The mixing of one s – orbital and one p – orbital of the same atom of nearly same energy to form a set of diagonally arranged two identical hybrid orbitals of equivalent energy is called sp hybridization. These hybrid orbitals are arranged in a linear manner around central atom and are at an angle of 180^o to one another.

Formation of BeF₂ Molecule:

Ground State of Beryllium Atom:

Atomic number of beryllium is 4. Its configuration in ground state is 1s², 2s², 2p⁰.

Beryllium atom in ground state:

Excited state of Beryllium Atom:

During combination with fluorine, the 2s electron pair is split up and one electron is promoted to empty 2p_x orbital. This condition is called excited state of beryllium. In excited state one electron of 2s migrates to 2p orbital forming 2 – half filled orbitals.
Beryllium atom in excited state:

Hybridization of Beryllium Atom:

One 2s orbital and one 2p orbitals of beryllium mix up forming two hybrid orbitals of equivalent energy. These two new equivalent orbitals are called sp hybrid orbitals. They are identical in all respect.

Beryllium atom in excited state:

Angle and Geometry :

Two sp hybridized orbitals formed, repel each other and These hybrid orbitals are arranged in a linear manner around central beryllium atom and are at an angle of 180^o to one another. Each sp hybrid orbital contain unpaired electron. In each sp hybrid orbital, one of the lobes is bigger because of more concentration of electron density. Only bigger lobe is involved in bond formation.

Thus in BeF₂ molecule has linear or diagonal structure with boron atom at the centre and two fluorine atoms at the either sides of beryllium. F-Be-F bond angle is 180^o.

Bond:

Two sp hybrid orbitals of boron atom having one unpaired electron each overlap separately with 1p orbitals of two fluorine atoms along the axis forming two covalent bonds (sigma bonds). The bonds between beryllium and fluorine are sp- p overlap. Thus F – Be — F bond angles are 180^o. Molecule is diagonal or linear. Both Be-F bonds in beryllium difluoride are of equal strength.

Diagram:

Type and Geometry of Beryllium difluoride Molecule:

BeF₂ Is linear molecule, while H₂O is angular molecule.

In BeF₂ molecule, beryllium undergoes sp hybridization and achieve electronic configuration 1s², 2s¹2p_x¹ in excited state. During formation of beryllium difluoride boron undergoes sp hybridization One 2s orbital and one 2p orbital of beryllium mix up forming two hybrid orbitals of equivalent energy. These two new equivalent orbitals are called sp hybrid orbitals. They are identical in all respect. Two sp hybridized orbitals formed, repel each other and they are directed diagonally opposite in space.  Angle between them is 180⁰. Two sp hybrid orbitals of boron atom having one unpaired electron each overlap separately with 1p orbitals of two fluorine atoms along the axis forming two covalent bonds (sigma bonds). Thus BeF₂ Is linear molecule.

In water, the oxygen atom is sp³ hybridized. Two hybrid orbitals have paired electrons (lone pair) and they are non – bonding orbitals.  Other two orbitals are half – filled (singly occupied) and they are bonding orbitals. These hybridized orbitals are in four directions of four corners of tetrahedron. Four sp³ hybridized orbitals formed, repel each other and they should be directed towards the four corners of a regular  tetrahedron and  Angle between them should be 109.5⁰.  The non bonding electron repel each other strongly and occupy more space than the electron pairs involved in bonding.  The force of repulsion between electron pair decreases in following order. lone pair – lone pair > lone pair- bond pair >  bond pair – bond pair. Hence the bond angle between two lone pairs i.e. H-O-H angle decreases from109.5⁰ to 104.5⁰. Thus water molecule is angular.

Formation of acetylene (C₂H ₂) Molecule:

Ground State of Carbon Atom:
Atomic number of carbon is 6. Its configuration in ground state is 1s², 2s², 2p² i.e. 1s² 2s², 2p_x¹ 2p_y¹ 2p_z⁰

Carbon atom in ground state:

Excited state of Carbon Atom:

During combination with hydrogen, the 2s electron pair is split up and one electron is promoted to empty 2p_z orbital. This condition is called excited state of carbon. In excited state one electron of 2s migrates to 2p orbital forming 4 – half filled orbitals.
Carbon atom in excited state:

Hybridization:

In acetylene there is sp hybridization. One 2s orbital and one 2p orbitals of carbon mix up forming two hybrid orbitals of equivalent energy. These two new equivalent orbitals are called sp hybrid orbitals. They are identical in all respect. Two ‘p’ orbitals of each carbon atom remains unhybridized.

