Chemistry 11Unit 8 – Atoms and the Periodic Table

Part II – Electronic Structure of Atoms

1. Atomic number and atomic mass

In the previous section, we have seen that from 50 to

100 years after Dalton proposed his atomic theory,

scientists had collected many evidence for the more

subtle structure of atoms.

By 1920, people had already identified electrons

and protons as two major constituents of atoms.

(Plus neutron which was not yet identified until 1932.)

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It has been discovered that chemical elements differ

from one another by the number of protons in their

nuclei.

For example, hydrogen has 1 proton, nitrogen has 7

protons and oxygen has 8 protons.

Conversely, an atom that has 1 proton must be

hydrogen, while an atom that has 8 protons must be

oxygen.

The number of protons in a nucleus is called the

atomic number (Z).

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Atomic number also implies the followings:

(1) Each proton bears one unit of positive charge.

Hence, the atomic number equals the total positive

charges on the nucleus.

(2) Since a neutral atom has zero net charge, the

number of protons must be equal to the number of

electrons (each of which has a negative charge).

So, atomic number is also equal to the number of

electrons for neutral atoms.

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There are three pieces of information about each

element that are always present in the periodic

table.

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Atomic number (Z)Position in PT; also

equals the number

of protons

Atomic symbol (X)

Unique label to

identify the

element

Atomic mass (A)Mass of the

element

How do we calculate atomic mass?

Proton, neutron and electron have their own masses.

They are not measured in terms of grams but in

atomic mass unit (amu).

Usually in quick calculations, we assume both proton

and neutron have the mass of 1 amu while

neglecting the mass of electron.

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Particle Mass (in amu)

Proton 1.00728

Neutron 1.00894

Electron 0.0005414

So, the atomic mass of an atom is determined

by the combined total masses of protons and

neutrons.

Example: To the nearest integer, calculate the

mass in amu of a nucleus that contains (a) 17

protons and 18 neutrons, and (b) 17 protons and

20 neutrons.

(a) Mass = 17 amu + 18 amu = 35 amu

(b) Mass = 17 amu + 20 amu = 37 amu

Note that these atoms are equal in type but

different in mass.

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Atoms that have the same atomic number but

different in masses are called isotopes.

That means, isotopes have the same number of

protons (type) but different number of neutrons

(mass).

The total number of protons and neutrons is called

the mass number (A) of an isotope. For instance, 612C

has the mass number of 12, while 614C has the mass

number of 14.

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In general, isotopes are written in either form:

where X is the atomic symbol of the element.

For example, 𝟏𝟏𝟐𝟑𝐍𝐚 is equivalent to Na-23.

This isotope of sodium (Na) has 11 protons(of course,

as it is sodium), 12 neutrons (because 23 – 11 = 12),

and 11 electrons. Its mass number is 23.

Sometimes, the atomic number can be dropped for

redundancy.

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ZAX X − A

Most elements in nature exist as a mixture of different

isotopes. Therefore, the atomic mass reported in the

periodic table is the weighed average of the

isotopes of an element.

For example: Naturally occurring copper consists of

69.17% of Cu-63 and 30.83% Cu-65. The mass of Cu-

63 is 62.939598 amu, and the mass of Cu-65 is

64.927793 amu. What is the atomic mass of Cu?

The weighed average is

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62.939598 0.6917 + 64.927793 0.3083 = 63.55 amu

Practice: Experiments show that chlorine is a mixture

which is 75.77% Cl-35, and 24.23% Cl-37. If the

precise mass of Cl-35 is 34.968853 amu and of Cl-37

is 36.965903 amu, what is the weighed average

mass of chlorine?

[35.45 amu]

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Through certain processes, electrons could be

added or removed from an atom to produce ions.

(1) If electrons are removed, the resulting species is

called cation.

The ion is positively charged because there are

fewer electrons than protons.

(2) If electrons are added, the resulting species is

called anion.

The ion is negatively charged because there are

more electrons than protons.

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Example: Fill up the following table.13

Particle # Protons # Neutrons # Electrons

1327Al 13 27-13=14 13

3375As 33 75-33=42 33

51122Sb3+ 51 122-51=71 51-(+3)=48

919F− 9 19-9=10 9-(-1)=10

2. Electronic structure of atoms

When hydrogen is irradiated by electricity, some

energy is absorbed and re-emitted. With an aid of a

prism, the emitted light can be transformed into a

line spectrum.

