What principle explains the arrangement of electrons that gives atoms their stability and magnetic properties? Why do electrons prefer to occupy separate orbitals before pairing up in an atom? This happens because of Hund's rule of maximum multiplicity. Hund's rule is a fundamental concept of atomic structure.
The concept of chemical bonding explains how the atoms are combined to form molecules. Atoms need to achieve a stable electronic configuration by filling their outermost shells. To achieve this stable electronic configuration, the arrangement of electrons is guided by several rules, and Hund's rule is one of them. Hund's rule states that the electrons are filled in the orbitals of the same energy levels with the parallel spin before pairing up. By doing this, the electron-electron repulsion is minimized and the atom is stabilized.
The Aufbau principle tells us that the lowest energy orbitals will get filled up by electrons first. Thereafter, the electrons move on to energetically higher orbitals. The problem with this rule is that it does not tell about the order in which they will be filled in three 2p orbitals and five 3d orbitals, consequently. Hund's Rule of Maximum Multiplicity depicts the perfect order of electrons filled up in energetically higher orbitals with higher principal number,s such as 2,3,4,........ so on.. It states that for a particular electronic configuration, the term with maximum multiplicity is of the lowest energy. By this rule, pairing of electrons in p, ,d and f orbitals cannot occur until each orbital of a given subshell contains one electron each or becomes singly occupied.
Hund's rule states that:
1. For a particular electronic configuration, the electron having the maximum spin multiplicity has the lowest energy. The multiplicity can be depicted as ( 2S+1), where S represents the total spin angular momentum of the electrons.
2. For a particular multiplicity, the term with the maximum value of total orbital angular momentum quantum numbers (L) occupies the lowest energy.
3. In an atom having the outermost subshell half-filled or less, for a particular term, the level with the lowest value of the total angular momentum quantum number (J) lies in the lowest energy. If the outermost shell is more than half-filled, the level with the highest value of J is the lowest in energy.
Where, total angular momentum quantum number, J = L + S
Hund's rule of maximum multiplicity was discovered by Friedrich Hund in the year 1925. Hund's principle states that, for a particular electronic configuration, the greatest value of spin multiplicity has the lowest energy term. It says if two or more than two orbitals having the same amount of energy are unoccupied then the electrons will start occupying them individually before they get paired up during filling up. This statement depends on the observation of atomic spectra, which is helpful in predicting the ground state of a molecule or an atom with one or more open electronic shells.
The electrons enter into an empty orbital before they get paired up. While considering the 1st statement, there comes a problem. The electrons repel each other as they are negatively charged. Hence, the electrons will not share orbitals to reduce repulsion. But when we consider the 2nd statement, the spins of unpaired electrons in singly occupied orbitals are the same. The spin of initial electrons at the sub-level decides what the spin of the upcoming electrons will be.
For example, a nitrogen atom’s electronic configuration would be 1s22s22p3. The same orbital will be occupied by the two 2s electrons, although different orbitals will be occupied by the three 2p electrons in accordance with Hund’s rule.
Let's consider carbon as an example.
The electronic configuration for carbon atoms: 1s22s22p2:
Here, the two 2s electrons will occupy the same orbital, whereas the two 2p electrons will be in different orbitals (and aligned in the same direction) in accordance with Hund's rule. Consider also the electronic configuration of oxygen. Oxygen has 8 electrons.
The electronic configuration can be written as 1s22s22p4.
The first two electrons will be paired up in the 1s orbital; the next two electrons will be paired up in the 2s orbital. The remaining 4 electrons must be placed in the 2p orbitals. According to Hund’s rule, all orbitals will be singly occupied before being doubly occupied. Therefore, two p orbitals get one electron and one will have two electrons. Hund's rule also stipulates that all of the unpaired electrons must have the same spin. In keeping with convention, the unpaired electrons are drawn as "spin-up".
In spectroscopy and in quantum chemistry, the multiplicity of an energy level can be calculated by using 2S+1, where S indicates the total spin angular momentum. States of electrons with multiplicity 1, 2, 3, 4, and 5 are respectively called singlets, doublets, triplets, quartets, and quintets.
According to the spin multiplicity rule, for a given electron configuration, the lowest energy term is the one with the greatest value of spin multiplicity. This indicates that if two or more orbitals of equal energy are available, electrons will occupy them singly before filling them in pairs.