Angle and Geometry:

Two sp hybridized orbitals formed, repel each other and These hybrid orbitals are arranged along x- axis in a linear manner around central carbon atom and are at an angle of 180⁰ to one another. The unhybridized p_y and p_z orbital remain perpendicular to hybrid orbitals along y-axis and z- axis ,
mutually perpendicular. Each sp hybrid orbital and unhybrid orbitals contain unpaired electron. In each sp hybrid orbital, one of the lobes is bigger because of more concentration of electron density. Only bigger lobe is involved in bond formation.

As all the four atoms in C₂H₂ molecule being in the same line, the molecule is diagonal or linear. H-C-C bond angle is 180^o.

Formation of Bonds:

1. Sigma Bond Formation :

A covalent bond formed by collinear or coaxial or in the line of internuclear axis. Overlapping of orbitals is known as sigma bond. One Sp hybrid orbital of one carbon atom overlaps with One hybrid orbital of other carbon atom by head on collision forming sigma bond. One (Sp- Sp ) overlap. Remaining one hybrid orbitals of each carbon atom overlap with ‘s’ orbital of two hydrogen atoms separately forming two sigma bonds. (2 C – H). Two (Sp– s)overlaps. Both C-H bond in Acetylene are of equal strength. Thus there are Three sigma bonds. Sigma bonds are stronger.

2) Formation of pi Bond :
The covalent bond formed by collateral or sidewise overlapping is called pi bond. The unhybridized 2 p_x and 2 p_z orbitals of each carbon atom being perpendicular to each other and to the plane of H-C-C-H axis overlap laterally with one another to form two week pi bond between two
carbon atoms by two p – p overlap. (one 2 p_y -2 p_y )and (one 2p_z-2 p_z) . Thus two (p-p) -overlaps.

In ethylene molecule there are 3 sigma bonds and 2 pi bonds. There is a triple bond between carbon and carbon consisting one sigma and two pi bonds.

Diagram:

Type and Geometry of Acetylene Molecule:

There is only one pi bond in ethylene molecule but there are two pi bonds in the acetylene molecule:

In ethylene molecule carbon atom shows sp² hybridization in excited state. The resulting three hybrid orbitals form two C-H bonds and One pi bond of sigma type. Thus each carbon atom is left with unhybridized p_z orbitals with lobes above and below the plane of hybridized orbitals. These two unhybridized orbitals overlap each other laterally and form a single pi bond between two carbon atoms.

In acetylene molecule carbon atom shows sp hybridization in excited state. The resulting two orbitals are linear and form one C-H bond and one C-C bond of sigma type. Thus each carbon is left with two unhybridized p_y and p_z orbitals, which are mutually perpendicular to H-C-C-H axis. These unhybridized orbitals overlap each other laterally and form two pi bonds between two carbon atoms.

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Mixing of one ‘s’ orbital and two ‘p’ – orbitals of nearly same energy forming set of trigonally arranged three identical orbitals of equal energy is known as sp² hybridization.

Geometry sp² Hybridization:

The hybrid orbitals are arranged around the central atom in a plane at an angle of 120° to one another. When these three orbitals overlap with appropriate orbitals of three other atoms, three bonds are formed and the resulting molecule has a trigonal planar structure. Each bond angle is 120°.

Diagram:

Formation of Boron Trifluoride Molecules:

Ground State of Boron Atom:

Atomic number of boron is 5. Its configuration in ground state is 1s², 2s², 2p¹

Boron atom in ground state:

Excited State of Boron Atom:

During combination with fluorine, the 2s electron pair is split up and one electron is promoted to empty 2p_y orbital. This condition is called excited state of boron. In excited state one electron of 2s migrates to 2p orbital forming 3 – half filled orbitals.

