Principles of distributing electrons

Understanding Quantum Numbers and Electron Configurations

This lesson delves into the fundamental concepts of quantum numbers and electron configurations. It covers the Pauli Exclusion Principle and Hund’s Rule, explaining how they influence the arrangement of electrons in atoms.

The lesson also explores the different quantum numbers (principal, azimuthal, magnetic, and spin) and their roles in specifying the location and energy of electrons within an atom. Understanding these principles is crucial for comprehending the behavior of atoms and their chemical properties.

Principles of distributing electrons (Electronic Configurations)

The distribution of electrons in an atom is governed by a set of principles and rules that help us understand how electrons occupy different energy levels and sublevels within the atomic structure.

These principles include :

• The Aufbau principle
• The Pauli exclusion principle,
• Hund’s rule.

Let’s explore each of these principles:

Pauli Exclusion Principle:

The Pauli Exclusion Principle is one of the fundamental principles in quantum mechanics and is a crucial concept in understanding the behavior of electrons in atoms.

This principle was formulated by Austrian physicist Wolfgang Pauli in 1925.

The Pauli exclusion principle states that :

“ no two electrons in an atom can have the same set of quantum numbers”.

• Quantum numbers describe the energy, shape, and orientation of an electron’s orbital.
• As a result, each orbital can hold a maximum of two electrons with opposite spins.
• Electrons with opposite spins have different magnetic quantum numbers, and this prevents them from having the same set of quantum numbers and thus occupying the same orbital.

To understand this principle better, let’s break down the key components:

Electrons:

• Electrons are negatively charged subatomic particles that orbit the nucleus of an atom.
• They are organized into different energy levels and sublevels, each of which contains orbitals where electrons are likely to be found.

Quantum Numbers:

Electrons are described by a set of four quantum numbers that define their properties and specify their location within an atom.

These quantum numbers are:

• Principal Quantum Number (n): This number designates the energy level of the electron. It can have values of 1, 2, 3, and so on.
• Angular Momentum Quantum Number (l): This number defines the shape of the orbital and ranges from 0 to (n – 1).
• Magnetic Quantum Number (m_l): This number describes the orientation of the orbital in space and ranges from -l to +l.
• Spin Quantum Number (m_s): This number represents the spin of the electron and can have values of +1/2 or -1/2.

The Pauli Exclusion Principle

Asserts that no two electrons in an atom can have the same values for all four quantum numbers.

• In particular, it means that no two electrons can occupy the same orbital if they have the same spin (m_s) value.
• This is why you often hear that “electrons with opposite spins occupy the same orbital.”
• For example, in the same orbital, one electron might have a spin quantum number (m_s) of +1/2 (spin “up”), and the other electron must have a spin quantum number of -1/2 (spin “down”).
• This difference in spin ensures that the two electrons do not have the same set of quantum numbers and obey the Pauli Exclusion Principle.

Example:

• The Pauli Exclusion Principle plays a fundamental role in the organization of electrons in atoms and the periodic table, helping to explain the stability of chemical elements and their electronic configurations.
• It also underlies many aspects of quantum mechanics and quantum chemistry.

Example

 Here’s a simple example illustrating the Pauli Exclusion Principle with the electron configuration of carbon (atomic number 6):

Carbon has six electrons. We’ll follow the Aufbau principle, which states that electrons fill the lowest energy orbitals first, and the Pauli Exclusion Principle to distribute these electrons.

1)The first two electrons go into the 1s orbital.

The quantum numbers for these two electrons are as follows:

• Electron 1: n = 1, l = 0 (s orbital), m_l = 0, m_s = +1/2
• Electron 2: n = 1, l = 0 (s orbital), m_l = 0, m_s = -1/2
• These two electrons are allowed in the same orbital (1s) because they have opposite spins (+1/2 and -1/2), complying with the Pauli Exclusion Principle.

2)The next two electrons go into the 2s orbital.

The quantum numbers for these two electrons are:

• Electron 3: n = 2, l = 0 (s orbital), m_l = 0, m_s = +1/2
• Electron 4: n = 2, l = 0 (s orbital), m_l = 0, m_s = -1/2
• Once again, these two electrons are in the same orbital (2s) with opposite spins, adhering to the Pauli Exclusion Principle.

3)Finally, the last two electrons occupy the 2p orbital.

The quantum numbers for these electrons are as follows:

• Electron 5: n = 2, l = 1 (p orbital), m_l = -1, m_s = +1/2
• Electron 6: n = 2, l = 1 (p orbital), m_l = -1, m_s = -1/2
• In this case, the two electrons occupy different p orbitals with the same energy level and different orientations (m_l = -1). They also have opposite spins, which satisfies the Pauli Exclusion Principle.

So, the electron configuration of carbon is: 1s² 2s² 2p², and it follows the Pauli Exclusion Principle, as no two electrons in the atom have the same set of quantum numbers, especially the spin quantum numbers.

