain is computed by
is the principal quantum number.
, where
Table 2. Maximum number of electrons in a shell.
Value of n
Maximum number of electrons
1
2
2
8
3
18
4
32
5
50
6
72
7
98
Azimuthal Quantum Number
In the quantum mechanical model, a shell consists of subshells. The subshells
describe the shape of the atomic orbital. The subshell is also known as the
azimuthal quantum number . It is also called the orbital angular momentum
quantum number. The values of are zero to
. Each value of corresponds
to a subshell shape.
Value of
0
1
2
3
Table 3. Subshell shapes.
Subshell symbol
s
p
d
f
Shape(s)
spherical
dumbbell
cloverleaf and dumbbell with a ring
at the center
too abstract to describe
20
The subshells are designated by letters, where the first four are s, p, d and f
(alphabetical after f, excluding the vowels). The first four letters were taken from
the words sharp, principal, diffuse and fundamental. These are terms used to
describe the four spectral lines produced when hydrogen is heated.
The number of types of subshells in a shell is equal to the principal quantum
number assigned to the shell. For example, there are two types of subshells in the
shell with
(s and p subshells). Meanwhile, there are three types of subshells in
the shell with
(s, p, and d subshells).
Magnetic Quantum Number
Each subshell consists of orbitals where electrons are found. The number of
orbitals in a subshell is given by the magnetic quantum number,
. The value of
are
to
including zero. Each orbital can only hold two electrons.
Table 4. Possible values of
Value of
0
1
2
3
The value of
and maximum number of electrons per subshell.
Number of
Maximum number
Possible values of
orbitals
of electrons
0
1
2
–1, 0, +1
3
6
–2, –1, 0, +1, +2
5
10
–3, –2, –1, 0, +1, +2, +3
7
14
represents the possible orientations of the electron in the
three-dimensional space. To illustrate this, let’s take a look at the s orbital as an
example. The s orbital is spherical. Its
and
values are equal to zero. This
suggests that there is only one orientation possible for a
three-dimensional space. This, of course, is true for spherical models.
sphere in
The p-orbital is dumbbell-shaped. It is the next higher subshell to the s-orbital and
is found starting
. Its
value is equal to 1. This gives three
values which
are -1, 0 and +1. This suggests that there are three possible orientations of the
p-orbital in the three-dimensional space, which corresponds to the px, py and pz
orbitals. However, the assignment of px, py and pz to
values -1, 0, and +1 is only
arbitrary, which means that px is not necessarily assigned to
of -1 and so on.
21
These three p orbitals only differ in their orientations in space; they still have the
same energy level. Orbitals with the same energy level are called degenerate
orbitals. The same is true for other orbitals with integral values of
.
Fig. 7. The p-subshell
is dumbbell-shaped. It has 3 orbitals
denoted by px, py and pz.
The d-orbital is shaped like a cloverleaf. It is the next higher subshell to the
p-subshell and is found starting
. Its value is equal to 2. This gives five
values which are -2, -1, 0, +1 and +2. This suggests that there are five possible
orientations of the d-orbital in the three-dimensional space, which corresponds to
dyz, dxz, dxy, dx2- y2 and dz2 orbitals. These five orbitals are degenerate.
Fig. 8. The d-subshells
It has 5 orbitals
occur in planes.
.
22
The f-subshell has various shapes. It is the next higher subshell to the d-subshell
and is found starting
. Its
value is equal to 3. This gives seven
values
which are -3, -2, -1, 0, +1, +2 and +3. This suggests that there are seven possible
orientations of the f-orbital in three-dimensional space, which are also degenerate.
Fig. 9. The f-subshells
It has 7 orbitals
occur in planes.
.
Up to this point, it can be deduced that three quantum numbers are needed to
specify an orbital. The quantum numbers ,
and
can be used to identify a
specific atomic orbital. Numbers enclosed by braces are used to represent a set of
quantum numbers in the format of { , ,
}. For example, the set of quantum
numbers {2, 0, 0} corresponds to a 2s orbital, while the set of quantum numbers {3,
1, 1} may correspond to a 3px, a 3py, or a 3pz orbital.