Boron atom in excited state:

Hybridization of Boron Atom:
One 2s orbital and two 2p orbitals of boron mix up forming three hybrid orbitals of equivalent energy. These three new equivalent orbitals are called sp² hybrid orbitals. They are identical in all respect

Boron atom in hybridized state:

Angle and Geometry:

• Three sp² hybridized orbitals formed, repel each other and they are directed towards the three corners of an equilateral triangle. The angle between them is 120°.
• Each sp² hybrid orbital contains an unpaired electron.
• In each sp² hybrid orbital, one of the lobes is bigger because of more concentration of electron density. Only bigger lobe is involved in bond formation.
• Thus BF₃ molecule has a trigonal planar structure with boron atom at the centre and three fluorine atoms at the four corners of equilateral triangle. F-B-F bond angle is 120°.

Bond Formation:

Three sp² hybrid orbitals of boron atom having one unpaired electron each overlap separately with 2p orbitals of three fluorine atoms along the axis forming three covalent bonds (sigma). Thus in BF₃ molecule has a planar structure with a boron atom at the centre and three fluorine atoms at the three corners of an equilateral triangle. F-B-F bond angle is 120°.

Bond:

• There are three sigma bonds..
• The bonds between boron and fluorine are sp²– p.
• Thus F – B — F bond angles are 120°. The molecule is trigonal planar.
• All B-F bonds in boron trifluoride are of equal strength.

Diagram:

Type and Geometry of Boron trifluoride Molecule:


The BF₃ molecule has a planar structure while NH₃ molecule has a pyramidal structure.
During formation of boron trifluoride, boron undergoes sp² hybridization and achieve the electronic configuration 1s², 2s¹2p_x¹2p_y¹. In the excited state, one 2s orbital and two 2p orbitals of boron mix up forming three hybrid orbitals of equivalent energy. These three new equivalent orbitals are called sp² hybrid orbitals. They are identical in all respect. Three sp² hybridized orbitals formed, repel each other and they are directed towards the three corners of an equilateral triangle (in one plane). Angle between them is 120^o. Three sp² hybrid orbitals of boron atom having one unpaired electron each overlap separately with 1p orbitals of three fluorine atoms along the axis forming three covalent bonds (sigma bonds). Thus boron trifluoride has triangular planar structure.

During formation of ammonia nitrogen undergoes sp³ hybridization. One 2s orbital and three 2p orbitals of mix up forming four hybrid orbitals of equivalent energy. These four new equivalent orbitals are called sp³ hybrid orbitals. They are identical in all respect and they should be directed towards the four corners of a regular tetrahedron and Angle between them should be 109.5^o. Three hybridized orbitals contain unpaired electron. The fourth hybridized orbital has lone pair of electron. The three half filled (containing unpaired electron) sp³ hybrid orbitals of nitrogen overlap axially with three half filled 1s orbitals of three hydrogen atoms separately to form three covalent N-H bonds (sigma bonds). The fourth hybrid orbital containing lone pair of electron remains non bonded. The non bonding electron repel each other strongly and occupy more space than the electron pairs involved in bonding. The force of repulsion between lone pair- bond pair is greater than bond pair – bond pair. Hence the
bond angle i.e. H-N-H angle decreases from109.5^o to 107^o.

Formation of Ethylene Molecule:

Ground State of Carbon Atom:
Atomic number of carbon is 6. Its configuration in ground state is 1s², 2s², 2p² i.e. 1s² 2s², 2p_x¹ 2p_y¹ 2p_z⁰

Carbon atom in ground state:

Excited state of Carbon Atom:

During combination with hydrogen, the 2s electron pair is split up and one electron is promoted to empty 2p_z orbital. This condition is called excited state of carbon. In excited state one electron of 2s migrates to 2p orbital forming 4 – half filled orbitals.
Carbon atom in excited state:

Hybridization of Carbon Atom:

In ethylene there is sp² hybridization. One 2s orbital and two 2p orbitals of carbon mix up forming three hybrid orbitals of equivalent energy. These three new equivalent orbitals are called sp² hybrid orbitals. They are identical in all respect. One ‘p’ orbital of each carbon atom remains unhybridized

Carbon atom in hybridized state:

Angle and Geometry:

Three sp² hybridized orbitals formed, repel each other and they are directed in a plane towards the three corners of an equilateral triangle. Angle between them is 120^o. The unhybridized p_z orbital remain perpendicular to this plane. Each sp² hybrid orbital contain unpaired electron. In each sp² hybrid orbital, one of the lobes is bigger because of more concentration of electron density. Only bigger lobe is involved in bond formation.

