chapter ii: atomic chemistry

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Chapter II: atomic chemistry

Atom is the basic building block of matter. It consists of three parts which are technically known

as sub-atomic particles. These are the protons, neutrons and electrons.

Protons are positively charged sub-atomic particles with an absolute mass of 1.67 x 10-27 kg and

an absolute charge of +1.6 x 10-19 Coulombs (C). Protons give identity to an element. Each element has

their own proton number. The proton number of an element corresponds to the atomic number of that

element. For example, the atomic number of Lithium is three (3) which means that Lithium has 3

protons. If an element has 4 protons, then it is not anymore Lithium, but it is now Beryllium (atomic

number= 4)

Neutrons are neutrally charged sub-atomic particles (i.e., its total charge is zero) with an absolute

mass similar to that of proton. Together, the sum of proton and neutron gives the mass number or

atomic mass of an element. Unlike the absolute mass (true mass), the mass number or atomic mass of

an element is relative (i.e., it is considered in relation to or in proportion to something else). As an

analogy, take one deck of cards. One deck of cards does not mean one piece of card. The absolute pieces of

cards in one deck are 52 cards while its relative piece is one deck. If a person has two decks of cards

(relative piece), the absolute pieces are 104 cards. Now, the absolute mass of neutron and the absolute

mass of proton are just the same (i.e., both are 1.67 x 10-27 kg). Hence, the ratio of absolute mass of proton

and neutron is 1 : 1 (or 1 proton mass is equivalent to 1 neutron mass). Based on this ratio, if an atom has

2 protons and 1 neutron, then its atomic mass (relative) is 3 amu (atomic mass unit) or 3 Da (Daltons).

Atomic mass= number of proton + number of neutron

Atomic mass = 2 + 1

Atomic mass = 3 Da

At the end of this chapter, the students will be able to:

differentiate among atoms, molecules, ions and give examples

describe the quantum mechanical model of the atom

describe the electronic structure of atoms in terms of main energy

levels, sublevels, and orbitals, and relate this to energy

use quantum numbers to describe an electron in an atom

⦿

Based on our current knowledge, how do atoms look like electronically?

⧉ Big Question

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But, its absolute mass (true mass) is the sum of the true masses of 2 protons and 1 neutron which is

5.01x10-27 kg.

Absolute mass= true masses of all protons + true masses of all neutrons

Absolute mass = 2 (1.67 x 10-27 kg) + 1 (1.67 x 10-27 kg)

Absolute mass= 5.01 x 10-27 kg

Notice that atomic mass has different unit from absolute mass. Absolute mass is usually expressed

in terms of kilograms while the atomic mass is usually expressed in terms of atomic mass unit (amu) or

Dalton (Da), where 1 amu is equal to 1 Da. Both protons and neutron are found at the center of every

atom and together, they make up the atomic nucleus.

Electrons are negatively charged sub-atomic particles with an absolute mass of 9.11 x 10-31 kg and

an absolute charge of -1.6 x 10-19 Coulombs (C). Electrons let the elements to interact and bond with each

other to form compounds. As long as the number of electrons and protons are equal, the atom or element

will remain neutral (no charge). But, as they become unequal, the atom or element will gain some charges

and will now be known as ion. Ions are charged atoms/ elements. If there are more protons than

electrons, then, the atom/element is positively charged and is known as cation (i.e., positively charged

ion). On the other hand, if there are more electrons than protons, then, the atom/element is negatively

charged and is known as anion (i.e., negatively charged ion). For example, if a Sulfur atom (atomic

number = 16) has 16 electrons, then it has no charge at all. If it has 18 electrons, then its charge is -2

since there are two more electrons than protons (atomic number); while, if it has 10 electrons, then its

charge is +6 since there are 6 more protons than electrons. Now take note that the charges

aforementioned (+6 and -2) are just relative charges since in reality, the charge of one proton and one

electron are +1.6 x 10-19 C and -1.6 x 10-19 C respectively.

In the incoming discussions, the masses and charges that will be used are the relative atomic

masses and relative charges.

__________________________________________________________________________________________________

In early 1800’s an English chemist named John Dalton proposed the idea that matter is made of

tiny, indivisible particle known as atom. From the early works that he did, he postulated some

assumptions regarding the atom. These assumptions are now recognized as parts of Dalton’s Atomic

Theory.