Electron Spin Quantum Number
The electron spin quantum number is introduced to differentiate the first three
quantum numbers. The electron spin quantum number (
) indicates the spin of
the electron or the direction at which it revolves around the nucleus. The values of
23
are +½ and -½ only. An electron that has
= +½ will spin counterclockwise
and is represented by a half arrow pointing upwards (↿). An electron that has
= -½ will spin clockwise and is represented by a half arrow pointing downwards
(⇂). A pair of electron is represented by these two half arrows (↿⇂).
The electron spin quantum number differentiates the two electrons that reside in
an orbital. Recall that three quantum numbers are needed to specify an orbital. An
orbital can hold two electrons. To differentiate the identity of each electron, they
are designated different spins. By convention, the first electron spins upward while
the second electron spins downward.
The braced notation for quantum numbers can be extended to accommodate the
spin quantum number. The complete notation follows the format of
.
The following table will help you understand how these four quantum numbers are
related to one another.
Table 5. Possible values of the four quantum numbers.
Principal
quantum
number
Azimuthal
quantum
number
Subshell
Magnetic
quantum
number
1
0
1s
0
1
0
2s
0
1
Number of
orbitals in
the subshell
2
3
4
Electron Spin
quantum
number
Maximum
number of
electrons in
the shell (2n2)
2
8
1
2p
–1, 0, 1
3
0
3s
0
1
1
3p
–1, 0, 1
3
2
3d
–2, –1, 0, 1, 2
5
0
4s
0
1
18
32
24
1
4p
–1, 0, 1
3
2
4d
–2, –1, 0, 1, 2
5
3
4f
–3, –2, –1, 0, 1,
2, 3
7
An atom with
can only have the s-orbital with 2 electrons. An atom with
can have one s-orbital and three p-orbitals for a total of 8 electrons. The set of four
quantum numbers serve as an address for each electron in an atom. Hence, an
electron with
,
,
orbital with a positive spin.
, and
= +½ is an electron located in the 2s
Worked Examples
Example 1
Refer to this set of quantum numbers: {4, 4, -2, -½}. Is this set of quantum numbers
allowed or forbidden?
Solution
Step 1
Check the values of each quantum number and assess if they follow
the rules. Start from the leftmost and check whether they follow the
rules or not.
25
Principal quantum number,
Only integral values are allowed for
value.
. Hence,
Azimuthal quantum number,
The allowed values for are integers from 0 to
allowed values are 0, 1, 2 and 3. Hence,
is an allowed
. Since
, the
is a forbidden value.
Magnetic quantum number,
The allowed values for
are integers from
zero. Since the maximum allowed value for
to
is 3, the allowed
values for
are -3, -2, -1, 0, +1, +2, and +3. Hence,
allowed value.
Magnetic spin quantum number,
The allowed values for
are +½ and -½. Hence,
value.
Step 2
, including
is an
= -½ is an allowed
Assess the overall results. If at least one rule is violated, the set of
quantum numbers is forbidden.
The set of quantum numbers is forbidden because it violated the rule
for the azimuthal quantum number.
Let us Practice
For the following sets of quantum numbers, assess whether they are allowed or
forbidden. Justify your answer.
1. {2, 2, 0, -½}
2. {3, 1, -1, +½}
3. {1, 0, 0, +¼}
26
Key Points
● In the quantum mechanical model of an atom, the electrons are most likely
found in an orbital. They are arranged in a specific manner dictated by the
quantum numbers.
● There are four quantum numbers which dictate the shape of the orbital and
the arrangement of the electrons. These are the principal quantum number
, the azimuthal quantum number
, the magnetic quantum number
, and the magnetic spin quantum number
.
● The principal quantum number
is directly related to the distance of the
electron from the nucleus. It is also directly related to the energy of the
electron in a particular shell. It can have positive integer values of 1, 2, 3 and
so on.
specifies the shape of the orbital. The
● The azimuthal quantum number
shape of the orbital is spherical when
, dumbbell when
and
cloverleaf when
. It can have a whole number value from 0 to
.
tells us the number of ways the orbitals
● The magnetic quantum number
can be oriented in space. It can have a whole number value from
to
.
