Filling of Electrons in Orbitals

Filing of Electrons in Orbitals: The representation of electrons in various shells, subshells, and orbitals is known as electronic configuration. The arrangement of electrons is of great importance in chemistry. In chemistry, electron configurations can be utilised to justify the chemical properties of elements. It’s also used to interpret atomic spectra, a technique for determining the energy of light emitted by elements and compounds.

The filling of electrons is governed by certain rules or principles, which help us to understand the arrangement of electrons in the atom. We will look at how electrons are filled in various shells, subshells, and orbitals in this article.

Aufbau Principle

The electrons in the ground state of an atom tend to occupy the accessible orbitals in increasing order of energy, with the lower energy orbitals being filled first. This is referred to as the ‘building up principle’ or the Aufbau Principle. As a result, lower energy orbitals are better seats for electrons, and better seats are filled first. The energy level system of orbitals is shown in Fig., and this order can be easily recalled.

The following is the increasing order of energy of several orbitals:

\(1{\text{s}} < 2{\text{s}} < 2{\text{p}} < 3{\text{s}} < 3{\text{p}} < 4{\text{s}} < 3{\text{d}} < 4{\text{p}} < 5{\text{s}} \ldots \)

The sum of the principle quantum number \((\text {n})\) and the azimuthal quantum number \((\text {a})\) determines the energy of an orbital \((\text {l})\). This is called the \((\text {n+l})\) rule. This regulation is divided into two parts: 

(a) Orbitals with a lower \(({\text{n}} + {\text{l}})\) value have less energy than orbitals with a greater \(({\text{n}} + {\text{I}})\) value.

(b) When the \(({\text{n}} + {\text{l}})\) values of two orbitals are equal, the orbital with the lower \(\text {n}\) value has the lower energy. Let’s compare the \(({\text{n}} + {\text{l}})\) values for \(3\text {d}\) and \(4\text {s}\) orbitals, for example.

For \(3\text {d}\) orbital \(\text {n} = 3, \text {l} = 2\) and \(\text {n} + \text {l} = 5\) and for \(4\text {s}\) orbital \(\text {n} = 4, \text {l} = 0\) and \(\text {n} + \text {l} = 4\).

As a result, the 4s orbital fills before the \(3\text {d}\) orbital. Similarly, the \(({\text{n}} + {\text{l}})\) values for \(4\text {p}\) and \(5\text {s}\) orbitals are \((4 + 1)\) and \((5 + 0)\), respectively. In this scenario, the \(4\text {p}\) orbital has a lower \(\text {n}\) value. Hence it has less energy than the \(5\text {d}\) orbital and is filled first.

Because the latter has more energy than the former, \(4\text {s}\) orbitals (belonging to a lower shell, i.e., third) would be filled before \(3\text {d}\) orbitals (belonging to a higher shell, i.e., second).

Pauli’s Exclusion Principle

Wolfgang Pauli proposed an inventive principle that governs values to an electron’s four quantum numbers. The name “exclusion principle” comes from the fact that it limits the values of electrons in an atom. It goes like this: No two electrons in the same atom can have the same set of four quantum numbers. Even if two electrons have the same \({\text{n}},\,{\text{l}}\), and \(\text {m}\) values, their \(\text {s}\) values must differ. As a result, every electron in an atom has a different total energy than every other electron.

So, there can be as many electrons in a shell as there are feasible quantum number arrangements. The table below shows electron arrangements utilising the allowable quantum numbers \({\text{n}},\,{\text{l}},\,{\text{m}}\), and \(\text {s}\). Let us calculate the maximum number of electrons that an orbital can hold. We’ve seen that the initial shell \((\text {n} = 1)\) only contains one orbital, \(1\text {s}\). According to Pauli’s exclusion principle, quantum numbers can only be arranged in two ways.