The Four Assumptions in Dalton’s Atomic Theory

1) Matter and elements are made of atoms – Elements are made up of minute, discrete, indivisible,

and indestructible particles called atoms. Atoms cannot be divided anymore. It is the smallest possible

size a matter can have.

2) The atoms of an element are identical in their masses and atoms of different elements have

different masses – Atoms of the same element have the same properties, such as mass. Atoms of

different elements have different properties, including a different mass. Same elements must have same

mass; therefore, if two elements have different mass, they are NOT the same elements.

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3.) Compounds are formed by a combination of two or more different kinds of atoms – When two

or more atoms of different elements interact with each other, they form a pure substance known as

compounds. Chemical combination between two or more atoms occur in simple, numerical ratios (i.e., 1 to

1, 1 to 2; 2 to 3; etc.). No element combines only half or quarter of itself to another element to form a

compound or molecule. When two elements combine, their ratios are in whole numbers as in CO2 where

the ratio is for every 1 Carbon, there are 2 Oxygen atoms. There is no such thing as CO1/2.

4.) A chemical reaction is a rearrangement of atoms – An element's atoms do not change into other

element's atoms by CHEMICAL REACTIONS. For example, nitrogen and oxygen atoms stay as

themselves even when combined. No detectable gain or loss in mass occurs in chemical reactions. A

simple chemical reaction would not change the atom of an element to become a new atom of a new

element.

However, later studies and discoveries revealed some flaws in this theory. For example, because of

the discovery of sub-atomic particles (proton, neutron and electron), postulate number 1 was falsified.

Today, almost all people know that atoms are further divisible into the aforementioned sub-atomic

particles. In fact, current studies revealed that protons and neutrons are further divisible into even tinier

particles known as quarks. Quark is just one of the elementary particles that a matter has. These

elementary particles are, so far, the most indivisible component of a matter and not the atom. Moreover,

the initial discovery of isotopes in 1913 had falsified the postulate number 2 in Dalton’s atomic theory.

Isotopes are elements with the same atomic number (proton number) but have different atomic masses

(mass numbers). For example, 92Uranium-238 and 92Uranium-235 are isotopes of each other since they

have the same atomic number (i.e., 92), but they differ in atomic masses (i.e.,238 and 235). Therefore,

atoms of the same element can have different atomic masses and properties.

__________________________________________________________________________________________________

For a very long time, scientists had known that matter is made of tiny, indivisible particle known

as atom. It took over a century for people to realize that atom is still divisible and it has three major sub-

atomic particles. Early attempts to improve this concept seemed arduous for the scientists since there

were no advanced equipments to verify their assumptions back then. Below are the four major old model

of atoms and their proponents.

1. Atomos model- The first model of the atom was proposed by John Dalton. According to him, atom just

looks like a sphere which cannot be divided or torn anymore into smaller pieces. Later on, the

indivisibility of the atom was falsified as the sub-atomic particles were discovered.

Figure 1: Atom according to John Dalton

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2. Plum Pudding model- On April 30, 1897, Joseph John (J.J.) Thomson (1856-1940) announced that

the cathode rays from his experiment were negatively charged particles which he called 'corpuscles'- the

first name of electron. He also announced that they had a mass about 1000 times smaller than a hydrogen

atom, and he claimed that these corpuscles were the things from which atoms were built up. Because of

this, he proposed that electrons are just like plums embedded and scattered in a positively charged sphere

like a pudding. Thomson's corpuscle hypothesis was not generally accepted, even by British scientists,

until he spoke of it again in 1899. By this time, George Francis FitzGerald (1851-1901), an Irish physicist,

had suggested that Thomson's 'corpuscles' making up the cathode ray were actually free electrons. In fact,

this suggestion was published as a commentary to the publication of Thomson's April 30, 1897 lecture in

which he first announced his results. Thomson himself continued to use the term corpuscle until 1913.

Later on, the plum pudding model was falsified as the existence of positively charged proton in atomic

nucleus was discovered by Ernest Rutherford.

