Electronic Structure of Atoms

QUANTUM MECHANICAL DESCRIPTION OF ATOM
SCHRÖDINGER’S MODEL OF HYDROGEN ATOM AND WAVE FUNCTIONS
MAIN ENERGY LEVELS, SUBLEVELS, AND ORBITALS
QUANTUM NUMBERS
ELECTRON CONFIGURATION
REID CHRYSLER C. MANARES

Atoms are the basic units
of matter and the defining
structure of elements.
The term comes from the
Greek word atomos, or
indivisible, because it was
once thought that atoms
were the smallest things in
the universe and could not
be divided.
Atoms are made up of three
particles: protons, neutrons,
and electrons — which are
composed of even smaller
particles, such as quarks.

COASTLINE PARADOX
SUPERPOSITION

1. A body at ___ will remain at ___, and a body in motion will
remain in motion unless it is acted upon by an external force.
2. The net force acting on an object is equal to the ___ of that
object times its acceleration. (Hint: F=ma)
3. For every action, there is an equal and opposite _____.
4. The pull of gravity between two objects will be ______ to the
masses of the objects and inversely ______ to the square of the
distance between their centers of mass. (Hint: It starts with p)
5. Energy cannot be ____ nor destroyed, and instead changes
from one form to another.
6. In the absence of external forces such as friction, when objects
collide, the total momentum before the collision is the ___ as the
total momentum after the collision. (Hint: Equivalent, similar)
7. Within a continuous streamline of fluid flow, a fluid's hydrostatic
pressure will balance in contrast to its speed and elevation.

1. A body at rest will remain at rest, and a body in motion will
remain in motion unless it is acted upon by an external force.
2. The net force acting on an object is equal to the mass of that
object times its acceleration.
3. For every action, there is an equal and opposite reaction.
4. The pull of gravity between two objects will be proportional to
the masses of the objects and inversely proportional to the
square of the distance between their centers of mass.
5. Energy cannot be created nor destroyed, and instead changes
from one form to another.
6. In the absence of external forces such as friction, when objects
collide, the total momentum before the collision is the same as
the total momentum after the collision.
7. Within a continuous streamline of fluid flow, a fluid's hydrostatic
pressure will balance in contrast to its speed and elevation.
➢ Newton’s First Law of Motion
➢ Newton’s Second Law of
Motion
➢ Newton’s Third Law of Motion
➢ Newton’s Law of Universal
Gravitation
➢ Law of Conservation of Energy
➢ Law of Conservation of
Momentum
➢ Bernoulli’s Principle
These are some of the laws and principles that govern .

Quantum mechanics is the science that deals with the behavior
of matter and light on atomic and subatomic scale.
It results in what may appear to be some
very strange conclusions about the physical world.
At the scale of atoms and electrons, many
of the equations of classical mechanics cease to be useful.
In classical mechanics, objects exist in a specific place at a specific time.
In quantum mechanics, however, objects exist in a haze of probability.
Quantum mechanics seeks to understand the laws
governing the nature, behavior, and interactions of
matter and energy at very small scales and energies.

In 1924, Louis de Broglie hypothesized that atomic particles, such as electrons, have wavelike
behaviors.
➢ Electrons do not behave like particles flying through space.
➢ That meant that, in general, we cannot describe their exact paths.
In 1927, Werner Heisenberg showed that it is impossible to take any measurement of an object
without disturbing it.
➢ The Heisenberg Uncertainty Principle states that it is fundamentally impossible to know precisely both
the velocity and position of a particle at the same time.
➢ The only quantity that can be known is the probability for an electron to occupy a certain region around
the nucleus.
In 1926, Erwin Schrödinger proposed a new atomic model called the Quantum Mechanical
Model (or the so-called Electron Cloud Model), in which electrons are treated as waves.
➢ Unlike Bohr’s atomic model (1913), the Schrödinger equation can be applied equally to elements other
than hydrogen.

Summary
Atoms are made up of protons,
neutrons, and electrons, which,
in turn, are composed of quarks.
Atoms are the basic units of
matter. Comes from the word
atomos, meaning "indivisible".
Quantum mechanics seeks
to understand the laws
governing the nature, behavior,
and interactions of atomic
and subatomic particles.