Hund's rule of maximum multiplicity is a rule that is based on the observation of atomic spectra. This observation is used to predict the electronic configuration of the ground state of an atom or molecule with one or more open electronic shells. For example, from boron through neon, the electron filling order of the 2p orbitals follows Hund's Rule of maximum multiplicity. It has wide applications in atomic chemistry to predict the electronic configuration and spin of an electron, quantum chemistry, spectroscopy, etc.
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NCERT Solutions for Class 11 Chemistry Chapter 2 Structure of Atom |
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NCERT notes Class 11 Chemistry Chapter 2 Structure of Atom |
Example.1 The 71st electron of an element X with an atomic number of 71 enters into the orbital:
1)6p
2) (correct)5d
3)4f
4)6s
Solution
The 71st electron will having an atomic number 71, will enter 5d.
Hence, the answer is option (2).
Example.2 Which law indicates the pairing of electrons in the same orbital?
1)Newton’s first law
2) (correct)Hund’s rule
3)Aufbau principle
4)Pauli exclusion principle
Solution
Hund’s rule states that “pairing of electrons in the orbitals belonging to the same subshell (p, d or f) does not take place until each orbital belonging to that subshell has got one electron each. It is singly occupied”.
Hence, the answer is option (2).
Example. 3 Nitrogen has the electronic configuration 1s2,2s2,2px1,2py1,2pz1 and not 1s2,2s2,2px2,2py1,2pz0 which is determined by
1)Aufbau's Principle
2)Pauli's exclusion principle
3) (correct)Hund's rule
4)Uncertainty Principle
Solution
The above is determined by Hund's rule of maximum multiplicity which says that pairing will not start until and unless all the degenerate orbitals are singly occupied first.
Hence, the answer is option (3).
Example.4 Which of these orbitals has the highest penetration effect?
1) (correct)1s
2)2p
3)3d
4)4s
Solution
Penetration effect of electron -
Due to the different shapes and orientations of different orbital, the penetration effect decreases from 1s to f.
n(s)>n(p)>n(d)>n(f)
Hence, the answer is option (1).
Also check-
hund's rule is called the rule of maximum multiplicity because out of the various possible electronic configurations, only that configuration is correct for which the total spin value is maximum.
Every orbital of the same energy must have at least one electron which has identical spin before you deposit two in the same orbital.
The 1st part of the hund’s rule states that, for a particular electronic configuration, the electron having maximum spin multiplicity has the lowest energy. The multiplicity can be depicted as ( 2S+1), where S represents total spin angular momentum of the electrons.
The orbitals of the subshell will be singly occupied with electrons initially with parallel spin before pairing up occurs.
The nickname of the 1st part of the hund’s rule is spin-spin interaction.
If Hund's rule is not applied the number of singly occupied orbitals or unpaired electrons will decrease gradually. Total number of unpaired electrons is 5, if Hund's rule is followed. Hence, there will be only one electron unpaired if this rule is violated. Hund’s rule is not applicable for NO molecule.
Hund's rule is called maximum multiplicity because out of the various possible electronic configurations, only that configuration is correct for which the total spin value is maximum.
Spin multiplicity indicates the total number of maximum orientations of spin angular momentum corresponding to the spin quantum number.
If Hund's rule is not obeyed, the electron will get paired more easily without all the d orbital getting parallelly occupied.
Hund's rule guides the arrangement of electrons in an atom's orbitals. It ensures that electrons fill orbitals of equal energy singly and with parallel spins before pairing up, which affects the overall electron configuration.
Spin multiplicity is the number of possible orientations of the total spin in a molecule or atom. Hund's rule maximizes spin multiplicity by promoting unpaired electrons, which leads to greater stability in many atoms.
Parallel spins refer to electrons in different orbitals of the same energy level having the same spin direction (either all up or all down). This arrangement is favored by Hund's rule as it minimizes electron-electron repulsion.
Electrons follow Hund's rule to minimize repulsion between them. By occupying separate orbitals, they can stay farther apart, reducing electrostatic repulsion and lowering the overall energy of the atom.
Hund's rule generally leads to more stable atomic configurations. By maximizing the number of unpaired electrons, it reduces electron-electron repulsion and often results in lower overall energy states for atoms.
Hund's rule promotes the alignment of electron spins in the same direction (parallel) when occupying orbitals of equal energy. This maximizes the total spin of the atom, which is often associated with greater stability.