Figure 2: Atom according to Thomson

3. Nuclear model- In 1911, Ernest Rutherford published the result from his study- the Gold Foil

Experiment. In his experiment, he bombarded a Gold foil with radioactive Helium known as the alpha

particle (which is naturally positive). Surrounding the set-up was a fluorescent screen which can detect

the alpha particles that have passed and deflected after hitting the Gold foil. If the plum pudding model

was right, then after hitting the Gold foil, the alpha particles should deflect from it since the plum

pudding model suggested that the body of the atom is chiefly a “positively charged sphere” (review the

Law of Electrostatics: unlike charges attract, like charges repel or deflect from each other). However, this

was not the result from the Gold foil experiment. Instead of deflecting, most alpha particles had passed

the Gold foil at larger angles. This only suggested that the atom’s body was not really positively charged,

but is made of large spaces where alpha particles can pass. Also, there were some alpha particles that had

deflected at very small angles and there were alpha particles that had just reflected back from the source

of alpha particle. These suggested that there is a positively charged part in an atom which is concentrated

at the center. He called this central part as the nucleus which was concluded to have a positively charged

proton while electrons surround the nucleus and these electrons are moving in a large space. Later on,

this model was modified as James Chadwick discovered the existence of uncharged particle in nucleus

known as neutron. Chadwick announced his discovery in May 1932.

Figure 3: Gold foil experiment Figure 4: Atom according to Rutherford

corpuscles (electrons)

positively charged sphere

Nucleus (where

protons sit)

Scattered

electrons

Gold foil

Most alpha rays just

passed the gold foil

Alpha ray

Only few alpha rays

reflected back and did

not pass the foil

Screen

detector

Alpha particle

emitter

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4. Planetary model- On the prior Nuclear model, the nucleus was already discovered and the electrons

were explained as “moving in a large space”. However, in nuclear model, it was not explained how these

electrons move without colliding each other. Because of this, in 1913, Niels Bohr proposed a new model of

the atom which looked like a solar system- the planetary model of the atom. His model was just a

modification of the nuclear model where he suggested that electrons move only at a specific circular path

just like planets. He called these paths as orbits. The bigger the orbit, the higher the electron’s energy

level. The maximum number of electrons in each orbit can be determined by using the formula 2n2 where

n corresponds to the energy level/ orbit number. For example, on the first orbit (n=1), the maximum

number of electrons that it can hold is 2 since 2 (1)2 is equal to 2. The second orbit (n=2) can hold up to 8

electrons since 2(2)2 is 8. The third orbit (n=3) can hold up to 18 electrons since 2(3)2 is 18. Also according

to him, when an electron on higher energy level/ orbit jumps to the lower level/ orbit, it emits energy in

the form of light. The same way, light can elevate an electron from lower level/ orbit to higher one.

Figure 5: Atom according to Bohr

_______________________________________________________________________________________________

The current model that is scientifically accepted is known as the quantum mechanical model.

In particle physics, quantum is a pack or bundle of any particle or energy (Greek “quanta” which means

pack). The last model before the quantum mechanical model was Bohr’s planetary model, where according

to him, electrons can be found in a path known as orbits and each orbit has a maximum number of

electron which can be computed by the formula, 2n2 where n is the orbit number. For example, for the

first orbit (n=1), there are 2 maximum electrons since 2 (1) 2 is equal to 2; for the second orbit (n=2), there

are 8 maximum electrons since 2 (2) 2 is equal to 8 and so on. However, there are two main problems in

Bohr’s planetary model of atom.

Problems with Planetary Model of Atom

1.The electrons in one orbit can only have two types of spin: clockwise (+½) and counterclockwise (- ½) .

In relation to this, there is no problem with the first orbit which has a maximum of 2 electrons since one

electron can turn clockwise and the other one should turn counterclockwise. However, on second and

further orbits, there are more than two electrons. If in one orbit, there are just two possible spins, then

how can we compensate for the spin of other electrons in an orbit? For example, in second orbit, the

maximum number of electrons is 8. If two electrons out of that 8 already did the clockwise and

counterclockwise spin, what spin will the remaining 6 do? NOTHING. There are no more possible choices.

The only way to compensate for this is to bundle or “pack” each electron in an orbit by two. For example, if

the second orbit has 8 electrons, then these electrons can be packed by twos; so, there will be 4 “packs”

and each pack contains 2 electrons. Third orbit has a maximum of 18 electrons and if these electrons are

packed by twos, there will be 9 “packs” and again, each pack contains 2 electrons.