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How do we explain the line feature of the hydrogen

spectrum?

Niels Bohr in 1913

proposed that electrons

in an atom could not

exist in a stable way

anywhere outside the

nucleus unless they are

in a fixed, “quantized”

energy levels.

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The observed spectrum represents energy level

differences occurring when an electron in a higher

level gives off energy and drops down to a lower

level.

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The quantized nature of energy levels was explained

when the concept of matter wave and the modern

quantum theory were developed, respectively, by

Louis de Broglie in 1924, and independently by Erwin

Schrödinger and Werner Heisenberg in 1925.

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Louis de Broglie

(1892-1987)

Erwin Schrödinger

(1887-1961)Werner Heisenberg

(1901-1976)

According to the quantum mechanical model of

atoms, electrons possess both wave and particle

behaviors. (wave-particle duality)

Each energy level of an atom is associated with one

unique waveform of the electron wave. This

waveform is called an orbital.

More precisely, an orbital

is a region of space

occupied by an electron

in an energy level.

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Different orbitals that electrons can reside are

determined by solving the Schrödinger’s equation,

which is the central formula of quantum mechanics.

On solving this, it is found that orbitals (or electron

waves) are characterized by three quantum

numbers: 𝑛, 𝑙, and 𝑚.

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𝑛 Principal quantum number

𝑙 Orbital angular momentum quantum

number (or Azimuthal quantum number)

𝑚 Magnetic quantum number

(1) Principal quantum number 𝒏

This quantum number determines the size of the

orbital (or electron wave) and how far it is extended

from the nucleus.

Orbitals having the same 𝑛 are said to be in the

same shell.

𝑛 ranges from 1 to ∞ (in theory)

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(2) Orbital angular momentum quantum number 𝒍

It divides a shell into smaller groups of orbitals called

subshells.

The subshells are identified by the letter 𝑠, 𝑝, 𝑑, 𝑓, …

The values of 𝑙 range from 0 to 𝑛 − 1 for a shell with

the principal quantum number 𝑛.

The higher the level, the more subshells it has.

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Value of 𝒍 0 1 2 3 4

Letter designation s p d f g

(3) Magnetic quantum number 𝒎

It splits the subshells into individual orbitals.

This number describes the orientation of the orbital in

space.

𝑚 has the values ranging from 𝑙 − 1 to 𝑙 + 1 for a

subshell with the Azimuthal quantum number 𝑙.

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Type of subshell s p d f g

Azimuthal quantum

number 𝑙0 1 2 3 4

Number of possible

values of 𝑚1 3 5 7 9

Orbitals with different sets of 𝑛, 𝑙, 𝑚 values can be

visualized in the following diagrams.

(1) s-type orbitals

Spherical in shape

Two spheres are separated by a node.

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(2) p-type orbitals

Look like dumbbells

Each p-subshell has three p-orbitals which are

perpendicular to each other.

The two lobes are separated by a nodal plane.

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(3) d-type orbitals

The shapes are cross-like, except for one.

Each d-subshell has 5 orbitals.

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(4) f-type orbitals

There are 7 orbitals in the f-subshell.

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In summary (so far):27

Solving the Schrödinger equation for hydrogen

atom yields the energies for different orbitals. It is

found that the orbital energy depends only on the

principal quantum number 𝑛.

That means, all subshells with the same value of 𝑛,

such as 3𝑠, 3𝑝 and 3𝑑 subshells will have the same

energy (they are said to be degenerate).

In addition, the higher the value of 𝑛, the higher the

energy of the orbital.

Mathematically:

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𝐸𝑛 = −13.6 eV

𝑛2

Schematically:29

𝑛 = 1

𝑛 = 2

𝑛 = 3

𝑛 = 4

The diagram shown on the previous slide is true for

hydrogen atom and hydrogen-like ions (which have

only one electron).

For polyelectronic atoms and ions (that means,

many electrons), however, the subshells with the

same value of 𝑛 no longer have the same energy

(i.e., they are non-degenerate).