Another example

let’s take another example: oxygen (atomic number 8).

Oxygen has eight electrons, and we’ll apply the Pauli Exclusion Principle to determine its electron configuration:

1)The first two electrons go into the 1s orbital. The quantum numbers for these two electrons are as follows:

• Electron 1: n = 1, l = 0 (s orbital), m_l = 0, m_s = +1/2
• Electron 2: n = 1, l = 0 (s orbital), m_l = 0, m_s = -1/2
• These two electrons are in the same orbital (1s) with opposite spins, complying with the Pauli Exclusion Principle.

2)The next two electrons go into the 2s orbital. The quantum numbers for these two electrons are:

• Electron 3: n = 2, l = 0 (s orbital), m_l = 0, m_s = +1/2
• Electron 4: n = 2, l = 0 (s orbital), m_l = 0, m_s = -1/2
• Just like before, these two electrons occupy the same 2s orbital with opposite spins, adhering to the Pauli Exclusion Principle.

3)The remaining four electrons occupy the 2p orbitals.

The quantum numbers for these electrons are as follows:

• Electron 5: n = 2, l = 1 (p orbital), m_l = -1, m_s = +1/2
• Electron 6: n = 2, l = 1 (p orbital), m_l = -1, m_s = -1/2
• Electron 7: n = 2, l = 1 (p orbital), m_l = 0, m_s = +1/2
• Electron 8: n = 2, l = 1 (p orbital), m_l = 0, m_s = -1/2
• In this case, electrons 5 and 6 are in one set of 2p orbitals (2p_x), and electrons 7 and 8 are in another set of 2p orbitals (2p_y), with the same energy level and different orientations (m_l values).

They also have opposite spins, satisfying the Pauli Exclusion Principle.

So, the electron configuration of oxygen is: 1s² 2s² 2p⁴, and it follows the Pauli Exclusion Principle, as no two electrons in the atom have the same set of quantum numbers, especially the spin quantum numbers.

Fluorine: F₉

Neon: Ne ₁₀

Example :₇N

 let’s consider another example: the electron configuration of nitrogen (atomic number 7).

Nitrogen has seven electrons, and we’ll apply the Pauli Exclusion Principle to determine its electron configuration:

1)The first two electrons go into the 1s orbital. The quantum numbers for these two electrons are as follows:

• Electron 1: n = 1, l = 0 (s orbital), m_l = 0, m_s = +1/2
• Electron 2: n = 1, l = 0 (s orbital), m_l = 0, m_s = -1/2
• These two electrons are in the same orbital (1s) with opposite spins, complying with the Pauli Exclusion Principle.

2)The next two electrons go into the 2s orbital.

The quantum numbers for these two electrons are:

• Electron 3: n = 2, l = 0 (s orbital), m_l = 0, m_s = +1/2
• Electron 4: n = 2, l = 0 (s orbital), m_l = 0, m_s = -1/2
• Just like before, these two electrons occupy the same 2s orbital with opposite spins, adhering to the Pauli Exclusion Principle.

3)The remaining three electrons occupy the 2p orbitals.

The quantum numbers for these electrons are as follows:

• Electron 5: n = 2, l = 1 (p orbital), m_l = -1, m_s = +1/2
• Electron 6: n = 2, l = 1 (p orbital), m_l = +1, m_s = +1/2
• Electron 7: n = 2, l = 1 (p orbital), m_l = 0, m_s = +1/2
• In this case, electrons 5 and 6 are in one set of 2p orbitals (2p_x), and electron 7 is in another set of 2p orbitals (2p_y), with the same energy level and different orientations (m_l values).

These electrons also have opposite spins, satisfying the Pauli Exclusion Principle.

So, the electron configuration of nitrogen is: 1s² 2s² 2p³, and it follows the Pauli Exclusion Principle, as no two electrons in the atom have the same set of quantum numbers, especially the spin quantum numbers.

Write the possible values of the four quantum numbers for :An electron in 2p-sublevel

An electron in a 2p sublevel (p orbital) has the following possible values for the four quantum numbers:

Principal Quantum Number (n):

The principal quantum number (n) represents the energy level of the electron.

For a 2p sublevel, the value of n is 2. So, n = 2.

Angular Momentum Quantum Number (l):

The angular momentum quantum number (l) corresponds to the shape of the orbital.

For a p sublevel, l is equal to 1. Therefore, l = 1.

Magnetic Quantum Number (m_l):

The magnetic quantum number (m_l) indicates the orientation of the orbital in space.

For a p sublevel (l = 1), m_l can take the values of -1, 0, and +1.

These correspond to the three different orientations of the p orbitals along the x, y, and z axes.

Spin Quantum Number (m_s):

The spin quantum number (m_s) represents the spin of the electron.

It can have two possible values: +1/2 (spin “up”) or -1/2 (spin “down”).