2. In 1926, Erwin Schrödinger developed an equation which treated the electron as a wave, not just a

particle. In 1927, Werner Heisenberg developed the Heisenberg’s Uncertainty principle which states that,

it is impossible to tell exactly both the position and momentum of an electron at the same time. The more

we know about the momentum of the electron, the less we know about its position and vice versa. If an

electron

proton neutron nucleus

1st orbit with 2 electrons

2nd orbit with 8 electrons

3rd orbit with 16 electrons

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object is exactly at a position, then that object is not moving and thus, momentum is equal to 0. Likewise,

if the object is moving (has a momentum), then you cannot exactly tell where the object is at a given

moment because it is constantly moving. Since, according to Schrödinger, electron is a wave and as a

wave, it has a momentum (which means it is moving), then we are really uncertain about its exact

position, and since we are uncertain with its position, then we cannot say that an electron is exactly on a

specific orbit as opposed to what was claimed by Bohr’s planetary model of atom.

With the two problems given, the birth of quantum mechanical model of atom became possible. In

this model, there are some terminologies that are related but NOT interchangeable with each other. If

Bohr’s planetary model, electrons were moving in a two-dimensional, flat orbit, in quantum mechanical

model, electrons are assumed to move in a three-dimensional, space-filled orbital or electron cloud. Bear

in mind that orbit is different from orbital. Orbital or electron cloud is a three-dimensional region

surrounding the nucleus where MOST OF THE TIME the electrons are located. This is the most probable

electron location in an atom. Orbitals within the same energy level are known as shell. Remember the

“packing” of electrons mentioned earlier? Each pack represents the orbitals. For example, in third orbit of

Bohr’s planetary model, there are 18 electrons. These electrons can be packed by twos; hence, there will

be 9 packs (atomic orbitals) and each pack contains 2 electrons. Now, notice that these 9 atomic orbitals

are just found on the same orbit or energy level (i.e., 3rd orbit/ energy level). Hence, these 9 atomic orbitals

are found in the 3rd shell of the given atom. How about the 4th orbit of the atom? Can you tell how many

maximum electrons are there in that orbit, according to Bohr’s planetary model? How many orbitals can

be created out of the maximum number of electrons in the 4th orbit? On which shell number can these

orbitals be found? Try to find it!

There are four shapes of orbital according to the three-dimensional model of different axes. The z-

axis corresponds to the height of the orbital, the x-axis corresponds to the width of the orbital and the y-

axis corresponds to the length of the orbital. The four shapes of orbitals are the s, p, d, and f. The

simplest shape is s which is just a spherical probable electron location. The most complicated is f orbital.

Figure 7: Different Shapes of Orbitals

Each shape above has its own maximum number of magnetic orientation. For example, the s

orbital (sharp) which is spherical has only one (1) possible magnetic orientation. If we rotate this

spherical s orbital in any direction, we will still see the same sphere at the center of the axes (0); thus, the

orientation of s orbital is denoted as zero (0). On the other hand, p orbital (principal) has three (3)

possible magnetic orientation-- one p orbital can be oriented towards z-axis (as shown in the picture

above), the other p orbital can be oriented towards y-axis while the last one can be oriented towards x-

axis. These 3 orientations of p orbitals are numerically denoted as -1, 0 and +1. More complex

orientations are available for d orbital (diffuse) as it has five (5) maximum magnetic orientations which

are numerically denoted as -2, -1, 0, +1 and +2; while f orbital (fundamental) has a maximum of seven (7)

z

y

x

z

y

x

z

y

x

z

y

x

s orbital (sharp)

p orbital

(principal)

d orbital

(diffuse)

f orbital

(fundamental)

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magnetic orientations and these are -3, -2, -1, 0 +1, +2, and +3. Figure 8 on the next page shows how these

magnetic orientations look like for every shape of orbital.

Now recall that for every orbital, there should only be a maximum of 2 electrons. Since s orbital

has only one magnetic orientation, then s orbital can carry a maximum of 2 electrons (i.e., 2 electrons

multiplied to 1 orientation). On the other hand, p orbital which has 3 possible magnetic orientations can

carry a maximum of 6 electrons (i.e., 2 electrons multiplied to 3 orientations). Moreover, d orbital which

has 5 possible magnetic orientations can carry a maximum of 10 electrons (i.e., 2 electrons multiplied to 5

orientations), while f orbital which has 7 possible magnetic orientations can carry a maximum of 14

electrons (i.e., 2 electrons multiplied to 7 orientations)

Figure 8: The Orientations of Each Orbital (Source: UCDavis Chemwiki, CC BY-NC-SA 3.0 US)

Below is a table which summarizes the aforementioned characteristics of each orbital.