The repulsion between electrons in the same or

different orbitals cause the orbitals to have different

energies.

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31The resulting energy level diagram looks like the

following:

Orbital energy depends on both 𝑛 and 𝑙. The larger

the value of 𝑙, the higher the orbital energy.

(FYI) The effect of disturbance is directly proportional

to the charges on the nucleus and the number of

electrons.

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3. Electron configurations of atoms

With each successive increase in atomic number, a

given atom has one more electron than the previous

atom.

Therefore, starting from hydrogen, we can build up

the electron configuration of each of the other

elements by adding electron one at a time.

However, what is the sequence of orbitals in which

electrons are added?

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There are 3 rules that govern the order of orbitals

which are filled.

(1) Aufbau principle

It is also called building-up principle. (Aufbau means

“building-up” in German)

This principle states that the electrons of an atom fill

the lowest-energy available subshell before filling

higher ones.

It ensures that the resulting electron configuration

corresponds to the most stable form of the element.

(Some exceptions, however!)

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The sequence of the orbitals in ascending order of

energy is depicted by the diagram on p.31.

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < …

There is a trick that helps memorize this pattern.

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(2) Pauli exclusion principle

In addition to the three quantum

numbers as proposed in the

Schrödinger’s quantum mechanics,

Wolfgang Pauli (1900-1958)

proposed in 1924 that there is the

fourth quantum number called spin

quantum number.

Only 2 possible values: +1

2or −

1

2

The identity of spin was verified by

George Uhlenbeck (1900-1988) and

Samuel Goudsmit (1902-1978) in

1925.

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The actual statement of the Pauli exclusion principle

is beyond the scope of chemistry 11. (Something

related to the symmetry of wave functions of

particles)

But in simple words, this principle states that it is

impossible for two electrons of a poly-electron atom

to have the same values of the four quantum

numbers.

Its implication is important: Each orbital could have

two electrons in maximum!

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(3) Hund’s rule

This rule was proposed by Friedrich Hund (1896-1997) in 1927.

There are indeed three Hund’s rules, but they are usually abbreviated to just Hund’s rule.

The first rule states that if two or more orbitals of equal energy are available, electrons will occupy them singly before filling them in pair.

The other two rules are related to the analysis of atomic and molecular spectra.

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Using these three rules, we can determine the

occupancy of electron shells in an atom.39

Energy

level

Types of

subshells

Number of

subshells

Number of

orbitals

Maximum

number of

electrons

1 S 1 1 2

2 s, p 2 4 8

3 s, p, d 3 9 18

4 s, p, d, f 4 16 32

5 s, p, d, f, g 5 25 50

A common way of representing the electron

configurations of atoms is as follows:

For example: Hydrogen

Rule: consecutively write the number of the energy

level, the type of subshell, and the number of

electrons in that subshell, as superscript.

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Example: Determine the electron configurations of

the first ten elements41

Element Electron configuration

Hydrogen 1s1

Helium 1s2

Lithium 1s2 2s1

Beryllium 1s2 2s2

Boron 1s2 2s2 2p1

Carbon 1s2 2s2 2p2

Nitrogen 1s2 2s2 2p3

Oxygen 1s2 2s2 2p4

Fluorine 1s2 2s2 2p5

Neon 1s2 2s2 2p6

Practice: Predict the electron configuration of the

following elements.

(1) Silicon

(2) Technetium

(3) Calcium

(4) Zirconium

(5) Gallium

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The electron

configurations of

atoms can also be

depicted by energy

level diagrams.

Each electron that is

located in an orbital is

represented by an

arrow, whose

direction (up or down)

shows its spin.

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Example: Draw the energy diagrams for the

following elements:

(1) Potassium (2) Gallium

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There are two scenarios we have to pay attention on

when constructing the energy level diagrams of

atoms.

(1) Due to the Hund’s rule, electrons will occupy

degenerate orbitals singly whenever possible.

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(2) It has been observed that fully filled or half-filled

subshells have a greater stability than subshells

having some other numbers of electrons.

It results from a quantum mechanical effect

between electrons.

It happens for atoms with d4 and d9 configurations.