● Orbitals with the same energies are known as degenerate orbitals.
● The magnetic spin quantum number
tells us the spin of the electron.
Depending on the spin of the electron,
can have values of +½ or -½ only.
● Three quantum numbers { , ,
} are needed to identify an orbital, while
four quantum numbers { , ,
} are needed to identify an electron.
,
Web Links
For further readings, you can check on the following links:
● Do you need to review the basics of quantum numbers? Read
here.
The Bodner Group, Division of Chemistry Education, Purdue University. n.d..
Quantum Numbers and Electron Configurations.
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch6/quantum.html
27
● How does an actual orbital really look like in three-dimensional
space? Watch this video
Anna Tanczons. 2009. Electron Orbitals - s,p & d.’
https://www.youtube.com/watch?v=K-jNgq16jEY
● Still can’t imagine orbital shapes? Check out the balloon model
on the link below
NCSSMDistanceEd. 2011. ‘p-orbitals with Balloons.’
https://www.youtube.com/watch?v=unjjYOzEjuY
Check Your Understanding
A. List all Possibilities
List the following values of
1. 1s orbital
2. 2p orbital
3. 3s orbital
,
and
for the orbitals in the following subshell.
4. 4d orbital
5. 5f orbital
B. Give me Four
Write the four quantum numbers for an electron described below.
6. The first electron to enter the 1s orbital.
7. The second electron to enter the 4py orbital.
8. The last electron to enter the 5fz3 orbital.
9. The first electron to enter the 4dxy orbital.
10. The first electron to enter the 7px orbital.
C. Allowed or Forbidden
Identify if the following set of quantum numbers is allowed. Write check if the set
of quantum numbers is allowed. If not, identify the error(s) in the set of quantum
numbers.
11. {1, 0, 1, +½}
12. {5, 5, 0, +½}
13. {4. 3. -1, -½}
14. {3, 0, -1, 1}
15. {7, 6, 0, -½}
28
D. True or False
Identify if the statement is true or false. Write true if the statement is true.
Otherwise, write false.
16. Two or more electrons can have the same set of quantum numbers.
17. The quantum number
is needed to describe an orbital.
18. The quantum number describes the energy and shape of the orbital.
19. The orbital 2px has a higher energy than the orbital 2py.
20. A value of 1 for the quantum number
indicates two electrons are
spinning counterclockwise.
Challenge Yourself
Indicate what is asked.
1. Identify the four quantum numbers of the first electron to exit the orbital
5dyz.
2. List all possible sets of quantum numbers , and
for the 8h subshell.
At what value of will the orbital h begin to appear?
For the next few items, consider the atom F. Consult your periodic table whenever
needed.
3. What is the highest value of ? From here, list all possible values of the next
three quantum numbers. Follow the table format presented in the discussion
section.
4. How many orbitals does the atom have?
5. Draw the boundary surface diagram of the F atom. Superimpose all orbitals
in one diagram. Use three-dimensional axes (xyz axes) to present your
diagram.
29
Lesson 5.3: Electron Configuration
Objectives
In this lesson, you should be able to:
● assign quantum numbers to electrons in an atom;
● write the electron configuration of an atom; and
● draw orbital diagrams to represent the electron configuration of
the atom.
In the quantum mechanical model, electrons are most probably found in subshell
orbitals. However, for an atom to be stable, its electrons must be distributed in a
way that will maximize its stability. This unique arrangement in an atom also
provides them to have characteristic reactivities. But how are electrons
distributed in an atom?
Warm-Up
Balloons? Orbitals!
Materials:
● 10 pieces, elongated and spherical
balloons
● 10 pieces, rubber bands
Procedure:
Secure some balloons and inflate them. Spherical balloons are used for s-orbitals
while elongated balloons are used for p- and d-orbitals. Create models for the
following orbitals and answer the follow-up questions.