Table 1: Shapes, Magnetic Orientations and Maximum number of Electrons

Shape of Orbital Magnetic Orientations Maximum number of

electrons

s orbital 0 2 electrons

p orbital -1 0 +1 6 electrons

d orbital -2 -1 0 +1 +2 10 electrons

f orbital -3 -2 -1 0 +1 +2 +3 14 electrons

_______________________________________________________________________________________________

In language, to exactly describe an object, certain adjectives are used before the noun that they

modify. Similarly, in chemistry, to describe the characteristics of an electron, certain criteria are

determined. These criteria are the (a) energy level of the orbital, (b) shape of the orbital, (c) magnetic

orientation of electron and (d) spin orientation of electron. These four criteria are enough descriptors to

http://chemwiki.ucdavis.edu/@api/deki/files/8855/Single_electron_orbitals.jpg

http://creativecommons.org/licenses/by-nc-sa/3.0/us/

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uniquely describe an electron. Bear in mind that there are no two electrons with absolutely the same

energy level, shape of orbital, magnetic orientation and spin orientation all at the same time as asserted

by an Austrian physicist named Wolfgang Pauli in his Pauli’s exclusion principle. Two or more

electrons may have 3 identical descriptors but there will never be electrons with 4 identical descriptors.

Somewhere, there will be difference/s between two electrons which are almost the same. The difference/s

may exist in their energy level, shape of orbital, magnetic orientation or spin orientation.

In quantum chemistry, the 4 descriptors aforementioned are represented by the quantum

numbers. Quantum numbers are descriptors of an electron which are translated into numerical form.

There are four types of quantum numbers.

1. Principal Quantum Number (n)- this describes the energy level of the orbital where the valence

electron can be found. The allowed numbers here are positive whole numbers only such as 1, 2, 3, 4, etc.

The higher the principal quantum number, the higher the energy level. Currently, the largest principal

quantum number reflected on periodic table of elements is 7. In fact, these principal quantum numbers

correspond also to the period (row) in periodic table of elements. For example, Hydrogen (H) and Helium

(He) are on the first period (row) of periodic table and therefore, we know that their outermost electrons

(valence electrons) have the principal quantum number of 1. On the other hand, Sodium (Na), Magnesium

(Mg), Aluminum (Al), Silicon (Si), Phosphorus (P), Sulfur (S), Chlorine (Cl) and Argon (Ar) are on the

third period and therefore, their valence electrons have principal quantum number of 3. However, bear in

mind that the period numbers in periodic table represent the energy levels of the valence electrons or

outermost electrons only and not the whole electrons of a specific element.

Legends:

∎ valence electrons are in 1st energy level ∎ valence electrons are in 2nd energy level

∎ valence electrons are in 3rd enery level

Figure 9: The Blocks in Periodic Table of Elements

Peri

od

/ P

rin

cip

al

Qu

an

tum

Nu

mb

er

1 H

∎ valence electrons are in 4th energy level




He

2 Li

Be B C N O F Ne

3 Na

Mg Al Si P S Cl Ar

4 K

Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr

5 Rb

Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe

6 Cs

Ba Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn

7 Fr

Ra Rf Db Sg Bh Hs Mt Ds Rg Cn Nh Fl Mc Lv Ts Og

La

Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

Ac

Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr

s block p block (except He)

d block

f block (except La and Ac)

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Above is the periodic table of elements. There are many ways on how elements can be grouped in

periodic table of elements. One of the ways to group these elements are based on their outermost orbital.