So, for an electron in a 2p sublevel, the four quantum numbers can be expressed as:

n = 2

l = 1

m_l can be -1, 0, or +1

m_s can be +1/2 or -1/2

These quantum numbers define the properties and location of the electron within the 2p orbital.

Write the possible values of the four quantum numbers for :the first electron in 4d-sublevel?

The first electron in a 4d sublevel (d orbital) has the following possible values for the four quantum numbers:

• Principal Quantum Number (n):

The principal quantum number (n) represents the energy level of the electron. For a 4d sublevel, the value of n is 4. So, n = 4. 

• Angular Momentum Quantum Number (l):

The angular momentum quantum number (l) corresponds to the shape of the orbital. For a d sublevel, l is equal to 2. Therefore, l = 2. 

• Magnetic Quantum Number (m_l):

The magnetic quantum number (m_l) indicates the orientation of the orbital in space. For a d sublevel (l = 2), m_l can take multiple values. In the case of the first electron in the 4d sublevel, m_l will be -2, which corresponds to one of the orientation possibilities for the d orbital. 

• Spin Quantum Number (m_s):

The spin quantum number (m_s) represents the spin of the electron.

It can have two possible values: +1/2 (spin “up”) or -1/2 (spin “down”).

So, for the first electron in a 4d sublevel, the four quantum numbers can be expressed as:

n = 4

l = 2

m_l = -2

m_s can be +1/2 or -1/2

These quantum numbers define the properties and location of the first electron within the 4d orbital.

Write the possible values of the four quantum numbers for :the second electron in  1s-sub-level ?

The second electron in a 1s sublevel (s orbital) has the following possible values for the four quantum numbers:

• Principal Quantum Number (n):

The principal quantum number (n) represents the energy level of the electron.

For a 1s sublevel, the value of n is 1.

So, n = 1.

 Angular Momentum Quantum Number (l):

The angular momentum quantum number (l) corresponds to the shape of the orbital.

For an s sublevel, l is equal to 0.

Therefore, l = 0. 

• Magnetic Quantum Number (m_l):

The magnetic quantum number (m_l) indicates the orientation of the orbital in space.

For an s sublevel (l = 0), there is only one possible orientation, so m_l must be 0. 

• Spin Quantum Number (m_s):

The spin quantum number (m_s) represents the spin of the electron.

It can have two possible values: +1/2 (spin “up”) or -1/2 (spin “down”).

So, for the second electron in a 1s sublevel, the four quantum numbers can be expressed as:

n = 1

l = 0

m_l = 0

m_s can be +1/2 or -1/2

These quantum numbers define the properties and location of the second electron within the 1s orbital.

Aufbau (bulding-principle)

The Aufbau Principle, often referred to as the “building-up principle,” is a fundamental concept in chemistry and quantum mechanics.

It describes the order in which electrons fill atomic orbitals of an atom, from lower-energy orbitals to higher-energy orbitals.

The Aufbau Principle provides a systematic approach for determining the electron configuration of an atom, which is essential in understanding the organization of electrons in the periodic table.

The Aufbau principle states that :

“electrons fill the lowest energy orbitals first before moving to higher energy orbitals”.

In other words, electrons will occupy the orbitals in order of increasing energy. This principle is often represented using the building-up order of electron configuration in the periodic table.

The key points of the Aufbau Principle are as follows:

• Lowest Energy First: Electrons enter the lowest energy orbitals first. In other words, they begin by filling the orbitals closest to the nucleus before moving to higher energy levels.
• Energy Levels (Principal Quantum Numbers): Electrons are arranged in energy levels, designated by the principal quantum number (n).

Electrons first occupy the 1s orbital, then the 2s and 2p orbitals, followed by the 3s, 3p, and 3d orbitals, and so on.

• Sublevels (Angular Momentum Quantum Numbers): Within each energy level, there are sublevels defined by the angular momentum quantum number (l).

Electrons fill the sublevels in a specific order: s, p, d, and f.

The s sublevel has the lowest energy, followed by p, d, and f.

• Maximum Electron Capacity: Each orbital can hold a maximum of two electrons with opposite spins, as dictated by the Pauli Exclusion Principle.

Hund’s Rule:

Hund’s rule deals with the distribution of electrons within a sublevel (a set of orbitals with the same energy level and shape).

It states that :”electrons will occupy degenerate (having the same energy) orbitals singly before pairing up”.

 In other words, if there are three degenerate p orbitals, electrons will enter each of them with the same spin (parallel spins) before any of them pair up with opposite spins.

• When electrons fill degenerate orbitals (orbitals with the same energy level and sublevel), they fill them singly before pairing
• This is known as Hund’s Rule and helps distribute electrons in a way that minimizes electron-electron repulsion.
• By following the Aufbau Principle, chemists and physicists can determine the electron configuration of any element, which describes the arrangement of electrons in its atomic orbitals.

