## ORBITALS OF THE ATOM

Atomic orbitals are a fundamental concept in quantum mechanics that describes the behavior and distribution of electrons within an atom. They provide a mathematical representation of the probability density of finding an electron at a specific location in the atom’s electron cloud.

Table of Contents

The most commonly known atomic orbitals are the s, p, d, and f orbitals, which are named after their respective azimuthal quantum numbers. Each orbital type has a unique shape and orientation, which determines the spatial distribution of the electron density.

1. S Orbitals: S orbitals are spherical in shape and are characterized by their azimuthal quantum number (l) of 0. They are centered around the nucleus and exhibit maximum electron density at their nucleus. The probability of finding an electron decreases as you move away from the nucleus. The s orbital can accommodate a maximum of two electrons.

2. P Orbitals: P orbitals have a dumbbell shape and consist of three mutually perpendicular dumbbells oriented along the x, y, and z axes. They correspond to l = 1. There are three p orbitals in each energy level, labeled as px, py, and pz. Each p orbital can hold up to two electrons, resulting in a total of six electrons in the p sublevel.

3. D Orbitals: D orbitals have more complex shapes and correspond to l = 2. They have five distinct orientations, labeled as dxy, dxz, dyz, dx2-y2, and dz2. These orbitals have a cloverleaf shape and can accommodate a maximum of ten electrons, with two electrons per orbital.

4. F Orbitals: F orbitals are the most complex in terms of shape and correspond to l = 3. They have seven different orientations and can hold up to fourteen electrons. The f orbitals are labeled as fxz2, fyz2, fz3, fx(x2-y2), fy(3×2-y2), fxyz, and fz(x2-y2).

It’s important to note that these orbital shapes represent the probability distribution of finding an electron and not the actual path or trajectory of the electron. The behavior of electrons within atoms is described by the principles of quantum mechanics, and the atomic orbitals provide a mathematical framework to understand their properties and behavior.

The arrangement and filling of electrons into these orbitals follow the Aufbau principle, Pauli exclusion principle, and Hund’s rule, which dictate the order and rules for filling electrons into different orbitals based on their energies. This electron configuration determines the chemical properties and reactivity of elements.

Shapes of s and p orbitals are as follows:

s-orbital

p_{x} orbital

p_{y} orbital p_{z }orbital

## ELECTRONIC STRUCTURE OF THE ATOM

The electronic structure of an atom refers to the arrangement of electrons within its atomic orbitals. Understanding the electronic structure is crucial for explaining various properties of atoms, including their chemical reactivity and the spectra they produce.

In more complex atoms, such as those beyond **hydrogen**, the electronic structure is determined by the distribution of electrons among different atomic orbitals. The distribution of electrons follows the principles of quantum mechanics, primarily the Aufbau principle, Pauli exclusion principle, and Hund’s rule.

The Aufbau principle states that electrons fill the lowest energy orbitals first before occupying higher energy orbitals. This principle provides a basis for understanding the order in which electrons occupy atomic orbitals, known as the building-up or filling order. For example, in the ground state of an atom, the 1s orbital is filled before the 2s orbital, which is then followed by the 2p orbitals.

The Pauli exclusion principle states that no two electrons in an atom can have the same set of quantum numbers. This means that within a given orbital, there can be a maximum of two electrons with opposite spins (one with spin-up and one with spin-down). This principle ensures the stability and uniqueness of electron configurations.

Hund’s rule states that when orbitals of equal energy (degenerate orbitals) are available, electrons occupy them singly with parallel spins before pairing up. This rule explains why electrons tend to occupy separate orbitals within a subshell rather than pairing up immediately. It results in an arrangement with unpaired electrons, which can affect an atom’s magnetic properties and reactivity.

The electronic structure of an atom can be represented using electron configuration notation, which describes the distribution of electrons among various orbitals and energy levels. For example, the electron configuration of carbon (C) is 1s² 2s² 2p², indicating that it has two electrons in the 1s orbital, two electrons in the 2s orbital, and two electrons in the 2p orbital (specifically, one electron in each of the 2p suborbitals: 2px and 2py).

The electronic structure of an atom influences its chemical behavior and the spectra it produces. The distribution of electrons among different energy levels and orbitals determines the atom’s ionization energy, electron affinity, and the nature of its chemical bonds. Moreover, the electronic configuration directly affects an atom’s **absorption** and emission of electromagnetic radiation, leading to the unique spectra observed for different elements.

By understanding the electronic structure of atoms, scientists can explain and predict the behavior of elements and their compounds, interpret the results of spectroscopic experiments, and gain insights into the underlying quantum mechanical principles governing matter at the atomic level.

a) that within a given principal quantum number or energy level, there are sub-energy levels, i.e. energy levels otherwise called K,L,M,N,O,P, AND Q shells have sub-energy levels otherwise called s,p,d and f orbitals

(b) The total number of sub-shells within a shell is given by n^{2}

while the maximum number of electrons is provided by 2n^{2} where n is the number of energy levels.

