11

General Chemistry 1

TOPIC: THE QUANTUM MECHANICAL DESCRIPTION OF THE ATOM

AND IT’S ELECTRONIC STRUCTURE
COMPETENCY:
 Use quantum numbers to describe an electron in an atom
 Determine the magnetic property of the atom based on its electronic configuration
 Draw an orbital diagram to represent the electron configuration of atoms

CODE: STEM_GC11ESIIa-b-54, STEM_GC11ESIIa-b-57, STEM_GC11ESIIa-b-58

OBJECTIVES:
At the end of the week, you shall have:
Knowledge  Describe electrons using quantum numbers
Skill  Draw orbital diagrams to represent the electron configuration of atoms
 Create models depicting the shape of the s, p, and d orbitals
Attitude  Determine whether an atom is paramagnetic or diamagnetic based on its electron
configuration
 Cite practical applications of quantum numbers/orbital diagrams/magnetic property in
real life

Week 1 – January 4
– 8, 2021
Wednesday / 1:00 –
4:00 P.M.
Jennette G. Belliot
 References /
I. Lesson Contents
Resources
Chang, Raymond.
CHEMISTRY- 10th
Edition. 1221
A. Quantum Numbers: Avenue of the
 Determine the home address of your friends or relatives using the format of house Americas, New
number, street, purok name, barangay, municipality and zip code. How many of your York, NY 10020:
Mc Graw Hill,
friends/relatives live on the same street? How many have the same house number?
Companies, Inc,
Just as there are no two houses that have the same address (they could have the same 2010
purok but they are of different house number/street), no two electrons in an atom have the
same set of four quantum numbers. Quantum numbers tell where an electron is located
around the nucleus of an atom. It is kind of like the address of electrons. Mendoza, Estrella
 There are four quantum numbers, three of which, the principal quantum number (n), the E. and Teresita F.
angular momentum quantum number (ℓ), and the magnetic quantum number (ml) Religioso You and
the Natural World
describe the atomic orbitals that is a region of space where you can most probably find the CHEMISTRY 927
electron. A fourth quantum number, the spin quantum number (ms) completes the Quezon Ave.,
description (spin orientation) of the electrons in the atoms. Quezon City 927
Phoenix Publishing
House,
 The Principal Quantum Number (n) Inc, 2008
a. Determines the energy of an orbital; describes the energy
level an electron is placed in
b. Determines the orbital size
c. Is associated with the average distance of the
electron from the nucleus in a particular orbital; the
larger the value of n, the farther the average
distance of the electron from the nucleus
d. n can have the values 1, 2, 3, …

e. Orbitals with the same principal quantum number (n) are

said to be in the same shell.

 The Angular Momentum Quantum Number (ℓ)

a. Describes the “shape” of the orbitals
b. ℓ can have the values 0, 1, 2, up to n-1.
So if the principal quantum number (n) is 2, ℓ could be 0 and 1. Why 1? study the calculation
below:
ℓ=n-1
ℓ=2-1
ℓ=1
c. Orbitals that have the same n and ℓ values belong to the same subshell.
d. It is usually designated by letters s, p, d, f, … which have a historical origin from spectral
lines. The s, p, d, f designations of the orbitals refer to sharp, principal, diffuse, and
fundamental lines in emission spectra.
 The Magnetic Quantum Number (ml)
a. Describes the orientation of the orbital in space
b. Describes the number of orbitals within a subshell
c. ml can have the values -ℓ up to +ℓ:
- ℓ, (-ℓ + 1), … 0, … (+ ℓ -1), + ℓ
The following table summarizes the relationship of n, ℓ, and ml:
 The Electron Spin Quantum Number (ms)
a. The first three quantum numbers (n, ℓ, ml) describe the energy, shape and orientation of
the orbitals. The 4th quantum number (ms) refers to two different spin orientations of electrons
in an orbital.
b. In 1925, Uhlenbeck, Goudsmit, and Kronig introduced the idea of the self-rotation of the
electron. The spin orientations are assigned the number ms = ½, ms = -½ which are called
“spin-up” and “spin-down”, respectively.

c. The electrons are paired such that one spins upward and one downward. This neutralizes
the effect of their spin on the action of the atom as a whole. But in the valence shell of atoms
where there is a single electron whose spin remains unbalanced, the unbalanced spin
creates spin magnetic moment, making the electron act like a very small magnet.