Hund's rule favors high-spin configurations in free atoms. In complexes, the competition between Hund's rule and the crystal field splitting determines whether a high-spin (following Hund's rule) or low-spin (pairing electrons) configuration is adopted.
Hund's rule affects the number and arrangement of unpaired electrons in an atom's outermost shell. This directly influences an element's valence and reactivity, as unpaired electrons are often available for bonding.
While Hund's rule deals with electron spin alignment, spin-orbit coupling involves the interaction between an electron's spin and its orbital angular momentum. In heavier atoms, spin-orbit coupling can sometimes overcome the effects predicted by Hund's rule.
Atomic term symbols describe the angular momentum state of an atom. Hund's rule helps determine the ground state term symbol by maximizing the total spin (S) and then the total orbital angular momentum (L), which are key components of term symbols.
Hund's rule is a principle in quantum chemistry that states electrons in an atom will occupy orbitals of equal energy individually before pairing up. This maximizes the total spin and minimizes electron repulsion.
While both deal with electron arrangement, the Pauli exclusion principle states that no two electrons in an atom can have the same four quantum numbers. Hund's rule, on the other hand, dictates how electrons of the same energy level are distributed across orbitals.
Hund's rule is crucial for understanding atomic structure as it explains the distribution of electrons in orbitals, which affects an atom's chemical and physical properties, including its reactivity, magnetic behavior, and spectroscopic characteristics.
While the Aufbau principle determines the order in which orbitals are filled, Hund's rule dictates how electrons are distributed within orbitals of the same energy level. Together, they guide the complete electron configuration of atoms.
For nitrogen, Hund's rule results in three unpaired electrons in the 2p orbitals. The electron configuration is 1s² 2s² 2p³, with each 2p orbital containing one electron with parallel spins, maximizing the total spin.
Hund's rule is particularly important for transition metals as it explains their tendency to have unpaired electrons in d-orbitals. This results in their unique magnetic and spectroscopic properties.
While Hund's rule is generally reliable, there are exceptions, particularly in excited states or in some complex molecules. In these cases, other factors like orbital hybridization or molecular geometry may override Hund's rule.
Hund's rule promotes unpaired electrons, which contribute to paramagnetism in atoms. Atoms with more unpaired electrons (following Hund's rule) tend to be more strongly paramagnetic.
Hund's rule influences chemical bonding by affecting the number and arrangement of unpaired electrons in atoms. This impacts an atom's ability to form covalent bonds and determines its valence and reactivity.
Hund's rule affects the electronic structure of atoms, which in turn influences their spectroscopic properties. The arrangement of electrons according to Hund's rule determines the possible electronic transitions, affecting absorption and emission spectra.
Exchange energy is the quantum mechanical effect that favors electrons with parallel spins. Hund's rule maximizes this exchange energy by promoting unpaired electrons with parallel spins, contributing to the stability of the atom.
While Hund's rule primarily applies to atomic orbitals, it indirectly affects molecular orbital formation. The electron configurations determined by Hund's rule in individual atoms influence how these atoms combine to form molecular orbitals.
While Hund's rule doesn't directly predict color, it influences the number of unpaired electrons in transition metal ions. This affects the energy of d-d transitions, which are responsible for many of the colors observed in transition metal complexes.
Hund's rule promotes unpaired electrons with parallel spins, which is crucial for ferromagnetism. Materials with many unpaired electrons aligned by Hund's rule are more likely to exhibit ferromagnetic properties.
While Hund's rule is most commonly applied to ground states, it can also influence excited states. However, in excited states, other factors may become more significant, sometimes leading to configurations that don't strictly follow Hund's rule.
Hund's rule indirectly affects electron affinity. Atoms with half-filled or fully filled subshells (often a result of following Hund's rule) tend to have lower electron affinities, as adding an electron would disrupt this stable configuration.
Hund's rule contributes to periodic trends by affecting electron configurations. This influences trends in properties like atomic size, ionization energy, and magnetic behavior across the periodic table.
Hund's rule contributes to the extra stability observed in atoms with half-filled or fully-filled subshells. This is due to the maximized exchange energy in half-filled shells and the symmetry in fully-filled shells, both of which lower the overall energy.