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The electron configurations of most atoms can be

deduced easily using the “orbital version” of the

periodic table.

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The expressions of electron configurations of atoms

we have talked about so far are called full

configurations because they include all the electrons

of the atoms.

In fact, the electrons in an atom can be divided into

two types:

(1) Core electrons: the set of electrons with the

configuration of the preceding noble gas. They are

not involved in chemical reactions usually.

(2) Outer electrons: electrons outside the core. They

are the electrons that are involved in chemical

reactions.

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Since the core electrons are usually not significant

chemically, they can be represented by a core

notation, [X], in which X is the chemical symbol of

the preceding noble gas.

For example: Aluminum

Full configuration: 1s2 2s2 2p6 3s2 3p1

Core notation: [Ne] 3s2 3p1

For example: Cobalt

Full configuration: 1s2 2s2 2p6 3s2 3p6 4s2 3d7

Core notation: [Ar] 4s2 3d7

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3. Electron configurations of ions

The determination of the electron configurations of

ions is similar to that for atoms.

(1) For negative ions (anions):

Starting from the electron configuration of the

neutral atom, add the extra electrons one by one to

the orbitals according to the Aufbau principle.

For example: O2-

Configuration for O: 1s2 2s2 2p4

Configuration for O2-: 1s2 2s2 2p4 + 2e- = 1s2 2s2 2p6

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(2) For positive ions (cations):

When electrons are removed, the order does not

follow exactly as predicted by the Aufbau principle.

Instead, electrons in the outermost shell (i.e., the

shell with the largest value of 𝑛) are removed first.

If electrons fill more than one subshell in the

outermost shell, then the electrons in the 𝒑 subshells

are removed first.

The order of removing electrons is

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𝑝 electrons > 𝑠 electrons > 𝑑 electrons

For example: Sn2+ and Sn4+

Configuration of Sn: [Kr] 5s2 4d10 5p2

Configuration of Sn2+: [Kr] 5s2 4d10

Configuration of Sn4+: [Kr] 4d10 (not [Kr] 5s2 4d8)

For example: V2+ and V3+

Configuration of V: [Ar] 4s2 3d3

Configuration of V2+: [Ar] 3d3 (not [Ar] 4s2 3d1)

Configuration of V3+: [Ar] 3d2

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Practice: Write down the full electron configurations

of the following ions.

(1) S2-

(2) K+

(3) Co2+

(4) Fe3+

(5) Tl3+

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4. Valence electrons

Depending on the chemical behavior, electrons in

an atom can be classified as either core electrons or

outer electrons. (p.48 of the notes)

The electrons that actively participate in chemical

reactions are called valence electrons.

But valence electrons are not necessarily outer

electrons. The outer electrons in filled 𝑑 or 𝑓 subshells

do not react and therefore are not valence

electrons.

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For example, for aluminum whose electron

configuration is [Ne] 3s2 3p1. Only the electrons in the

3s and 3p orbitals are counted toward valence

electrons. Hence, it has 2 + 1 = 3 valence electrons.

On the other hand, gallium has the configuration of

[Ar] 4s2 3d10 4p1. Although it has 13 outer electrons,

the 3d subshell is filled; therefore these 10 electrons

are excluded. The total number of valence electrons

is thus 2 + 1 = 3.

Similarly, lead, whose configuration is [Xe] 6s2 4f14

5d10 6p2, has only 4 valence electrons rather than 28

because its 5d and 4f subshells are filled.

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If the d subshell is not filled such as Mn: [Ar]4s2 3d5, all

the 3d electrons should be included, and therefore it

will have 2 + 5 = 7 valence electrons.

Special cases are those for noble gases. For

instance, xenon has the electron configuration of

[Kr] 5s2 4d10 5p6. All the outer subshells are filled.

These electrons are dormant and will not participate

in any chemical reactions. Hence, it has zero

valence electron. This explains why noble gases are

“noble” and unreactive.

(FYI: Noble gases do react! We will see more in Part

III of Chapter 8)

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There is a trick to help memorize the numbers of

valence electrons for main group atoms.

# valence electrons = group number

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Practice: Determine the number of valence

electrons for the following species.

(1) Silicon

(2) Krypton

(3) Antimony

(4) Iron

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