 The Representations of the Shapes of Atomic Orbitals

a. Strictly speaking, an orbital does not have a definite shape, but the electron’s probability
of being in a certain place has a shape. While electron can be found anywhere around the
nucleus, there are regions where there is much higher probability of finding it. For s orbital,
the probability distribution is spherical as shown in figure a. All the s orbitals are spherical in
shape but they differ in size, which
increases as the value of the principal quantum number (n) increases.

b.

There

are

three 2p
orbitals: 2px,
2py, 2pz indicating the axes along which they
are oriented. The electron probability density of p orbitals is not spherically symmetric; it
has a double teardrop shape or a dumbbell shape (as described in some books). The
electron can most probably be found within the two lobes of the dumbbell region; there is a
zero probability of finding it along the nodal planes found in the axes. All three 2p orbitals are
identical in shape and energy but differ in orientation as shown in figure (b). The p orbitals of
higher principal
Image Source:
quantum numbers have similar shapes. (a-c) Wyona C
Patalinghug et al.,
Teaching Guide for
Senior High School
General Chemistry
1 (Diliman, Quezon
City, Philippines:
Commission on
Higher Education,
2016), 171-172.

c. Figure c shows that d orbitals occur for the first time when n = 3; d orbitals have five
orientations. Four of the d orbitals have identical basic shapes except for their orientation
with respect to the axes. The wave functions exhibit positive and negative lobes along the
axes; there is a zero probability of finding the electron at the origin. The fifth wave function,
dz2, has a similar shape with that of the p-orbital with a donut-shape region along the x-axis.
 The four quantum numbers compose the numbers that describe where an electron
is located around the nucleus of an atom. It is kind of like the electron's address. The
quantum numbers shall be in the order: energy level (n), sub-level or orbital type (ℓ),
the
orientation of the orbital specified in (mℓ), and the orientation of the spin of the electron (ms).
It is written in the order (n, ℓ, mℓ, ms).
 Example 1: What is the allowed set of quantum numbers for an electron that is found in
the first energy level?
a. The energy level, n = 1.
b. The orbital type is only s, thus, ℓ = 0
c. From ℓ, the orbital type is s. An s orbital has only one orientation, designated as 0, so, mℓ
=0
d. In the 1s orbital, an electron can have an up-spin or a down-spin. Therefore, ms could be
1/2 or -1/2.
The allowed set of quantum numbers for 1s electron are (1,0,0,1/2) and (1,0,0,-1/2).
How does (1,0,0,1/2) differ from (1,0,0,-1/2)? The first set corresponds to the electron with
spin up and the second set refers to the electron with spin down.
 Example 2: Given the following information for the three electrons:

Quantum Electron A Electron Electron C

 Number B
n 4 5 4
ℓ 2 0 2
mℓ -2 0 +1
ms 1/2 1/2 -1/2

Describe the electrons based on quantum numbers. Answer:

Electron A first electron in the 4d orbital (4d1) Image source:
Electron B first electron in the 5s orbital (5s1) Kevin Boudreaux,
Electron C ninth electron in the 4d orbital (4d9) “Quantum
Numbers, Atomic
Orbitals, and
Electron
Configurations,”
 Electron Configuration 2020,
The distribution of electrons among the orbitals of an atom is known as electron https://www.angelo.
edu/faculty/kboudre
configuration. The order in which the electrons are filled in can be read from the periodic
a/index.htm.
table of elements in the following manner:

- You can refer to the periodic table presented above to assign electron configurations for
each element. To write the electron configurations, indicate the orbitals that are occupied by
electrons, then write a superscript that indicates how many electrons are in the set of
orbitals. For instance, write the electron configuration of lithium:
Lithium has an atomic number of 3. The atom’s atomic number is the number of protons of
the atom; thus, it is also the number of electrons in an atom with 0 charge. So for lithium, it
has 3 electrons in its ground state. The 1st and 2nd electrons are in 1s orbital and the 3rd
electron is in 2s orbital, so its electron configuration is 1s22s1.
- Condensed electron configuration can be used to shorten the process of writing a long
electron configuration. To do this, write the symbol of the nearest noble gas with fewer
electrons than your atom in brackets, after which, continue with the electron configuration for
the orbital sets. For instance, the electron configuration of lithium which is 1s22s1 can also be
written as [He]2s1. Helium is the nearest noble gas with fewer electrons than lithium.