Example: electronic configuration of carbon

Electron configurations are often represented using a series of numbers and letters, such as “1s² 2s² 2p⁶ 3s²,” where the numbers represent the energy level and the superscripts indicate the number of electrons in each orbital.

Hund’s Rule states the following:

Each orbital in a subshell is singly occupied before any orbital is doubly occupied: Electrons fill the degenerate orbitals one at a time with parallel spins (e.g., one “up” spin and one “down” spin) before pairing up with opposite spins.

Electrons in degenerate orbitals have the same energy:

• When multiple orbitals within a subshell have the same energy (degenerate), electrons occupy these orbitals to maximize their total spin, resulting in lower overall energy.
• Hund’s Rule is a consequence of the Pauli Exclusion Principle, which states that no two electrons in an atom can have the same set of quantum numbers (including spin).
• By following Hund’s Rule, the electrons in degenerate orbitals can be thought of as spreading out to minimize repulsion between negatively charged electrons, which results in a more stable electron configuration.

For example, in the p subshell, there are three degenerate p orbitals (px, py, and pz). According to Hund’s Rule, when filling these orbitals with electrons, each orbital is singly occupied with parallel spins before any orbital receives a second electron with opposite spin.

Hund’s Rule helps in understanding the electron configurations of atoms and their ground-state configurations. It also plays a significant role in chemical bonding and reactivity by determining the distribution of electrons in an atom’s valence shell.

For example, in the p subshell, there are three degenerate p orbitals (px, py, and pz). According to Hund’s Rule, when filling these orbitals with electrons, each orbital is singly occupied with parallel spins before any orbital receives a second electron with opposite spin.

Hund’s Rule helps in understanding the electron configurations of atoms and their ground-state configurations. It also plays a significant role in chemical bonding and reactivity by determining the distribution of electrons in an atom’s valence shell.

Filling up of 2-p orbital

Example:N₇

 let’s use the electron configuration of nitrogen (N) as an example to illustrate Hund’s Rule in a tabular format.

Nitrogen has an atomic number of 7.

When filling the electron configuration of nitrogen, we follow Hund’s Rule, which states that electrons fill degenerate orbitals one at a time with parallel spins before pairing up.

Here’s how it’s done:

The first two electrons go into the 1s orbital.

One electron has an “up” spin (↑), and the other has a “down” spin (↓).

The next electron goes into the 2s orbital with an “up” spin (↑).

Orbital       Electrons (Up ↑ / Down ↓)

Finally, the remaining three electrons go into the 2p orbitals.

According to Hund’s Rule, these electrons are singly occupied in the 2p orbitals with parallel spins (↑) before any of them are paired.

2p     1 ↑ 1 ↑ 1 ↑

This electron configuration illustrates how Hund’s Rule is applied in filling the degenerate p orbitals of nitrogen with unpaired electrons (↑) before pairing them up (↓).

Hund’s Rule for: O8

Let’s use the electron configuration of oxygen (O), which has an atomic number of 8, to illustrate Hund’s Rule:

Here’s how the electron configuration of oxygen is filled following Hund’s Rule:

The first two electrons go into the 1s orbital. One electron has an “up” spin (↑), and the other has a “down” spin (↓).

Orbital       Electrons (Up ↑ / Down ↓)

1s      1 ↑ 1 ↓

2s     

2p    

The next two electrons go into the 2s orbital. These electrons are both “up” spins (↑).

Orbital       Electrons (Up ↑ / Down ↓)

1s      1 ↑ 1 ↓

2s      1 ↑ 1 ↑

2p    

Finally, the remaining four electrons go into the 2p orbitals. According to Hund’s Rule, these electrons are singly occupied in the 2p orbitals with parallel spins (↑) before any of them are paired.

This electron configuration illustrates how Hund’s Rule is applied in filling the degenerate p orbitals of oxygen with unpaired electrons (↑) before pairing them up (↓).

How to arrange of sublevels according their energy level ?

Sublevels, also known as subshells, are arranged in order of increasing energy level.

The energy order of sublevels is primarily based on their angular momentum quantum number (l). Here’s the typical order of sublevels by increasing energy:

• s sublevel: The s sublevel has the lowest energy and is characterized by an angular momentum quantum number (l) of 0. It is a spherical-shaped orbital.
• p sublevel: The p sublevel has slightly higher energy than the s sublevel. It is characterized by l = 1 and consists of three sets of dumbbell-shaped orbitals oriented along the x, y, and z axes.
• d sublevel: The d sublevel has higher energy than both the s and p sublevels. It is characterized by l = 2 and consists of five sets of complex-shaped orbitals. These orbitals have various orientations in space.
• f sublevel: The f sublevel has the highest energy among the sublevels.

It is characterized by l = 3 and contains seven sets of even more complex-shaped orbitals, each with distinct orientations in space.

The order of increasing energy based on the angular momentum quantum number (l) is s < p < d < f.

This order is important when determining the electron configuration of an atom using the Aufbau Principle.

