Electronic Structure of Atoms

When trying to comprehend the structure of the atom, it is best to imagine it similar to a solar system, with the nucleus being the sun and the electrons are the planet.

Internal structure of an atom

Made up of Subatomic particles, which are the building blocks of the atom.

• Electron - Possesses a negative electrical charge. ( $e^{-}$ )
• Proton - Possesses a positive charge. ( $p^{+}$ )
• Neutron - No charge associated with it. ( $n$ )

The charge neutrality of an atom

An atom as a whole is electrically neutral meaning it has no net electrical charge.

To achieve this, the same number of positive protons and negative electrons must be observed.

$\text{number of }{e}^{-}=\text{number of }{p}^{+}$

Atomic Number, Mass Number, and Atomic Mass

Atomic Number ( $Z$ ) is the number of protons in the nucleus of an atom. It is also the number of electrons present.

Mass Number ( $A$ ) is the sum of the number of protons and number of neutrons in the nucleus of the atom.

Atomic Mass is the average mass of all isotopes of an element weighted according to natural abundance

Isotopes

Isotopes are atoms of an element with the same number of protons and electrons but a varying amount of neutrons.

In other terms, a change in the Mass Number while maintaining the same Atomic Number.

Quantum Mechanics & Atomic Orbitals

In 1926, Erwin Schrodinger proposed an equation now known as the Schrodinger’s wave equation, which incorporates both the wave-like and particle-like behaviors of the electron.

Orbitals & Quantum Numbers

Quantum Numbers are requires to describe the distribution of electrons in an atom.

Think of quantum numbers like the addresses of your electron within an atom. The placement of your electrons are called orbitals ( $s$, $p$. $d$, $f$ ).

The quantum number are the following:

• $n$ - Principal
• $l$ - Azimuthal
• $m_l$ - Magnetic Quantum Number

The orbitals and their shape are the following:

• $s$ - Sphere shape
• $p$ - Dumbbell shape
• $d$ - Double dumbbell shape
• $f$ - Complex shape

The quantum-mechanical model does not refer to orbits because the motion of an electron in an atom cannot be precisely determined (Heisenberg’s uncertainty Principle).

Principal Quantum Number ( $n$ )

This quantum number denotes the size of your orbital and can have positive integral values ($1,2,3\cdots$)

As the value of $n$ increases, the orbital becomes larger and the electron spends more time farther away from the nucleus.

An increase in $n$ also means that the electron has a higher energy and is therefor less tightly bound to the nucleus.

The collection of orbitals with the same value of $n$ is called an electron shell.

Azimuthal ( $l$ )

This quantum number is also known as the Angular Momentum Quantum Number.

This quantum number defines your orbital’s shape as opposed to size; the values of this quantum number ranges from $0–(n-1)$, where $n$ is your principal quantum number.

The values of $l$ for a particular orbital is generally designated by the letters $s$, $p$, $d$, $f$.

Value of $l$	Name of sub shell	Shape
$0$	$s$	Sphere
$1$	$p$	Dumbbell
$2$	$d$	Double Dumbbell / Clover
$3$	$f$	Complex

Magnetic Quantum Number ( $m_l$ )

This quantum number can have integral values between $-l$ and $l$, including zero ( $0$ ).

This quantum number will determine the orientation of your orbital shape determined by your Azimuthal Quantum Number ( $l$ ).

Spin Quantum Number ( $m_s$ )

This quantum number dictates the orientation of your electron and can have a value of either $-\frac{1}{2}$ or $+\frac{1}{2}$ which denote counter-clockwise and clockwise spin respectively.

Electrons, denoted by a number 1, are prefixed by an up arrow for “Spin-up” or clockwise spin ( $\uparrow$ ) or a down arrow for “Spin-down” or counter-clockwise spin ( $\downarrow$ ).

Restrictions to the orbitals

Pauli’s Exclusion Principle

No two electrons in an atom can have the same four quantum numbers.

If two electrons in an atom should have the same $n$, $l$, and $m_l$ quantum numbers, they must have different $m_s$.

Only two electrons must have the same atomic orbital with both having opposing spins.

Hund’s Rule of Maximum Multiplicity

The most stable arrangement of electrons in a sub shell is the one with the greatest number of parallel spins.

This states that electrons must be placed singly.

Afbau’s Building-up Principle

As protons are added one by one to the nucleus to build up the elements, electrons are similarly added to the atomic orbitals.

1. Fill orbitals by energy, one by one.
2. Up to two electrons must be observed per orbital.
3. Filling degenerate orbitals.

Electron Configuration

The way electrons are distributed among the various orbitals of an atom.

The most stable electron configuration is that in which the electrons are in the lowest possible energy states.