- Caution: the d and f orbital regions in the periodic table correspond to energy levels that are
different from the period they're located in. Notice that the first row of the d orbital block
corresponds to the 3d orbital even if it is in period 4, while the first row of the f orbital
corresponds to the 4f orbital even if it is in period 6.

B. Orbital Diagrams:

 Writing the quantum numbers of electrons in set notation like (3,1,-1,-1⁄2) is time
consuming and difficult to compare so an abbreviated form was developed. With electron
configuration, the first two quantum numbers, n and ℓ, are listed; it also shows how many
electrons exist in each orbital. Many times it is needed to see all the quantum numbers in an
electron configuration, this is the purpose of the orbital diagram. Orbital diagrams pictorially
describe the electrons in an atom. In addition to listing the principal quantum number, n, and
the subshell, ℓ, (which can also be seen in the electron configuration) the orbital diagram
shows all the different orientations and the spin of every electron. Orbital diagrams illustrate
the number of subshells using lines or boxes for electrons (one box/line for s-orbital, three for
p-orbitals, five for d-orbitals, and 7 for f-orbitals). In each box, electron spin is noted by using
arrows; up arrows indicate 1⁄2 spin and down arrows mean –1⁄2 spin.

 Rules for Filling Orbitals:

a. Aufbau Principle states that the lowest energy orbital is filled first. Electrons usually fill
the lowest energy level and the simplest orbital shape first before the higher energy orbitals
are filled. The order of filling based on the Aufbau Principle is presented in the following
diagram.
Figure f. The order of orbital filling based on the Aufbau Principle
- Based on figure f, examine why the first orbital diagram below violates Aufbau
Principle.

- The Aufbau Principle is not a universal rule; not all atoms obey it. Around ten
transition metals violate the Aufbau Principle (Cr, Cu, Nb, Mo, Ru, Rh, Pd, Ag, Pt,
and Au). In each element, the d orbital had an extra electron from the s orbital,
except in Pd where two electrons are consumed by the d orbital. In lanthanides and
actinides, ten elements go against the Aufbau Principle (La, Ce, Gd, Ac, Th, Pa, U,
Np, Cm, and Lr). In the said elements, the d orbital takes an electron from the f
orbital; Th and Lr are special cases. In Th, 6d takes both electrons from 5f while in
Lr 6d is replaced by 7p.
b. Pauli Exclusion Principle states that no two electrons in an atom can have the
same four quantum numbers. This is why each orbital only has two electrons, one
with up-spin (1⁄2) and one with down-spin (–1⁄2).

c. Hund’s Rule states that same-energy orbitals, those which differ only in their
orientation, are filled with electrons that have the same spin before the second
electron is added to any of the orbitals.

Example:
What element has the following quantum numbers for their last electron (in the
subshell with highest energy level):
(a) 3,1,1,1/2; (2) 1,0,0,-1/2?
Illustrate the orbital diagram of the element.
a) The quantum numbers 3,1,1,1/2 corresponds to Phosphorus. n indicates that
the element has 3 energy levels, the element is in the 3rd period in the periodic
table; ℓ indicates that the orbital type is p, the mℓ is equal to 1 suggesting that all 3
orientations of the p-orbital are occupied; ms is equal to 1/2 indicating up-spin of
the last electron and that the last orbital only has 1 electron, all orientations of the
p-orbital have unpaired electrons. With this, it can be deduced that the valence
subshell of the element is 3p3, the only element in the 3rd period of the periodic
table having this valence subshell is phosphorus.

b) The quantum numbers 1,0,0,-1/2 corresponds to Helium. n indicates that the

element has 1 energy level, the element is in the 1st period in the periodic table; ℓ
indicates that the orbital type is s, there is only one orientation of the s orbital thus
mℓ=0; ms is equal to -1/2 indicating down-spin of the last electron and that
the last orbital has 2 electrons. With this, it can be deduced that the valence
subshell of the element is 1s2, the only element in the 1st period of the periodic table
having this valence subshell is helium.