Elements from s block have partially of fully filled s orbital as their outermost or valence orbital; elements

from p block have partially or fully filled p orbitals as their outermost orbital (except for Helium which

belongs to s block); elements from d block have partially or fully filled d orbital as their outermost orbital,

while elements from f block have partially or fully filled f orbital as their outermost orbital. Also, the

energy level of the valence electrons in d orbital of d block elements have principal quantum number of

n-1 where n is the period (row) where they are lined. For example, Niobium (Nb) is located on 6th period

and it belongs to d block. Hence, the energy level of its valence electrons in d orbital is 5 (i.e., n – 1 or

6 – 1= 5). On the other hand, the energy level of the valence electrons in f orbital of f block elements have

principal quantum number of n-2. For example, Dysprosium (Dy) is located on 6th period and it belongs to

f block. Hence, the energy level of its valence electrons in f orbital is 4 (i.e., n –2 or 6 – 2= 4). Lastly, the

valence electrons in s orbital of s block elements and p orbital of p block elements have principal quantum

number of n only. For example, since Rubidium (Rb) is located on the 5th period of s block, then its

principal quantum number is 5, while Nitrogen (N) which is located on the 2nd period of p block has a

principal quantum number of 2.

Also, the principal quantum number may change depending on the charge (q) of the element. If the

charge of an element is positive, then it should step backward in periodic table of elements and follow

the principal quantum number of the element to where it landed. On the other hand, if the charge of an

element is negative, then it should step forward in periodic table of elements and follow the principal

quantum number of the element to where it landed. The magnitude or value of the charge determines the

number of step/s that will be taken by the elemental ion. For example, if Manganese has a charge of

negative 6 (i.e., Mn-6), then its principal quantum number is not anymore 3 although Manganese is on the

third energy level of d block (recall that despite it is on the 4th period, since it is a d block element, then

its original energy level is n-1 or 4-1 = 3). Instead, it should take six (6) steps forward from its original

position in periodic table and it will land on Gallium (Ga). Hence, the principal quantum number of Mn-6

follows the principal quantum number of Gallium (Ga) which is 4 (recall that the principal quantum

number of p block elements only follow their period number). Other examples are shown below.

Table 2: Examples of Principal Quantum Numbers for Elemental Ions

Elemental

Ion

Supposed Principal

Quantum Number

Process Element where

it will land

Correct Principal

Quantum Number

Sn+2 5 2 steps backwards Cadmium (Cd) 4

Cl-2 3 2 steps forward Potassium (Cl) 4

Ba+2 6 2 steps backward Xenon (Xe) 5

2. Azimuthal Quantum Number (l)- this describes the shape of the orbital where the valence electrons

can be found. The allowed numbers here are 0, 1, 2, 3, 4, etc. Currently, there are 4 shapes of orbitals

where electrons can be located- the s orbital, p orbital, d orbital and f orbital (see Figure 7: Different

Shapes of Orbitals, p.6). The azimuthal quantum number of s orbital is denoted by zero (0). On the other

hand, the azimuthal quantum numbers of p, d and f orbitals are denoted by one (1), two (2) and three (3),

respectively. In periodic table of elements, one can determine the azimuthal quantum number of an

element by identifying the block location of that specific element. Elements in s block have azimuthal

quantum number of 0. Elements in p block have azimuthal quantum number of 1. Elements in d block

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have azimuthal quantum number of 2. Lastly, elements in f block have azimuthal quantum number of 3.

For example, Potassium (K), Calcium (Ca) and Strontium (Sr) have azimuthal quantum number of 0 since

they are on the s block while Antimony (Sb), Bromine (Br) and Selenium (Se) have azimuthal quantum

number of 1 since they are on the p block. Bear in mind that Lanthanum (La) and Actinium (Ac)

belong to d block; therefore, their azimuthal quantum number is 2.

Also, the azimuthal quantum number may change depending on the charge (q) of the element. If

the charge of an element is positive, then it should step backward in periodic table of elements and

follow the azimuthal quantum number of the element to where it landed. On the other hand, if the charge

of an element is negative, then it should step forward in periodic table of elements and follow the

azimuthal quantum number of the element to where it landed. The magnitude or value of the charge

determines the number of step/s that will be taken by the elemental ion. For example, if Manganese has a

charge of positive 7 (i.e., Mn+7), then its azimuthal quantum number is not anymore 2 although

Manganese is on the d block. Instead, it should take seven (7) steps backward from its original position in

periodic table and it will land on Argon (Ar). Hence, the azimuthal quantum number of Mn+7 follows the

azimuthal quantum number of Argon (Ar) which is 1. Other examples are seen below.