1. Create models for a 1s orbital and a 2s orbital. How many electrons can a 1s
orbital hold? How many electrons can a 2s orbital hold? What is the major
difference between the two orbitals you made? Discuss your models in front
30
of the class.
2. Consider the set of 2p orbitals. As discussed in the previous lesson, three
degenerate orbitals belong to the 2p subshell. Create models for these
orbitals. What are the similarities and the differences between the three
orbitals?
● Tie them up together to represent the 2p subshell. How many
electrons can each p orbital hold? How many electrons can the whole
set of p orbitals hold?
● What does the whole set look like? Is this the complete set under the
second shell? How many electrons are there all in all in the second
shell?
● Present your models in front of the class and briefly discuss your
answers to the previous questions.
3. Consider the set of the 3d orbitals. As discussed in the previous lesson, five
degenerate orbitals belong to the 3d subshell. Create models for these
orbitals. What are the similarities and the differences between the five
orbitals?
● How many electrons can each d orbital hold? How many electrons can
the whole set of d orbitals hold?
● Present your models in front of the class and briefly discuss your
answers to the previous questions.
Learn about It
Electron Configuration
Each element in the periodic table are atoms that have their electron
configuration. The electron configuration is simply a description of how electrons
are distributed in an atom. The atomic orbitals organize the electrons inside the
atoms in pairs. The order in which the electrons are arranged depend on the
energies of the orbitals. These basic ideas form the foundations of electron
configuration.
31
An electron configuration follows the spdf notation shown below.
The first number in the notation is the principal quantum number. It is followed by
the subshell designation. The number in superscript is the number of electrons in
each subshell.
There are several rules to follow when distributing electrons. These are the Aufbau
principle, Hund’s rule, and Pauli’s exclusion principle.
1. In filling up electrons in atomic orbitals, the Aufbau principle is followed.
Atomic orbitals are filled from the lowest energy to the highest energy as
shown in the diagram below.
Fig. 10. Orbitals are filled from lowest energy to highest energy.
32
The order of atomic orbitals in increasing energy is 1s, 2s, 2p, 3s, 3p, 4s, 3d,
4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5d, 6p, 7s, 5f, 6d, 7p and so on.
The 1s orbital has the lowest energy, followed by 2s, and so on as indicated
by the arrows in the diagram. Take note that the s-subshell has 1 orbital, the
p-subshells have 3 orbitals, the d-subshells have 5 orbitals, and the
f-subshells have 7 orbitals. It means that the s orbitals could fill up to a
maximum of 2 electrons, for the p orbitals up to 6 electrons, for the d orbitals
up to 10 electrons, and for the f orbitals up to 14 electrons.
To identify the orbital with a lower energy, you may use the
rule where
corresponds to the principal quantum number and corresponds to the
azimuthal quantum number. The lower the value of
energy of the orbital. The higher the value of
of the orbital.
, the lower is the
, the higher is the energy
For example, nitrogen (Z = 7) has 7 electrons. The seven electrons of nitrogen
will fill the 1s orbital first with 2 electrons, followed by the 2s orbital with 2
electrons, and three 2p orbitals with 3 electrons.
Oxygen (Z = 8) has 8 electrons. The eight electrons of oxygen will fill the 1s
orbital first with 2 electrons, followed by the 2s orbital with 2 electrons, and
three 2p orbitals with 4 electrons.
2. Hund’s rule states that every orbital in the same subshell must be filled
singly before being paired. In other words, all electrons in singly occupied
orbitals should have parallel or same spins.
An orbital diagram is a graphical way of distributing electrons. An upward
spin represented by an upward arrow corresponds to the counterclockwise
spin of an electron. On the other hand, a clockwise spin is represented as a
downward arrow. The box represents the atomic orbital.
For nitrogen (Z = 7), the 1s and 2s orbitals will be fully filled. In filling up the 3
orbitals for 2p with 3 electrons, the 3 electrons will be first distributed singly
with the same spin for each orbital. Below is the orbital diagram for nitrogen.