C. Paramagnetism and Diamagnetism

Paramagnetism refers to the magnetic state of an atom that has one or more
unpaired electrons. Due to the electrons' magnetic dipole moments, the unpaired
electrons are attracted by a magnetic field. Hund's Rule states that electrons have
to occupy every orbital singly before any orbital is doubly occupied. This could leave
the atom with many unpaired electrons. Since unpaired electrons can spin in either
direction, they exhibit magnetic moments in any direction. This capability lets
paramagnetic atoms to be attracted to magnetic fields.
Diamagnetic substances are characterized by paired electrons. According to the
Pauli Exclusion Principle, no two electrons could occupy identical quantum state at
the same time, the electron spins are oriented in opposite directions. With this, the
magnetic fields of the electrons cancel out; thus there is no net magnetic
moment, and the atom cannot be attracted into a magnetic field.
How to tell if a substance is paramagnetic or diamagnetic:
Electron configuration can be used to determine the magnetic properties of an
element: If it has unpaired electrons, then the substance is paramagnetic and if all
electrons are paired, the substance is diamagnetic. This process can be broken into
these steps:
1. Write down the electron configuration
2. Draw the valence orbitals
3. Identify if unpaired electrons exist
4. Based on the orbital diagram, determine whether the element is diamagnetic or
paramagnetic

Example: Zinc Atoms

o Step 1: Determine the electron configuration
For Zn atoms, the electron configuration is [Ar]4s23d10
o Step 2: Draw the valence orbitals

Focus on the valence electrons only (ignore the core electrons).

o Step 3: Look for unpaired electrons
There are no unpaired electrons.
o Step 4: Determine whether the substance is diamagnetic or paramagnetic

Since there are no unpaired electrons, zinc atoms are diamagnetic.

II. Activities References

/
Resources

Activity 1: Complete me!

What you need: Pen, Paper, Periodic Table of Elements
What to do: Look at the given elements on the periodic table. Write the electron
configuration in the second column. In the third column, draw the orbital diagram of
the subshell in the highest energy level containing the last electron. In the fourth
column, determine whether it is paramagnetic or diamagnetic. Lastly, assign quantum
numbers as directed. Write your answers on a separate sheet of paper.

Element Condens Draw the Is it Quantum Number of the Last Electron

ed orbital paramag
Electron diagram netic or
Configu- of the diamagn
ration subshell etic?
in the
highest N ℓ ml ms
energy
level
containin
g the last
electron

↑
Ca paramag 3 O O 1/2
netic
Cl
 Sc
Zn

Activity 2: Skills Objective

Activity 3: Attitude Objective

III. Performance Task (Authentic) Rubric

Make me! The learners’ output will be evaluated
- What you need: paper, pen, scissors/cutter, scotch tape, according to the rubrics:
sticks, cardboard or acetate, styrofoam balls or balloons or
any locally available materials that could depict an orbital Creativity - 20 points
shape such as mansanitas, and the likes. Content/ Accuracy - 20 points
- What to do: In this activity, you will be crafting models Timeliness - 10 points
depicting the shape of the s, p, and d orbitals. Follow the -----------------
steps below: Total 50 points
1. Create a model of the s, p, and d orbitals using locally
available materials. You may refer to the key concepts section
for the shapes of the orbitals. Use the
styrofoam/balloon/other materials to depict the region where
you can most likely find an electron. Use the
cardboard/acetate and sticks to depict the nodal planes.
2. Label your model using strips of paper.
3. If you are using perishable items such as fruits for your
models, take pictures of your model. There should be
pictures where you are holding your output and other

pictures showing close-up look of your model. Print the

pictures and attach them in your activity sheet. If you don’t
have printers at home, you may send the pictures in your
class’ group chat instead.
4. If you are using non-perishable items for your models, you
may submit the model itself to your teacher during the
retrieval of modules/activity sheets. Make sure to pack the
 model securely to keep it intact.
- Guide Questions:
1. Describe the shape of the s, p, and d orbitals.
2. Can electrons be exactly found on the regions depicted by
the orbital shapes? Explain.

3. If you are using perishable items such as fruits for your

models, take pictures of your model. There should be pictures
where you are holding your output and other

IV. Answer Key

Activity 2
Activity 1

Activity 3

Answers may vary.

The science of today is the technology of tomorrow.

Prepared By: Jennette G. Belliot- T-III

Subject Teacher

Checked & Evaluated: 11/5/2020

RANEL D. BRIONES- MT-1