Electrons fill the sublevels in this energy order, with the s sublevel filling first, followed by the p, d, and f sublevels as needed.

It’s important to note that in some cases, when elements have partially filled energy levels, there can be exceptions to this energy order due to electron-electron interactions. However, as a general rule, this is the typical order in which sublevels are arranged by increasing energy level.

 Arrangement  of sublevels according their energy level :sum of (n+l)

• The arrangement of sublevels (subshells) according to their energy level can also be determined using the sum of the principal quantum number (n) and the angular momentum quantum number (l).
• This sum, (n + l), provides an alternative way to order sublevels by energy.
• When (n + l) is used to compare sublevels, the sublevel with the lowest (n + l) value has the lowest energy, and the one with the highest (n + l) value has the highest energy.

Here’s the order of sublevels based on increasing (n + l) values:

s sublevel: (n + l) = (1 + 0) = 1

The s sublevel has the lowest energy, as (n + l) is the smallest value.

p sublevel: (n + l) = (2 + 1) = 3

The p sublevel has a higher (n + l) value than the s sublevel.

d sublevel: (n + l) = (3 + 2) = 5

The d sublevel has a higher (n + l) value than both the s and p sublevels.

f sublevel: (n + l) = (4 + 3) = 7

The f sublevel has the highest (n + l) value and, therefore, the highest energy among the sublevels.

Using the (n + l) rule, you can determine the relative energy order of sublevels within an energy level.

This rule is particularly useful when comparing sublevels with the same principal quantum number (n).

It ensures that sublevels are filled in the correct order when determining electron configurations according to the Aufbau Principle.

Example

Let’s use the (n + l) rule to determine the order of sublevels for different energy levels.

Consider the following energy levels (n) and their respective sublevels, arranged by increasing (n + l) values:

Energy Level 1 (n = 1):

s sublevel: (1 + 0) = 1

Energy Level 2 (n = 2):

s sublevel: (2 + 0) = 2

p sublevel: (2 + 1) = 3

Energy Level 3 (n = 3):

s sublevel: (3 + 0) = 3

p sublevel: (3 + 1) = 4

d sublevel: (3 + 2) = 5

 Energy Level 4 (n = 4):

s sublevel: (4 + 0) = 4

p sublevel: (4 + 1) = 5

d sublevel: (4 + 2) = 6

f sublevel: (4 + 3) = 7

Based on the (n + l) values, the sublevels are ordered by increasing energy level as follows:

s

p

d

f

This order is consistent with the usual energy order of sublevels based on the angular momentum quantum number (l).

Both methods provide the same sequence of sublevels with respect to energy.

The (n + l) rule is particularly helpful when comparing sublevels within the same energy level, ensuring that they are filled in the correct order when determining electron configurations in accordance with the Aufbau Principle.

Example

 let’s take an example by comparing the (n + l) values for the sublevels of different elements within the same principal quantum number (n) to see how the sublevels are arranged by energy:

Energy Level 2 (n = 2):

For the 2s sublevel: (2 + 0) = 2

For the 2p sublevel: (2 + 1) = 3

Since 2s has a lower (n + l) value (2) compared to 2p (3), the 2s sublevel is lower in energy than the 2p sublevel.

Energy Level 3 (n = 3):

For the 3s sublevel: (3 + 0) = 3

For the 3p sublevel: (3 + 1) = 4

For the 3d sublevel: (3 + 2) = 5

Here, you can see that the (n + l) values indicate the energy order:

3s has the lowest (n + l) value of 3.

3p has a higher (n + l) value of 4.

3d has the highest (n + l) value of 5.

This means the order of sublevels by energy for this example, within the n = 3 energy level, is 3s < 3p < 3d.

Using the (n + l) rule, you can determine the relative energy order of sublevels within the same energy level when calculating electron configurations. It ensures that electrons are placed in the correct order according to the Aufbau Principle.

The order of all sublevels

The order of all sublevels (subshells) within an atom, arranged by increasing energy, is as follows:

• 1s sublevel: This is the lowest energy sublevel, consisting of one s orbital.
• 2s sublevel: Higher in energy than the 1s sublevel, it also contains one s orbital.
• 2p sublevel: Following the 2s sublevel, the 2p sublevel includes three p orbitals oriented along the x, y, and z axes.
• 3s sublevel: Higher in energy than the 2p sublevel, it contains one s orbital.
• 3p sublevel: Following the 3s sublevel, the 3p sublevel includes three p orbitals.
• 4s sublevel: Higher in energy than the 3p sublevel, it contains one s orbital.
• 3d sublevel: This is the first appearance of d orbitals, and it is higher in energy than the 4s sublevel. It contains five d orbitals with various shapes and orientations.
• 4p sublevel: Following the 3d sublevel, the 4p sublevel includes three p orbitals.
• 5s sublevel: Higher in energy than the 4p sublevel, it contains one s orbital.
• 4d sublevel: The second appearance of d orbitals, this sublevel is higher in energy than the 5s sublevel and contains five d orbitals.
• 5p sublevel: Following the 4d sublevel, the 5p sublevel includes three p orbitals.
• 6s sublevel: Higher in energy than the 5p sublevel, it contains one s orbital.
• 4f sublevel: The first appearance of f orbitals, this sublevel is higher in energy than the 6s sublevel and contains seven f orbitals with complex shapes and orientations.
• 5d sublevel: The third appearance of d orbitals, it is higher in energy than the 4f sublevel and contains five d orbitals.
• 6p sublevel: Following the 5d sublevel, the 6p sublevel includes three p orbitals.
• 7s sublevel: Higher in energy than the 6p sublevel, it contains one s orbital.
• 5f sublevel: The second appearance of f orbitals, this sublevel is higher in energy than the 7s sublevel and contains seven f orbitals.
• 6d sublevel: The fourth appearance of d orbitals, it is higher in energy than the 5f sublevel and contains five d orbitals.
• 7p sublevel: Following the 6d sublevel, the 7p sublevel includes three p orbitals.
• 8s sublevel: Higher in energy than the 7p sublevel, it contains one s orbital.

These are the primary sublevels within the electron energy levels (n) from 1s through 8s, including the appearance of p, d, and f sublevels as energy increases. The order of filling these sublevels follows the Aufbau Principle and the (n + l) rule, as discussed earlier.

The order of all sublevels in a linear format

Here is the order of all sublevels in a linear format, arranged by increasing energy:

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p < 8s

[Ss  ps  ps  dps  dps  fdps  fdps]

This linear sequence represents the energy order of sublevels within the electron energy levels (n) from 1s through 8s.

The order is based on the Aufbau Principle, which guides the filling of sublevels in atoms.

 Write the electronic configuration  according to building up principle for:Na

The electronic configuration of sodium (Na), based on the Aufbau Principle (building up principle), is as follows:

Sodium has an atomic number of 11, meaning it has 11 electrons to distribute among its atomic orbitals.

The first two electrons go into the 1s orbital:1s²

The next two electrons go into the 2s orbital:2s²

The next six electrons go into the 2p orbitals:2p⁶

At this point, we’ve used 10 out of the 11 electrons:1s² 2s² 2p⁶

The last electron goes into the 3s orbital:3s¹

So, the complete electron configuration of sodium (Na) is:

1s² 2s² 2p⁶ 3s¹

Here is the linear sequence of the electron configuration of sodium (Na) according to the Aufbau Principle (building up principle), arranged by increasing energy:

1s² 2s² 2p⁶ 3s¹

The electronic configuration of :Calcium :ca

The electronic configuration of calcium (Ca), based on the Aufbau Principle (building up principle), is as follows:

Calcium has an atomic number of 20, meaning it has 20 electrons to distribute among its atomic orbitals.

The first two electrons go into the 1s orbital:1s²

The next two electrons go into the 2s orbital:2s²

The next six electrons go into the 2p orbitals:2p⁶

The next two electrons go into the 3s orbital:3s²

The next six electrons go into the 3p orbitals:3p⁶

At this point, we’ve used 18 out of the 20 electrons:

1s² 2s² 2p⁶ 3s² 3p⁶

The last two electrons go into the 4s orbital:4s²

So, the complete electron configuration of calcium (Ca) is:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s²

The linear sequence of the electron configuration of calcium (Ca) according to the Aufbau Principle is:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s²

Electronic configuration of Zn:

The linear sequence of the electron configuration of zinc (Zn) according to the Aufbau Principle is:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 

The electronic configuration of Copper :cu

The linear sequence of the electron configuration of copper (Cu) according to the Aufbau Principle is:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s¹

The electronic configuration of Iron :Fe

The linear sequence of the electron configuration of iron (Fe) according to the Aufbau Principle is:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶

The electronic configuration of Cobalt: Co

The linear sequence of the electron configuration of cobalt (Co) according to the Aufbau Principle is:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁷

The electronic configuration of Sc

The linear sequence of the electron configuration of scandium (Sc) according to the Aufbau Principle is:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹

The electronic configuration of Ti

The linear sequence of the electron configuration of titanium (Ti) according to the Aufbau Principle is:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d²

The electronic configuration of V

The linear sequence of the electron configuration of vanadium (V) according to the Aufbau Principle is:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d³

The electronic configuration of Cr

The electron configuration of chromium (Cr) has an interesting exception due to electron stability. According to the Aufbau Principle, it should be:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁴

However, in the case of chromium, it’s more stable to have one unpaired electron in the 4s orbital and half-filled 3d orbitals. This gives the electron configuration as:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁵

The electronic configuration of Mn

The linear sequence of the electron configuration of manganese (Mn) according to the Aufbau Principle is:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁵

The electronic configuration of Ni

The linear sequence of the electron configuration of nickel (Ni) according to the Aufbau Principle is:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁸

Quiz

Quiz: Principles of Electron Distribution (Electronic Configurations)

Question 1: Aufbau Principle

1.1 What does the Aufbau principle state regarding the filling of electron orbitals?

a) Electrons fill orbitals with increasing energy, from the lowest to the highest.

b) Electrons fill orbitals randomly.

c) Electrons fill orbitals with decreasing energy, from the highest to the lowest.

d) Electrons fill orbitals with the same energy simultaneously.