SCHRÖDINGER’S MODEL
OF HYDROGEN ATOM AND WAVE FUNCTIONS

John Dalton
(1803)
J. J. Thomson
(1904)
Ernest Rutherford
(1911)
Niels Bohr
(1913)
Billiard Ball Model Plum Pudding Model Planetary Model Bohr Model

Quantum Mechanical Model
Erwin Schrödinger
(1926)
In this model, electrons were no
longer depicted as particles moving
around a central nucleus in a fixed
orbit.
Instead, Schrodinger proposed a model
whereby scientists could only make
educated guesses as to the positions
of electrons.
Hence, their locations could only be
described as being part of a “cloud”
around the nucleus where the electrons
are likely to be found.

Quantum Mechanical Model
Erwin Schrödinger
(1926)
In this model, electrons were no
longer depicted as particles moving
around a central nucleus in a fixed
orbit.
Instead, Schrodinger proposed a model
whereby scientists could only make
educated guesses as to the positions
of electrons.
Hence, their locations could only be
described as being part of a “cloud”
around the nucleus where the electrons
are likely to be found.
Electron Cloud Model
The Quantum Mechanical (or
Electron Cloud) Model differs
from the Bohr Model in that it
does not define the exact
path of an electron.

In 1926, Erwin Schrödinger reasoned that if electrons behave as
waves, then it should be possible to describe them using a wave
equation.
A wave function is defined to be a function describing the probability
of a particle's quantum state as a function of position, momentum,
time, and/or spin.
Wave functions are commonly denoted by the variable Ψ.
Every electron has an associated wave function, and the wave
function tells you everything there is to know about the electron.

Wave functions are used in formulating the Schrödinger equation.
Schrödinger equation describes the form of the probability waves that govern the motion of
small particles.
➢ Schrödinger established the correctness of the equation by applying it to the hydrogen atom, predicting
many of its properties with remarkable accuracy.
The form of the Schrödinger equation depends on the physical situation.
➢ The most general form is the time-dependent Schrödinger equation (above), which gives a
description of a system evolving with time.
i – imaginary unit
ħ – Planck’s constant
Ѱ – wave function
H or Ĥ – Hamiltonian operator

Summary
A wave function is defined as the
probability of a particle's position,
momentum, time, and/or spin.
The Quantum Mechanical Model
depicts electrons as waves moving in
an electron cloud. That means their
locations are defined in terms of their
most likely position inside an atom.
The Schrödinger equation
describes the form of probability
waves that govern the motion
of small particles.

Electron orbits around the nucleus are called energy
levels.
➢ Levels are definite stable energies that a quantum
mechanical particle can have.
➢ According to quantum theory, only certain energy levels
are possible.
➢ Main levels are numbered from 1, 2, 3, 4, and so on, with
the 1st level being the orbit closest to the nucleus.
These main energy levels can be broken down into
sublevels.
➢ Sublevels are comprised of sharp (s), principal (p), diffuse
(d), and fundamental (f) orbitals.
➢ 1st level has 1 sublevel (s).
➢ 2nd level has 2 sublevels (s, p).
➢ 3rd level has 3 sublevels (s, p, d).
➢ 4th level has 4 sublevels (s, p, d, f).

Orbitals are spaces which have high probability of
finding an electron.
➢ In other words, an orbital is an area where electrons live.
➢ Orbitals also refer to the mathematical function that
describes the wave-like behavior of electrons in an atom.
➢ Orbitals are located and are part of energy sublevels.
Each orbital can be occupied by a maximum of two
electrons, each with its own electron spin.
➢ Electron spin has a value of ±½, which depends with its
orientation.
➢ If the electron spins clockwise on its axis, it is
described as spin-up or +½.
➢ Else, If the electron spins counterclockwise, it is
described as spin-down or -½.

1 s 1 2
2 s, p 4 (1+3) 8 (2+6)
3 s, p, d 9 (1+3+5) 18 (2+6+10)
4 s, p, d, f 16 (1+3+5+7) 32 (2+6+10+14)

Summary
Main energy levels can be
broken down into sublevels.
Sublevels are comprised of sharp
(s), principal (p), diffuse (d), and
fundamental (f) orbitals.
Levels are definite stable energies that
a quantum mechanical particle can
have. Main levels are numbered from
1, 2, 3, 4, and so on, with the 1st being
the orbit closest to the nucleus.
Orbitals are spaces with high
probability of finding an electron.
Each orbital are occupied by two
electrons, each with its own
electron spin (+½ or -½).