33
3. Pauli’s exclusion principle states that no two electrons can have the exact
same set of quantum numbers. Electrons in the same orbital must have
opposite spins. In this case, electrons with opposite spins will have lower
repulsion than two electrons with the same spin. Hence, when a singly
occupied orbital is paired, the electron that should be added must be in the
opposite spin.
For oxygen (Z = 8), the 1s and 2s orbitals will be fully filled. In filling up the 3
orbitals for 2p with 4 electrons, the 3 electrons will be first distributed singly
with the same spin for each orbital. The remaining electron will be
distributed to the first 2p orbital.
Writing Electron Configuration of Neutral Atoms
There are several ways of writing the electron configuration. It could be the
longhand electron configuration or the shorthand electron configuration (also
called noble gas electron configuration).
Longhand Electron Configuration
To write the longhand electron configuration, follow the steps outlined below.
Step 1
Determine the atomic number of the element in the periodic table. For
neutral atoms, the atomic number (Z) is equal to the number of
electrons.
Step 2
Fill up the maximum number of electrons per orbital according to the
Aufbau principle.
34
Noble Gas Electron Configuration
A shorthand way of writing electron configuration is also called the noble gas
electron configuration. To write the noble gas electron configuration, the electron
configuration of a noble gas is substituted by writing the element in brackets and
writing the additional orbitals. The additional orbitals beyond the electron
configuration of the noble gas are called the valence orbitals. They are the
outermost orbitals in an atom.
To write the noble gas electron configuration, follow the steps below.
Step 1
Determine the atomic number of the element in the periodic table. For
neutral atoms, the atomic number (Z) is equal to the number of
electrons.
Step 2
Fill up the maximum number of electrons per orbital according to the
Aufbau principle.
Step 3
Determine the nearest preceding noble gas. Substitute the electron
configuration of the noble gas by writing the element symbol of the
noble gas in brackets.
Step 4
Retain the atomic orbitals that are not part of electron configuration of
the noble gas.
35
In fact, the periodic table is divided into blocks to determine the configuration of
noble gases easily.
Figure 11. The periodic table of elements is divided based on the type of subshells.
36
Worked Examples
Example 1
Write the longhand electron configuration of neon. Draw its orbital diagram.
Solution
Step 1
Identify the number of electrons for the given element.
Neon has the atomic number 10. It has 10 electrons.
Step 2
Fill up the maximum number of electrons per orbital according to the
Aufbau principle.
For neon (Z = 10), the 1s, 2s, and 2p orbitals will be fully filled.
Step 3
Identify the preceding noble gas. Substitute the electron configuration
of the noble gas by writing the element symbol of the noble gas in
brackets. Draw the orbital diagram.
Hence, the electronic configuration for neon is 1s2 2s2 2p6.
Let us Practice
Write the longhand electron configuration of krypton. Draw its orbital diagram.
Example 2
Write the longhand electron configuration of argon. Draw its orbital diagram.
Solution
Step 1
Step 2
Identify the number of electrons for the given element.
Argon has the atomic number 18. It has 18 electrons.
Fill up the maximum number of electrons per orbital according to the
Aufbau principle.
37
For argon (Z = 18), the 1s, 2s, 2p, 3s, and 3p orbitals will be fully filled.
Step 3
Identify the preceding noble gas. Substitute the electron configuration
of the noble gas by writing the element symbol of the noble gas in
brackets.
Hence, the electronic configuration for argon is 1s2 2s2 2p6 3s2 3p6.
Let us Practice
Write the longhand electron configurations of xenon and radon. Draw their
orbital diagrams.
Example 3
Write the longhand and shorthand electron configuration of aluminum. Draw its
orbital diagram.
Solution
Step 1
Identify the number of electrons for the given element.
Aluminum has the atomic number 13. It has 13 electrons.
Step 2
Fill up the maximum number of electrons per orbital according to the
Aufbau principle.
For aluminum (Z = 13), the 1s, 2s, 2p, and 3s orbitals will be fully filled,
while among the 3p orbitals one will have a single unpaired electron.