In computational chemistry, Hund's rule is important for accurately predicting electronic structures and properties of atoms and molecules. Many computational methods incorporate Hund's rule to ensure correct electron configurations in calculations.
Hund's rule maximizes the number of unpaired electrons in an atom, which directly affects its magnetic moment. The more unpaired electrons (with parallel spins) an atom has, the higher its magnetic moment will be.
Hund's rule is related to electron correlation, which describes the interaction between electrons. By promoting configurations with unpaired electrons, Hund's rule minimizes electron-electron repulsion, which is a form of electron correlation.
Hund's rule helps predict the ground state configuration of atoms, which is crucial for understanding atomic spectra. The transitions between states that follow Hund's rule and excited states give rise to the characteristic spectral lines of elements.
While Hund's rule doesn't directly address electron shielding, it affects the distribution of electrons in orbitals. This distribution influences the effective nuclear charge experienced by outer electrons, which is a key aspect of electron shielding.
Hund's rule influences the number of unpaired electrons in transition metal ions, which affects their ability to form coordination compounds. The electron configuration determined by Hund's rule impacts the geometry, magnetic properties, and color of these compounds.
The spin-only magnetic moment is calculated based on the number of unpaired electrons, which is often determined by Hund's rule. This concept is particularly useful for predicting the magnetic properties of many transition metal complexes.
Hund's rule can help explain the relative stability of some radical species. Radicals with unpaired electrons distributed according to Hund's rule may have lower energy and greater stability compared to those that violate the rule.
While Hund's rule primarily deals with electron distribution in atomic orbitals, it can influence hybridization. The initial electron configuration determined by Hund's rule may be altered during hybridization to achieve lower energy molecular configurations.
Hund's rule helps determine the ground state electron configuration of atoms, which is crucial for understanding the photoelectric effect. The energy required to remove an electron (work function) is related to how the electrons are arranged according to Hund's rule.
Hund's rule affects electron distribution, which indirectly influences atomic size. Atoms with more unpaired electrons (following Hund's rule) may have slightly larger radii due to increased electron-electron repulsion.
In quantum chemistry calculations, Hund's rule is often used as a starting point for determining electron configurations. It helps in constructing initial wavefunctions and is crucial for accurate predictions of atomic and molecular properties.
In carbon, Hund's rule leads to two unpaired electrons in the 2p orbitals. This configuration (1s² 2s² 2p² with two unpaired 2p electrons) is more stable than alternatives with paired electrons in the 2p orbital.
An orbital diagram shows electron distribution using boxes (orbitals) and arrows (electrons). To illustrate Hund's rule, draw orbitals of equal energy side by side and fill them with single electrons (up arrows) before adding any down arrows for electron pairs.
In lanthanides, Hund's rule applies to the filling of 4f orbitals. It predicts that these orbitals will be filled with one electron each before any pairing occurs, leading to many lanthanides having multiple unpaired electrons and strong paramagnetic properties.
For transition metal ions, Hund's rule dictates that electrons fill the d-orbitals singly with parallel spins before pairing. This often results in partially filled d-subshells with unpaired electrons, explaining many of the unique properties of transition metal compounds.
When forming anions, atoms gain electrons. Hund's rule still applies to these added electrons, influencing how they are distributed in the available orbitals and affecting the overall electronic structure and properties of the anion.
In oxygen, Hund's rule leads to two unpaired electrons in the 2p orbitals. The electron configuration is 1s² 2s² 2p⁴, with four electrons in the 2p orbitals arranged as two pairs and two unpaired electrons with parallel spins.
While Hund's rule primarily applies to ground states, understanding it is crucial for comprehending electron promotion. Excited states often involve configurations that deviate from Hund's rule, highlighting the energy difference between ground and excited states.
Chromium is a notable example where Hund's rule leads to an unusual configuration. Instead of 3d⁴ 4s², one 4s electron is promoted to the 3d orbital, resulting in a 3d⁵ 4s¹ configuration. This maximizes the number of unpaired electrons, following Hund's rule.
Hund's rule and crystal field theory both influence electron distribution in transition metal complexes. While Hund's rule favors unpaired electrons, strong crystal fields can overcome this preference, leading to paired electrons and low-spin complexes.
Hund's rule is fundamental to understanding how electrons occupy atomic orbitals, which in turn forms the basis for molecular orbital theory. It helps explain the electronic structure of atoms and how these atoms combine to form molecules with specific properties.
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