As a result, an orbital can only hold a maximum of two electrons, and they must spin in opposite directions. Consider the second shell \((\text {n} = 2)\), which has four orbitals: one s orbital \((\text {l} = 0)\) and three p orbitals \((\text {l} = 1)\), resulting in the following possible number of electrons with distinct quantum numbers:

In the second shell, the total number of electrons that may be accommodated is \(2 + 6 = 8\). It may also be demonstrated that the maximum number of electrons in the third and fourth shells is \(18\) and \(32\), respectively. The \(\text {s}\) sublevel can have up to two electrons, the \(\text {p}\) sublevel up to six, the \(\text {d}\) sublevel up to ten, and the \(\text {f}\) sublevel up to fourteen.

Each sublevel can only hold twice as many orbitals as there are available at that level. The exclusion principle of Pauli is extremely useful in determining the maximum number of electrons that may be accommodated in any shell.

Hund’s Rule of Maximum Multiplicity

As we move from one element to the next on the periodic table, we see that one electron is added to the next atom each time. What should happen to the arriving electron? The quantum numbers that can be assigned to the electron in accordance with Pauli’s exclusion principle–prohibiting an orbital from accommodating two electrons with the same set of quantum numbers–provide the solution.

Hund proposed another empirical rule based on magnetic measurements, which similarly aid in determining the electronic configuration of elements. This rule is known as Hund’s Rule of Maximum Multiplicity. It says that electrons are dispersed throughout the orbitals of a subshell in such a way that the maximum number of unpaired electrons and electrons with the same spin direction is obtained.

As a result, before beginning to the couple, the orbitals available at a subshell are first filled individually. The order of electron filling in the orbitals of the \(\text {n} = 1\) and \(\text {n} = 2\) shells is depicted in the diagram below. The orbitals are shown by circles, and the numbers typed in them reflect the sequence of filling for the first ten electrons.

Filling of Electrons in Orbitals

Following rules have to be kept in mind while filling the electrons in orbitals:

Rule 1: Each electron shell can only accommodate \(2 \text {n}^{2}\) electrons, where \(\text {n}\) denotes the shell number.

Rule 2: These electrons are placed in the \(\mathrm{s}, \mathrm{p}, \mathrm{d}\), and \(\text {f}\) orbitals, with the maximum number of electrons in each type of orbital specified by its electron-holding capacity (for \(\text {s}=2, \text {p}=6, \text {d}=10\), and \(\text {f}=14\))

Rule 3: In the ground state of an atom, electrons prefer to fill accessible orbitals in increasing order of energy, with the lowest energy orbitals being filled first. This is referred to as the ‘building up principle’ or the Aufbau Principle.

Rule 4: Each orbital can only have one or two electrons. Pauli’s exclusion principle states that two electrons can only occupy the same orbital if their spins are opposing.

Rule 5: When numerous degenerate orbitals (orbitals of equivalent energy) are available, electrons prefer to occupy different orbitals rather than being coupled in the same orbital. The spins of such electrons tend to be the same (Hund’s rule).

An orbital is commonly shown by a horizontal line, a circle, or a square, whereas an electron is represented by an arrow over it. The spin is indicated by the direction of the arrow, with an upward arrow signifying a clockwise spin and a downward arrow denoting an anticlockwise spin. When a subshell has many orbitals (degenerate orbitals), they are represented by an equal number of horizontal lines at the same energy level. Now we’ll go over the electron configurations of the first ten elements.

(a) Hydrogen and Helium

These have one and two electrons in the \(1{\text{s}}\) orbital, respectively, while the others are unoccupied. The lone electron in hydrogen occupies the \(1{\text{s}}\) orbital and the second electron in helium occupies the \(1{\text{s}}\) orbital as well because it can accommodate another electron with the opposite spin.

(b) Lithium and Beryllium

There are three and four electrons in each of these. Lithium’s third electron enters the \(2{\text{s}}\) orbital, while Beryllium’s fourth electron enters the same orbital but with the opposite spin orientation.

c) Boron and Carbon

Each of these atoms has five and six electrons. The fifth electron of boron would go into one of the \(2{\text{p}}\) orbitals, say \(2{{\text{p}}_{\text{x}}}\)_, because the \(1{\text{s}}\) and \(2{\text{s}}\) orbitals are completely filled with four electrons. Instead of travelling to the \(2{{\text{p}}_{\text{z}}}\) orbital, the sixth electron in carbon would prefer to be accommodated in another vacant \(2{\text{p}}\) orbital, say \(\left( {2{{\text{p}}_{\text{y}}}} \right)\). The spins of the two unpaired electrons must be identical, as shown.