Step 3
Identify the preceding noble gas. Substitute the electron configuration
of the noble gas by writing the element symbol of the noble gas in
brackets. Draw the orbital diagram.
38
Hence, the electronic configuration for aluminum is 1s2 2s2 2p6 3s2 3p1
or [Ne] 3s2 3p1.
Let us Practice
Write the longhand and shorthand electron configurations of chlorine and
magnesium. Draw their orbital diagrams.
Example 4
Write the longhand and shorthand electron configurations of calcium. Draw its
orbital diagram.
Solution
Step 1
Identify the number of electrons for the given element.
Calcium has the atomic number 20. It has 20 electrons.
Step 2
Fill up the maximum number of electrons per orbital according to the
Aufbau principle.
For calcium (Z = 20), the 1s, 2s, 2p, 3s, 3p, and 4s orbitals will be fully
filled.
Step 3
Identify the preceding noble gas. Substitute the electron configuration
of the noble gas by writing the element symbol of the noble gas in
brackets. Draw the orbital diagram.
Hence, the electronic configuration for calcium is 1s2 2s2 2p6 3s2 3p6 4s2
or [Ar] 4s2.
Let us Practice
Write the longhand and shorthand electron configurations of carbon and sulfur.
Draw their orbital diagrams.
39
Example 5
Write the longhand electron configuration of copper. Draw its orbital diagram.
Solution
Step 1
Identify the number of electrons for the given element.
Copper has the atomic number 29. It has 29 electrons.
Step 2
Fill up the maximum number of electrons per orbital according to the
Aufbau principle.
For copper (Z = 29), it is predicted that the 1s, 2s, 2p, 3s, 3p, and 4s
orbitals will be fully filled; one 3d orbital will remain singly filled.
However, half-filled and fully-filled orbitals are favored because of their
stability. This changes the configuration such that the 4s orbital
becomes half-filled and the 3d orbitals become fully-filled.
Step 3
Identify the preceding noble gas. Substitute the electron configuration
of the noble gas by writing the element symbol of the noble gas in
brackets. Draw the orbital diagram.
Hence, the electronic configuration for copper is 1s2 2s2 2p6 3s2 3p6
4s13d10 or [Ar] 4s13d10.
Let us Practice
Write the longhand and shorthand electron configurations of Cr, Ag, Au, and Mo.
Draw their orbital diagrams.
Key Points
● Electrons are specifically distributed in the orbitals using rules of electron
configuration.
40
● The electron configuration follows the spdf notation, where the principal
quantum numbers come into play.
● The electron configuration of a neutral atom follows the principles of Aufbau,
Hund’s, and Pauli’s.
○ Aufbau principle states that the electrons are filled up from the lowest
energy orbital to the highest energy orbital.
○ Hund’s rule states that degenerate orbitals in a specific subshell are
filled with electrons one at a time first, with all spins parallel to one
another.
○ Pauli’s exclusion principle states that no two electrons in the same
atom can have the same set of quantum numbers.
● The electron configuration can be written in other ways aside from the
complete, longhand version. The shorthand notation focuses only on the
noble gas core and the valence orbitals, while the orbital diagram notation
focuses on electron distribution in degenerate orbitals by illustrating the
electron spins of the electrons through arrows.
Web Links
For further readings, you can check on the following links:
● Want to know how the mnemonic for electron configuration
came into existence?
Nerea Iza and Manuel Gil. ‘A Mnemonic Method for Assigning the Electronic
Configurations of Atoms’. Journal of Chemical Education, 72. No. 11 (1995), 1025. DOI:
10.1021/ed072p1025.
https://pubs.acs.org/doi/abs/10.1021/ed072p1025
● Get your drawings done perfectly by watching how to draw
electron configuration diagrams properly.
FuseSchool - Global Education. 2014. ‘Electron Configuration Diagrams | Properties
of Matter | Chemistry | FuseSchool.’
https://www.youtube.com/watch?v=hSkJzE2Vz_w
41
Check Your Understanding
A. Electron Configuration Table
Fill up the table by indicating what is needed.