Question 2: Pauli Exclusion Principle

2.1 According to the Pauli exclusion principle, what is the maximum number of electrons that can occupy a single atomic orbital?

a) 1

b) 2

c) 3

d) 4

Question 3: Hund’s Rule

3.1 Hund’s Rule states that:

a) Electrons will occupy orbitals in a way that maximizes the total spin.

b) Electrons will pair up in an orbital before moving to the next one.

c) Electrons will always occupy the lowest energy level first.

d) Electrons will occupy orbitals of the same energy level in a way that maximizes the number of unpaired electrons.

Question 4: Application of Principles

4.1 If an atom has the electronic configuration 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹, which principle(s) is/are being followed?

a) Aufbau principle only.

b) Pauli exclusion principle only.

c) Hund’s rule only.

d) All of the above.

Question 5: Electron Configuration

5.1 What is the correct electron configuration for nitrogen (atomic number 7)?

a) 1s² 2s² 2p³

b) 1s² 2s² 2p⁴

c) 1s² 2s¹ 2p⁶

d) 1s² 2s² 3s²

Question 6: Exceptions to Aufbau Principle

6.1 Which of the following elements is an exception to the Aufbau principle?

a) Chromium (Cr)

b) Silicon (Si)

c) Neon (Ne)

d) Potassium (K)

Question 7: Electron Spin

7.1 When two electrons occupy the same orbital, how do their spins differ?

a) They have the same spin.

b) One has a clockwise spin, and the other has a counterclockwise spin.

c) It depends on the energy level.

d) Electrons cannot occupy the same orbital.

Question 8: Transition Metals

8.1 Why do transition metals often have multiple oxidation states?

a) Due to the Pauli exclusion principle.

b) Due to the Aufbau principle.

c) Due to the presence of unpaired electrons.

d) Due to the filling of d orbitals.

Question 9: Electron Configuration Notation

9.1 Write the electron configuration for chlorine (Cl) using the shorthand notation.

Question 10: Noble Gas Configuration

10.1 What is the noble gas configuration for sulfur (S)?

a) Neon (Ne)

b) Argon (Ar)

c) Krypton (Kr)

d) None of the above.

Answers:

1.1 – a) Electrons fill orbitals with increasing energy, from the lowest to the highest.

2.1 – b) 2

3.1 – d) Electrons will occupy orbitals of the same energy level in a way that maximizes the number of unpaired electrons.

4.1 – d) All of the above.

5.1 – a) 1s² 2s² 2p³

6.1 – a) Chromium (Cr)

7.1 – b) One has a clockwise spin, and the other has a counterclockwise spin.

8.1 – d) Due to the filling of d orbitals.

9.1 – 1s² 2s² 2p⁶ 3s² 3p⁵

10.1 – b) Argon (Ar)

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Question 11: Electron Configuration for Iron (Fe)

11.1 Write the electron configuration for iron (Fe) using the complete notation.

Question 12: Half-Filled and Fully Filled Orbitals

12.1 According to the Pauli exclusion principle and Hund’s rule, why are half-filled and fully filled orbitals considered more stable?

a) They have higher energy.

b) They have lower energy.

c) They have no effect on stability.

d) Stability is unrelated to the filling of orbitals.

Question 13: Anomalous Electron Configurations

13.1 Which element has an anomalous electron configuration, deviating from the expected pattern based on the Aufbau principle?

a) Nitrogen (N)

b) Oxygen (O)

c) Copper (Cu)

d) Fluorine (F)

Question 14: Sublevel Energies

14.1 Arrange the sublevels (s, p, d, f) in increasing order of energy.

a) s < p < d < f

b) f < d < p < s

c) s < d < p < f

d) f < p < d < s

Question 15: Electron Configuration of Iodine (I)

15.1 What is the electron configuration for iodine (I)?

a) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁵

b) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁴

c) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶

d) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s¹ 4d¹¹

Question 16: Electron Configuration Notation for Potassium (K)

16.1 Write the electron configuration for potassium (K) using the noble gas notation.

Question 17: Electron Spin and Magnetic Behavior

17.1 How does the spin of electrons contribute to the magnetic behavior of atoms?

a) Electron spins do not affect magnetic behavior.

b) Opposite spins lead to a net magnetic moment.

c) Identical spins lead to a net magnetic moment.

d) Spin has no relation to magnetic properties.