(d) Nitrogen and Oxygen

These atoms each have seven and eight electrons. After six electrons have been accommodated in the manner described above, a vacant \(2{{\text{p}}_{\text{z}}}\) orbital remains, which will be the seat of the seventh electron with the same spin orientation. As seen here, the eighth electron of the following element, oxygen, will pair up with the \(2{{\text{p}}_{\text{x}}}\) electron and possesses an antiparallel spin.

(e) Fluorine and Neon

These atoms each have nine and ten electrons, which are used to fill the remaining \(2\text {p}\) orbitals, as shown in Fig.

Summary

1. The filling of electrons is governed by certain rules or principles, which help us to understand the arrangement of electrons in the atom.
2. According to Aufbau principle, the electrons in the ground state of an atom tend to occupy the accessible orbitals in increasing order of energy, with the lower energy orbitals being filled first.
3. According to Pauli’s exclusion principle, no two electrons in the same atom can have the same set of four quantum numbers.
4. According to Hund’s rule of maximum multiplicity, electrons are dispersed throughout the orbitals of a subshell in such a way that the maximum number of unpaired electrons and electrons with the same spin direction is obtained.

FAQs on Filling of Electrons in Orbitals

Q.1. What is Aufbau Principle?
Ans: According to the Aufbau principle, the electrons in the ground state of an atom tend to occupy the accessible orbitals in increasing order of energy, with the lower energy orbitals being filled first. This is referred to as the ‘building up principle’ or the Aufbau Principle. As a result, lower energy orbitals are better seats for electrons, and better seats are filled first. The following is the increasing order of energy of several orbitals:
\(1{\text{s}} < 2{\text{s}} < 2{\text{p}} < 3{\text{s}} < 3{\text{p}} < 4{\text{s}} < 3{\text{d}} < 4{\text{p}} < 5{\text{s}} \ldots \)

Q.2. What is Pauli’s exclusion principle?
Ans: The name “exclusion principle” comes from the fact that it limits the values of electrons in an atom. It goes like this: No two electrons in the same atom can have the same set of four quantum numbers. Even if two electrons have the same \({\text{n}},\,{\text{l}}\), and \(\text {m}\) values, their \(\text {s}\) values must be different. As a result, every electron in an atom has a different total energy than every other electron, and so there can be as many electrons in a shell as there are feasible quantum number arrangements.

Q.3. Describe Hund’s rule of maximum multiplicity.
Ans: It says that electrons are dispersed throughout the orbitals of a subshell in such a way that the maximum number of unpaired electrons and electrons with the same spin direction is obtained.

Q.4.Discuss the filling of electrons in boron and carbon?
Ans: Each of these atoms has five and six electrons. The fifth electron of boron would go into one of the \(2{\text{p}}\) orbitals, say \(2{{\text{p}}_{\text{x}}}\)_, because the \(1{\text{s}}\) and \(2{\text{s}}\) orbitals are completely filled with four electrons. Instead of travelling to the \(2{{\text{p}}_{\text{z}}}\) orbital, the sixth electron in carbon would prefer to be accommodated in another vacant \(2{\text{p}}\) orbital, say \(\left( {2{{\text{p}}_{\text{y}}}} \right)\). The spins of the two unpaired electrons must be identical, as shown.

Q.5. What is the (n + l) rule?
Ans: The sum of the primary quantum number \(\left( {\text{n}}  \right)\) and the azimuthal quantum number \(\left( {\text{a}}  \right)\) determines the energy of an orbital \(\left( {\text{l}}  \right)\). This is called the \(({\text{n}} + {\text{l}})\) rule. This regulation is divided into two parts: 
(a) Orbitals with a lower \(({\text{n}} + {\text{l}})\) value have less energy than orbitals with a greater \(({\text{n}} + {\text{l}})\) value.
(b) When the \(({\text{n}} + {\text{l}})\) values of two orbitals are equal, the orbital with the lower \(\text {n}\) value has the lower energy.

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