Element
Shorthand notation
Longhand notation
Si
Sn
As
Co
Rb
[Kr] 5s2
1s22s22p4
1s22s22p63s23p64s23d8
An element with 20
electrons
An element with Z = 15
A neutral element with 7
protons
An element in period 4,
group 12
1s 22s 22p6 3s2 3p6 4s1 3d5
B. Coloring Periodic Table
Color the areas in the periodic table where the following element(s) appear.
1. Color the element(s) that have five unpaired electrons with red.
2. Color the element(s) that have no unpaired electrons with yellow.
42
3. Color period 3 transition metal(s) that have complete d orbitals but
incomplete s orbitals with blue.
4. Color period 4 transition metal(s) that have incomplete d orbitals but
complete s orbitals with yellow.
5. Color an element whose valence electrons are 3s2 3p4 with blue.
Answer the following.
1. Hund’s Rule states that orbitals must be first filled singly before being paired.
It also states that each singly paired orbital in a subshell should have parallel
spins. Explain.
2. Pauli’s exclusion principle states that paired electrons in each orbital cannot
have the same set of quantum numbers. Explain.
3. Write the longhand notation for Gd.
4. Write the shorthand notation for Se2-.
5. Draw the orbital diagram for Cu+2.
43
Laboratory Activity
Activity 5.1
Flame Test
Objectives
At the end of this laboratory activity, the students should be able to:
● observe characteristic colors produced from metals found in common
household reagents when they are burned; and
● identify an unknown metal based on the color of its flame
Materials and Equipment
● baking soda
● cream of tartar
● boric acid
● strontium citrate supplement
● de-icer spray
● ammonia
● iron filings
●
●
●
●
●
●
●
copper wire
vinegar
isopropyl alcohol
glass dishes
lighter
cups of water
cotton swabs
Procedure
Safety Precaution
Keep other flammable materials such as paper and cotton out of your working
space. Always wear proper personal protective equipment (PPE) to keep you from
harm. In case of fire, immediately call the attention of your instructor.
1. Put the required amounts of the following materials in separate glass plates
or dishes.
Solution
no.
Material
Preparation
1
boric acid
2 tsp boric acid
44
2
isopropyl alcohol
3 mL isopropyl alcohol
3
baking soda
2 tsp baking soda
4
cream of tartar
2 tsp cream of tartar
5
de-icer spray
Spray until the solution is visible.
6
copper solution
3 mL of copper* solution made by
dissolving 1 cm copper wire in
ammonia.
7
strontium supplement
1 strontium citrate supplement
8
iron solution
3 mL of iron** solution made by
dissolving iron filings in isopropyl
alcohol.
* Shake the solution vigorously until the solution turns blue.
** Let the iron stand with alcohol until the solution turns yellow.
2. Add enough isopropyl alcohol to cover the solutions in each glass plate or
dish.
3. Ignite the solution with a lighter and observe the flame color.
4. Record color of the flame.
5. Put out the flame.
Waste Disposal
All solids should be dried before disposing to trash bins. Solutions can be
disposed to sink with copious amounts of running water.
Observation
Record the colors you have observed from the flame of the ignited solutions.
Table 1. Colors observed from the flames of ignited solutions.
Solution
number
Element producing
the color
1
boron
Observations
45
2
carbon
3
sodium
4
potassium
5
calcium
6
copper
7
strontium
8
iron
Guide Questions
1. Why do you think the solutions have different flame colors?
2. What atoms are responsible for the production of colors?
3. How can the quantum mechanical model of the atom explain this
phenomenon?
Performance Task
Is Copper Present?
Goal
● Your task is to design a method for determining the presence of copper in
soils in your community.
● The goal is to determine whether copper is present or not in different soil
samples obtained near your area.
● The problem is how you will be able to create a method that requires low
cost but produces reliable results.
● The obstacle to overcome is the unavailability of chemical reagents and lack
of advanced technology in your community.
Role
● You are the head of a health committee in your community.
Audience
46
● The target audience is the whole barangay community.