Question 18: Quantum Numbers

18.1 Which quantum number describes the orientation of an orbital in space?

a) Principal quantum number (n)

b) Azimuthal quantum number (l)

c) Magnetic quantum number (m)

d) Spin quantum number (s)

Question 19: Electron Configuration of Chromium (Cr)

19.1 Chromium (Cr) is an exception to the Aufbau principle. What is its electron configuration?

a) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁵

b) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁵

c) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁴

d) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶

Question 20: Electron Configuration of an Ion

20.1 When an atom becomes a negatively charged ion, how does its electron configuration change, if at all?

a) It remains the same.

b) Electrons are added to the configuration.

c) Electrons are removed from the configuration.

d) The entire configuration is rearranged.

Answers:

11.1 – 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶

12.1 – b) They have lower energy.

13.1 – c) Copper (Cu)

14.1 – a) s < p < d < f

15.1 – c) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶

16.1 – [Ar] 4s¹

17.1 – b) Opposite spins lead to a net magnetic moment.

18.1 – b) Azimuthal quantum number (l)

19.1 – c) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁴

20.1 – b) Electrons are added to the configuration.

Question 21: Electron Configuration and Periodic Table

21.1 How does the electron configuration of elements relate to their position on the periodic table?

a) Elements in the same group have similar electron configurations.

b) Elements in the same period have similar electron configurations.

c) Elements with consecutive atomic numbers have identical electron configurations.

d) Electron configurations have no correlation with the periodic table.

Question 22: Electron Configuration of Noble Gases

22.1 Why are noble gases considered stable, and how does their electron configuration contribute to this stability?

a) They have completely filled orbitals, making them energetically stable.

b) They have the highest number of electrons.

c) They follow the Pauli exclusion principle.

d) They have the highest energy levels.

Question 23: Electron Configuration of Ions

23.1 When an atom becomes a positively charged ion, how does its electron configuration change, if at all?

a) Electrons are added to the configuration.

b) Electrons are removed from the configuration.

c) Protons are added to the configuration.

d) The entire configuration is rearranged.

Question 24: Electron Configuration of Transition Metals

24.1 Why do transition metals exhibit multiple oxidation states?

a) Due to the Aufbau principle.

b) Due to the Pauli exclusion principle.

c) Due to the filling of f orbitals.

d) Due to the incomplete filling of d orbitals.

Question 25: Electron Configuration and Chemical Properties

25.1 How does the electron configuration of an atom influence its chemical properties?

a) It determines the color of the element.

b) It dictates the atomic mass.

c) It governs the element’s reactivity and bonding behavior.

d) It has no impact on chemical properties.

Question 26: Anomalous Electron Configurations in the Periodic Table

26.1 Which element exhibits an anomalous electron configuration, deviating from the expected pattern based on the Aufbau principle, in the second period of the periodic table?

a) Beryllium (Be)

b) Boron (B)

c) Carbon (C)

d) Oxygen (O)

Question 27: Electron Configuration of Calcium (Ca)

27.1 Write the electron configuration for calcium (Ca) using the noble gas notation.

Question 28: Electron Configuration of Sulfide Ion (S²⁻)

28.1 What is the electron configuration of the sulfide ion (S²⁻)?

Question 29: Electron Configuration and Magnetic Behavior

29.1 Why do some substances, when in a magnetic field, exhibit magnetic behavior while others do not, based on electron configuration?

a) Substances with unpaired electrons are attracted to a magnetic field.

b) Substances with paired electrons are attracted to a magnetic field.

c) Electron configuration has no effect on magnetic behavior.

d) All substances are equally attracted to a magnetic field.

Question 30: Electron Configuration of Chromium and Copper

30.1 Chromium and copper are exceptions to the Aufbau principle. What is the electron configuration of chromium (Cr) and copper (Cu)?

a) Chromium: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁵, Copper: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d¹⁰ 4p¹

b) Chromium: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁵, Copper: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d¹⁰ 4p⁶

c) Chromium: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶, Copper: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d¹⁰ 4p⁶

d) Chromium: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d¹⁰ 4p⁶, Copper: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d¹⁰ 4p⁶

Answers:

21.1 – a) Elements in the same group have similar electron configurations.

22.1 – a) They have completely filled orbitals, making them energetically stable.

23.1 – b) Electrons are removed from the configuration.

24.1 – d) Due to the incomplete filling of d orbitals.

25.1 – c) It governs the element’s reactivity and bonding behavior.

26.1 – c) Carbon (C)

27.1 – [Ar] 4s²

28.1 – 1s² 2s² 2p⁶ 3s² 3p⁶

29.1 – a) Substances with unpaired electrons are attracted to a magnetic field.

30.1 – b) Chromium: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁵, Copper: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d¹⁰ 4p⁶

References 

• “Chemistry: The Central Science” by Theodore L. Brown, H. Eugene LeMay, and Bruce E. Bursten
• “General Chemistry” by Raymond Chang and Jason Overby
• “Physical Chemistry” by Peter Atkins and Julio de Paula