Table 3: Examples of Azimuthal Quantum Numbers for Elemental Ions

Elemental

Ion

Supposed Azimuthal

Quantum Number


it will land

Correct Azimuthal

Quantum Number

S+4 1 4 steps backwards Magnesium (Mg) 0

S-2 1 2 steps forward Argon (Ar) 1

Ba+2 0 2 steps backward Xenon (Xe) 1

Cd-2 2 2 steps forward Tin (Sn) 1

Gd-3 3 3 steps forward Holmium (Ho) 3

3. Magnetic Quantum Number (ml)- this describes the magnetic orientation of the orbital where the

valence electrons can be found. Magnetic orientation refers to the direction of an orbital along the three-

dimensional space as it is affected by external magnetic force. The three-dimensional space is composed of

x, y and z axes. The allowed numbers here are the negative azimuthal quantum number (-l) to the positive

azimuthal quantum number (+l) of each orbital, passing midway the zero (0). Hence, the s orbital with

azimuthal quantum number of 0 has a magnetic quantum number of zero (0) only. The p orbital with

azimuthal quantum number of 1 has magnetic quantum numbers of -1, 0 and +1. The d orbital with

azimuthal quantum number of 2 has magnetic quantum numbers of -2, -1, 0, +1 and +2. The f orbital with

azimuthal quantum number of 3 has magnetic quantum numbers of -3, -2, -1, 0, +1, +2 and +3. Each

integer represents the orientation of an orbital in three-dimensional space. This was already discussed in

Lesson 4: The Current Model of Atom: Quantum Mechanical Model. In periodic table of elements, the two

groups (columns) of elements in s block have magnetic quantum numbers of 0 and 0, respectively. On the

other hand, the six groups of elements in p block are divided into 2 three groups. The first three groups

have magnetic quantum numbers of -1, 0 and +1 respectively, while the second three groups also have

magnetic quantum numbers of -1, 0 and +1 respectively. Meanwhile, the ten groups of elements in d block

are divided into 2 five groups. The first five groups have magnetic quantum numbers of -2, -1, 0, +1 and

+2 respectively, while the second five groups also have magnetic quantum numbers of -2, -1, 0, +1 and +2

respectively. Lastly, the 14 groups of elements in f block are divided into 2 seven groups. The first seven

groups have magnetic quantum numbers of -3, -2, -1, 0, +1, +2 and +3 respectively, while the second seven

groups also have magnetic quantum numbers of -3, -2, -1, 0, +1, +2 and +3 respectively.

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-2 -3 -2 -1 0 +1 +2 +3 -3 -2 -1 0 +1 +2 +3

Legends:

∎ elements with 0 magnetic quantum number ∎ elements with -1 magnetic quantum number

∎ elements with -2 magnetic quantum number

0

Figure 10: The Magnetic Quantum Numbers in Periodic Table of Elements

Above is the periodic table of elements and the magnetic quantum numbers of the elements which

are highlighted with black above each group (column). For example, Iron (Fe), Dysprosium (Dy) and

Osmium (Os) have magnetic quantum number of -2. On the other hand, Sulfur (S), Cobalt (Co) and

Uranium (U) have magnetic quantum number of -1. Bear in mind that although Helium (He) is lined in

that group with +1 magnetic quantum number, Helium’s magnetic quantum number is 0, not +1.

Also, the magnetic quantum number may change depending on the charge (q) of the element. If the


the magnetic quantum number of the element to where it landed. On the other hand, if the charge of an

element is negative, then it should step forward in periodic table of elements and follow the magnetic


number of step/s that will be taken by the elemental ion. For example, if Vanadium (V) has a charge of

positive 2 (i.e., V+2), then its magnetic quantum number is not anymore 0 although originally, its magnetic

quantum number is 0. Instead, it should take two (2) steps backward from its original position in periodic

table and it will land on Scandium(Sc). Hence, the magnetic quantum number of V+2 follows the magnetic

quantum number of Scandium(Sc) which is -2. Other examples are seen on the next page.