● You need to convince them that your method offers high reliability and
requires low cost.
Situation
● You must carefully select five-point areas where you will collect soil samples.
Conduct an experiment.
Product, Performance, and Purpose
● You will create a written report based on the results of the experiment.
● You will explain your methods and how you arrived at the conclusion on
whether copper is present in the soil samples or not.
Standards and Criteria for Success
● Your work must meet the standards found in the rubric below.
Criteria
Below
Expectations,
0% to 49%
Needs
Improvement
50% to 74%
Successful
Performance
75% to 99%
Exemplary
Performance
100%
Comprehensiveness
Methods do not
justify the objectives
Shows some
comprehensiveness, but most
methods are not
in line with the
objectives
Comprehensive,
some methods
meet the
objectives but
are not planned
well
Very
comprehensive,
method
carefully
planned out,
and techniques
meet the
objectives
Reliability
Methods produced
no data
Shows some
reliability, data
can be gathered
but cannot be
analyzed further
Reliable, data
gathering and
analysis offers
reliable results
but sometimes
show
inconsistencies
Very reliable,
data gathering
and analysis
offer highly
reliable results
Innovativeness
Does not exhibit
effort to be original
Shows some
originality,
inadequate used
of resources
Original ideas,
adequate use of
resources
Very original,
shows
imaginative use
of resources
47
Self Check
After studying this unit, can you now do the following?
Check
I can…
explain why the quantum mechanical model is the most accurate model
of the atom up to date.
explain why metals produce characteristic color when heated.
explain the significance of the quantum numbers.
arrange the electrons in the orbitals of an atom using rules of electron
configuration.
Key Words
Degenerate orbitals
These are two or more orbitals that have the same
energy.
Electron
configuration
It describes the distribution of electrons in the atomic
orbitals of atoms.
Excited state
It is any energy state with a higher energy than the
ground state.
Ground state
It is the lowest energy state of an electron.
Orbital
It is a region in space where there is a high probability
that electrons are found.
Quantum number
It is a set of numbers that describe orbitals and electrons.
48
Wrap Up
The Electronic Structure of Matter
References
Chang, Raymond and Kenneth A. Goldsby. 2016. Chemistry. New York, NY:
McGraw-Hill Education.
Silberberg, Martin. 2009. Chemistry: The Molecular Nature of Matter and Change,
5th edition. New York, NY: McGraw-Hill Education.
Whitten, Kenneth W. 2006. General Chemistry. Thomson Brooks/Cole.
PennState Eberly College of Science. “Electromagnetic Radiation”. Accessed June 21,
2017. https://online.science.psu.edu/chem101_sp1/node/11822
49
University of Oregon. “Pauli Exclusion Principle”. Accessed June 21, 2017.
http://abyss.uoregon.edu/~js/glossary/pauli_exclusion_principle.html
Georgia State University. “Hund’s Rule”. Accessed June 21, 2017.
http://hyperphysics.phy-astr.gsu.edu/hbase/Atomic/Hund.html
Answer Key
Lesson 5.2: Atomic Orbitals and Quantum Numbers
Let us Practice
1. forbidden
2. allowed
3. forbidden
Lesson 5.3: Electron Configuration
Let us Practice
1. Kr: 1s22s22p63s23p64s23d104p6
2. Xe: 1s22s22p63s23p64s23d104p65s24d105p6
Rn: 1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p6
3. Cl: 1s22s22p63s23p5 or [Ne]3s23p5
Mg: 1s22s22p63s2 or [Ne]3s2
4. C: 1s22s22p2 or [He]2s22p2
S: 1s22s22p63s23p4 or [Ne]3s23p4
5. Cr: 1s22s22p63s23p64s13d5 or [Ar]4s13d5
Ag: 1s22s22p63s23p64s23d104p65s14d10 or [Kr] 5s14d10
Au: 1s22s22p63s23p64s23d104p65s24d105p66s14f145d10 or [Xe] 6s14f145d10
Mo: 1s22s22p63s23p64s23d104p65s14d5 or [Kr]5s14d5
50