A quantum number is a value that is used when describing
the energy levels available to atomic and subatomic particles.
An electron has four quantum numbers to describe its state
and yield solutions to the Schrödinger equation:
➢ Principal quantum number (n) describes the energy level of electrons.
➢ Angular momentum quantum number (ℓ) describes the energy sublevel.
➢ Magnetic quantum number (mℓ or m) describes the orbital of the sublevel.
➢ Spin quantum number (ms or s) describes the spin of an electron.

The principal quantum number can have integral values 1, 2,
3, and so on.
In a hydrogen atom, the value of n determines the energy of an
orbital.
➢ Although, this is not the case for many electron atoms.
The principal quantum number also describes the size of the
orbital.
➢ Orbitals for which n = 2 are larger than those for which n = 1, for
example.
➢ The larger the size of the orbital, the greater the distance of the
electron from the nucleus.
Principal quantum number (n) describes the energy level of electrons.

The angular momentum quantum number tells us the shape of
the orbital (i.e., spherical, polar, cloverleaf, or complex).
For a given value of n, ℓ has possible integral values in the
form n ≤ 1.
➢ If n = 1, then ℓ = 0.
➢ If n = 2, then ℓ = 0 and 1.
➢ If n = 3, then ℓ = 0, 1, and 2.
The value of ℓ is generally designated by letters.
➢ ℓ = 0 is called sharp or s
➢ ℓ = 1 is called diffuse or d
➢ ℓ = 2 is called principal or p
➢ ℓ = 3 is called fundamental or f
➢ After f, orbital designations follow alphabetical order (g, h, i, k, ...).
Angular momentum quantum number (ℓ) describes the energy sublevel.

A collection of orbitals with
the same value n is called
shell, while orbitals with the
same n and ℓ values are
referred to as subshell.
For example, the shell with
n = 2 is composed of two
subshells, ℓ = 0 and 1.
These subshells are called
2s and 2p, where 2 denotes
the value of n, and s and p
denote the values of ℓ.

The magnetic quantum number designates the orientation of
the orbital in space.
For a given value of ℓ, mℓ has possible integral values in the
form -ℓ ≤ mℓ ≤ ℓ.
➢ If ℓ = 0, then mℓ = 0.
➢ If ℓ = 1, then mℓ = -1, 0 and 1.
➢ If ℓ = 2, then mℓ = -2, -1, 0, 1, and 2.
Magnetic quantum number (mℓ) describes the orbital of the sublevel.

ℓ ℓ
1
0
(s)
0 1s1 1s2
2
0, 1
(s, p)
0
-1, 0, 1
2s1 2s2 2p1 2p2
2p3 2p4 2p5 2p6
3
0, 1, 2
(s, p, d)
0
-1, 0, 1
-2, -1, 0, 1, 2
3s1 3s2 3p1 3p2
3p3 3p4 3p5 3p6
3d1 3d2 3d3 3d4
3d5 3d6 3d7 3d8
3d9 3d10
4
0, 1, 2, 3
(s, p, d, f)
0
-1, 0, 1
-2, -1, 0, 1, 2
-3, -2, -1, 0, 1, 2, 3
4s1-2 4p1-6 4d1-10
4f1 4f2 4f3 4f4 4f5
4f6 4f7 4f8 4f9 4f10
4f11 4f12 4f13 4f14

According to the electromagnetic theory, a spinning charge
generates a magnetic field.
➢ If electrons are thought of as spinning on their own axes, their
magnetic properties can be announced for.
➢ To take the electron spin into account, it is necessary to introduce
a fourth quantum number, called the spin quantum number.
Spin quantum number suggests that electrons behave as if
they were spinning either clockwise or counterclockwise.
➢ Electrons in an orbital are arbitrarily assigned with ms of either +½
or -½, depending on how it is observed.
Spin quantum number (ms) describes the spin of an electron.