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1 H

0 ∎ elements with -3 magnetic quantum number

∎ elements with +1 magnetic quantum number



-1 0 +1 +2 -2 -1 0 +1

-1 0 +1 -1 0

He

2 Li

Be

-2

+2

B C N O F Ne

3 Na

Mg Al Si P S Cl Ar

4 K


5 Rb


6 Cs


7 Fr


La


Ac


s block

p block (except He)

d block

f block (except La & Ac)

+1

(except He)

12 | P a g e

+½ +½ +½ +½ +½ +½ +½ +½ -½ -½ -½ -½ -½ -½ -½

Table 4: Examples of Magnetic Quantum Numbers for Elemental Ions

Elemental

Ion

Supposed Magnetic

Quantum Number


it will land

Correct Magnetic

Quantum Number

S-2 -1 2 steps forward Argon (Ar) +1

Pt+3 0 3 steps backward Rhenium (Re) +2

Eu-2 2 2 steps forward Terbium (Tb) -3

4. Spin Quantum Number (ms)- this describes the spin orientation of the valence electrons. There are

only two allowed numbers that can be used here. Positive one-half (+ ½) denotes that the valence

electron’s spin is clockwise while negative one-half (- ½) denotes that the valence electron’s spin

counterclockwise. In periodic table of elements, the two groups (columns) of elements in s block have spin

quantum numbers of + ½ and – ½ , respectively. On the other hand, the six groups of elements in p block

are divided into 2 three groups. The first three groups have spin quantum number of + ½, while the

second three groups have spin quantum number of – ½. Meanwhile, the ten groups of elements in d block

are divided into 2 five groups. The first five groups have spin quantum number of + ½, while the second

five groups have spin quantum number of – ½. Lastly, the 14 groups of elements in f block are divided

into 2 seven groups. The first seven groups have spin quantum number of + ½, while the second seven

groups have spin quantum number of – ½.

Legends:

∎ elements with +½ spin quantum number ∎ elements with - ½ spin quantum number

+½

Figure 11: The Spin Quantum Numbers in Periodic Table of Elements

Above is the periodic table of elements and the spin quantum numbers of the elements which are

highlighted with black above each group (column). For example, Lithium (Li), Vanadium (V) and Silicon

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1 H

- ½

+½ +½ +½ +½ -½ -½ -½ -½

+½ +½ +½ -½ -½

He

2 Li

Be

+½

-½

B C N O F Ne

3 Na

Mg Al Si P S Cl Ar

4 K


5 Rb


6 Cs


7 Fr


La


Ac


s block p block (except He)

d block

f block (except La & Ac)

-½

13 | P a g e

(Si) have spin quantum number of + ½ (clockwise spin of valence electron). On the other hand,

Einsteinium (Es), Gold (Au) and Iodine (I) have spin quantum number of – ½ (counterclockwise spin of

valence electron).

Also, the spin quantum number may change depending on the charge (q) of the element. If the


the spin quantum number of the element to where it landed. On the other hand, if the charge of an

element is negative, then it should step forward in periodic table of elements and follow the spin


number of step/s that will be taken by the elemental ion. For example, if Molybdenum (Mo) has a charge

of negative 2 (i.e., Mo-2), then its spin quantum number is not anymore +½ although originally, its spin

quantum number is +½. Instead, it should take two (2) steps forward from its original position in periodic

table and it will land on Ruthenium (Ru). Hence, the magnetic quantum number of Mo-2 follows the

magnetic quantum number of Ruthenium (Ru) which is – ½. Other examples are seen below.

Table 5: Examples of Spin Quantum Numbers for Elemental Ions

Elemental

Ion

Supposed Magnetic

Quantum Number

Process Element where it

will land

Correct Magnetic

Quantum Number

S-2 -½ 2 steps forward Argon (Ar) -½

Na+1 +½ 1 step backward Neon (Ne) -½

Pt+3 -½ 3 steps backward Rhenium (Re) +½

Eu+4 +½ 4 steps backward Praseodymium(Pr) +½

Sometimes, some quantum numbers do not change even if the element gained charge/s. For

example, in the table above, the original spin quantum number of Europium (Eu) with no charge (i.e., +½)

is still the spin quantum number of Eu+4 (i.e., still +½).

Quantum number is an essential concept in understanding the basic characteristics of electrons

and its orbitals. With quantum numbers, scientists are able to differentiate one electron or orbital to

another electron or orbital and they able to extract the basic “identity” of a specific electron surrounding

an atom.

Antero, E.S., Alumaga, M.J.B., Padolina, M.C.D.(2010).Conceptual and Functional Chemistry. Quezon

City, Philippines: Vibal Publishing House, Inc.

Tabujara, G.D.(2016).General Chemistry. Pasay City, Philippines: JFS Publishing Service

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chapter ii: atomic chemistry

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