Energy Level Number of orbitals Maximum No of electrons

n = 1(K- shell) 1^{2} =1 2´1^{2 =2}

^{ }n =2 (L- shell) 2^{2 }= 4 2´2^{2 = 8}

n = 3 (M- shell) 3^{2} = 9 2´3^{2} = 18

n = 4 (N- shell) 4^{2} =16 2´ 4^{2} = 32

n = 5 (O- shell) 5^{2} = 25 2´ 5^{2} =50

n = 6 (P-shell) 6^{2} = 36 2´6^{2 }=72

n = 7 (Q – shell) 7^{2 }= 49 2´7^{2} = 98

(c) In a given orbital there could be a maximum of only two electrons and electrons in all orbitals of the same type within a principal quantum number possess equal energies.

(d) The electrons in the different sub-shells or orbitals within a principal quantum number do not all have equal energies.

The gradation of energies of orbitals is as follows:

1s< 2s<2p<3s<3p<3d<4s<4p<4d—

## FILLING OF ELECTRONS IN ORBITALS

The filling of electrons in orbitals is governed by the Aufbau Principle, Pauli Exclusion Principle, and Hund’s Rule of Maximum Multiplicity. These principles help determine the order and arrangement of electrons within an atom’s orbitals.

The Aufbau Principle states that electrons fill orbitals of lower energy before occupying higher energy orbitals. It follows a specific order based on the increasing energy levels of the orbitals. This principle provides a systematic way to determine the electron configuration of an atom. For example, in the ground state of carbon (C), the 1s orbital is filled first, followed by the 2s orbital, and finally, the 2p orbitals.

According to the Pauli Exclusion Principle, no two electrons in an atom can have the same set of quantum numbers. The four quantum numbers are n (principal quantum number), l (azimuthal quantum number), m (magnetic quantum number), and s (spin quantum number). The principle implies that within a given orbital, there can be a maximum of two electrons, each with opposite spin (one with spin-up and one with spin-down).

Hund’s Rule of Maximum Multiplicity states that when degenerate orbitals (orbitals with the same energy level) are available, electrons occupy them singly with parallel spins before pairing up. This rule maximizes the total spin, resulting in the most stable electron configuration. For example, when filling the three 2p orbitals (px, py, and pz), electrons will occupy each orbital singly with parallel spins before pairing occurs.

These principles work together to determine the filling order and arrangement of electrons in an atom’s orbitals. Following these rules ensures the stability and unique characteristics of electron configurations for different elements.

For example, let’s consider the electron configuration of oxygen (O). Oxygen has eight electrons, and its electron configuration is 1s² 2s² 2p⁴. According to the Aufbau Principle, the 1s and 2s orbitals are filled first, accommodating four electrons. Then, the remaining four electrons are placed in the 2p orbitals, following Hund’s Rule, with one electron in each of the three 2p orbitals before pairing up.

The understanding of these principles helps explain the periodic trends observed in the periodic table, such as atomic size, ionization energy, and chemical reactivity. Additionally, these principles are essential in predicting and interpreting the behavior of atoms and molecules in chemical reactions and understanding the electronic and magnetic **properties of materials**.

## QUANTUM NUMBERS

Studies show that the energy of an electron may be characterized by four quantum numbers. These are

{1}The principal quantum number represented by n with integral values of 1,2,3,4 e.t.c.

{2}The subsidiary or Azimuthal quantum number represented by l with integral values

ranging from O to (n-1).

(3) The magnetic quantum number represented by m with integral values ranging

from –l to +l.

(4) The spin quantum number represented by s with integral values – ^{1}/_{2} and = ^{1}/_{2}.

Element Atomic Number Electronic configuration.

H 1 1S^{1}

He 2 1S^{2}

Li 3 1S^{2 }2S^{1}

Be 4 1S^{2} 2S^{2}

B 5 1S^{2} 2S^{2 }2P^{1}

C 6 1S^{2} 2S^{2 }2P^{2}

N 7 1S^{2} 2S^{2 }2P^{3}

O 8 1S^{2} 2S^{2 }2P^{4 }

F 9 1S^{2} 2S^{2 }2P^{5 }

Ne 10 1S^{2} 2S^{2 }2P^{6 }

Na 11 1S^{2} 2S^{2 }2P^{6 }3S^{1}

Mg 12 1S^{2} 2S^{2 }2P^{6 }3S^{2}

Al 13 1S^{2} 2S^{2 }2P^{6 }3S^{2 }3P^{1}

Si 14 1S^{2} 2S^{2 }2P^{6 }3S^{2 }3P^{2}

P 15 1S^{2} 2S^{2 }2P^{6}3S^{23}3P^{3}

S 16 1S^{2} 2S^{2 }2P^{6}3S^{2 }3P^{4}

Cl 17 1S^{2} 2S^{2 }2P^{6 }3S^{2 }3P^{5}

Ar 18 1S^{2} 2S^{2 }2P^{6 }3S^{2}3P^{6}

K 19 1S^{2} 2S^{2 }2P^{6 }3S^{2}3P^{6 }4S^{1}

Ca 20 1S^{2} 2S^{2 }2P^{6 }3S^{2}3P^{6 }4S^{2 }

Atomic Number, Relative Atomic Masses, Isotopes & Calculations

IUPAC Nomenclature of Chemical Compounds

STANDARD SEPARATION TECHNIQUES