ℓ ℓ
1s1 1
0
(s)
0 ±½
2p2 2
1
(p)
-1, 0, 1 ±½
3d4 3
2
(d)
-2, -1, 0, 1, 2 ±½
4f6 4
3
(f)
-3, -2, -1, 0,
1, 2, 3
±½

Summary
A quantum number is a value
that is used to describe
the energy levels available
to atomic and subatomic particles.
n describes the size of the orbital.
ℓ tells the shape of the orbital. mℓ
defines the orientation of the
orbital. ms assigns the spin of
electrons inside an orbital.
Four quantum numbers are used
describe distribution of electrons
in an atom: principal (n), angular
momentum (ℓ), magnetic (mℓ),
and spin (ms).

Electron configuration is the distribution of electrons of an
atom or molecule in atomic or molecular orbitals.
➢ It describes each electrons as moving independently in an orbital,
in an average field created by all other orbitals.
➢ The electron configuration chart is a tabular representation of
patterns in the electron configuration as one goes down the
periodic table of elements.
According to the laws of quantum mechanics, electrons can
move from one configuration to another through emission or
absorption of photons.
➢ Mathematically, configurations are described by Slater
determinants or configuration state functions.

Orbital diagrams show the arrangement of electrons in
orbitals within an atom.
➢ Boxes are used to represent orbitals.
➢ Single arrow (↑) represents 1 electron.
➢ Double arrows (↑↓) represent 2 electrons.
Orbital diagram for Hydrogen.
1s

Orbital diagram for Carbon.
1s 2s 2p

Orbital diagram for Nitrogen.
1s 2s 2p

Pauli Exclusion Principle states that, in an atom or molecule,
no two electrons can have the same four quantum numbers.
Because an orbital only contains two electrons,
the two electrons must have opposing spins.
It was proposed by Austrian physicist Wolfgang Pauli
in 1925 to describe the behavior of electrons.
As a consequence, subshells have certain
electron arrangement that corresponds to the
electron configuration in which orbitals are written.

Hund's rule states that:
➢ Every orbital in a sublevel is singly-occupied before any
orbital is doubly-occupied.
➢ All of the electrons in singly-occupied orbitals have the same
spin, as to maximize the total spin.
When assigning electrons to orbitals, an electron first
seeks to fill all the orbitals with similar energy (also
referred to as degenerate orbitals) before pairing with
another electron in a half-filled orbital.
➢ Electrons always enter an empty orbital before they pair up.
➢ Atoms at ground states tend to have as many unpaired
electrons as possible.

The Aufbau Principle, simply put, means electrons are
added to orbitals as protons are added to an atom.
➢ Lower electron orbitals fill before higher orbitals do,
"building up" the electron shell.
➢ The end result is that the atom, ion, or molecule forms the
most stable electron configuration.
The term comes from the German word Aufbau, meaning
“built up” or “construction”.
➢ Aufbau Principle outlines the rules used to determine how
electrons are organized into shells and subshells.
➢ It is also known as the building-up principle or the Aufbau
Rule.
Like most rules, there are also exceptions to the rule.
➢ Half-filled and completely-filled d and f subshells add
stability to the atoms, so the d and f block elements don't
always follow the principle.

Any time two electrons share the same orbital, their spin
quantum numbers have to be different.
➢ One of the electrons has to be spin-up, while the other electron
has to be spin-down.
Whenever two electrons are paired together in an orbital, or
their total spin is 0, they are called diamagnetic electrons.
➢ Since electrons in the same orbital always have opposite
values for spin quantum number, they will always end up
cancelling each other out.
➢ Diamagnetic atoms are not attracted to a magnetic field, but
are rather slightly repelled.

Electrons that are alone in an orbital are called
paramagnetic electrons.
➢ If an electron has no pair, the orbital has a net spin, because
the spin of the lone electron does not get cancelled out.
An atom is considered to be paramagnetic when it contains
at least one paramagnetic electron.
➢ In other words, an atom could have as many paired electrons,
but as long as it also has an unpaired electron, it is still
considered a paramagnetic atom.
➢ Paramagnetic properties are due to the realignment of the
electron paths caused by the external magnetic field.

Electronic Structure of Atoms

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