As all the six atoms in C₂H₆ molecule being in the same plane, the molecule is planar. H-C-H bond angle is 120^o. H-C-C bond angle is 120^o.

Bonds Formation:
1. Sigma Bond Formation :

A covalent bond formed by collinear or coaxial or in the line of internuclear axis. Overlapping of orbitals is known as sigma bond. One Sp² hybrid orbital of one carbon atom overlaps with One hybrid orbital of other carbon atom by head on collision forming sigma bond. One (Sp²– Sp² ) overlap.

Remaining two hybrid orbitals of each carbon atom overlap with ‘s’ orbital of four hydrogen atoms separately forming four sigma bonds. (C – H). Four (Sp²– s) overlaps. All C-H bond in ethylene are of equal strength.

Thus there are five sigma bonds. Sigma bonds are stronger.

2. Formation of pi Bond:

The covalent bond formed by collateral or sidewise overlapping is called pi bond. The unhybridized 2 p_z orbitals of each carbon atom being perpendicular to the plane of four hydrogen atoms and carbon atoms overlap laterally with one another to form a week pi bond between two carbon atoms by p – p overlap. One (p-p) -pi bond. This bond consists of two equal electron cloud one lying above the plane of the atom and other lying below this plane.

Hence, in ethylene molecule there are 5 sigma bonds and 1 pi bond.

Diagram :

Type and Geometry of Ethylene Molecule :

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The mixing of one s-orbital and three p- orbitals of the same atom having nearly the same energy to form four orbitals of equal in all respects and tetrahedrally arranged is known as sp3 hybridization.

Geometry of sp3 Hybridization:

sp³ hybridized orbitals repel each other and they are directed to four corners of a regular tetrahedron. The angle between them is 109.5° and the geometry of the molecule is tetrahedral (non-planar). This type of hybridization is also known as tetrahedral hybridization. The sp³ hybridization is shown pictorially in the figure.

Formation of Methane Molecule ( CH₄ ):

Step -1: Formation of the excited state of a Carbon atom:

The carbon atom in the ground state takes up some energy and goes to the excited state.  In this process, a pair of electrons in 2s orbital splits up and one of the electron from this pair is transferred to empty 2pz orbital.  Thus the excited state has four half-filled orbitals.

Step – 2: Hybridization of Orbitals:

One orbital of 2s and three orbitals of 2p mix up forming four hybrid orbitals of equivalent energy. These four new equivalent orbitals are called sp³ hybrid orbitals. They are identical in all respect.

Angle and Geometry:

Four sp³ hybridized orbitals formed, repel each other and they are directed towards the four corners of a regular tetrahedron.    The Angle between them is 109.5°. Each sp³ hybrid orbital contains one unpaired electron.

In each sp³ hybrid orbital, one of the lobes is bigger because of more concentration of electron density. Only a bigger lobe is involved in bond formation. Due to this maximum overlapping is achieved.

Four sp³ hybrid orbitals of carbon atom having one unpaired electron each overlap separately with 1s orbitals of four hydrogen atom along the axis forming four covalent bonds. Thus in CH₄ molecule has a tetrahedral structure with a carbon atom at the centre and four hydrogens at the four corners of a regular tetrahedron. H-C-H bond angle is 109.5°.

Bonds:

Four sp³ hybrid orbitals of carbon atom having one unpaired electron each overlap separately with 1s orbitals of four hydrogen atom along the axis forming four covalent bonds (sigma bonds). The bonds between carbon and hydrogen are sp³– s. Thus H – C – H bond angles are 109.5°. The molecule is tetrahedral. All C-H bonds in methane are of equal strength.

Type and Geometry of Methane Molecule:

Formation of Ammonia Molecule ( NH₃):

Need of Hybridization in Ammonia Molecule:

In nitrogen atom, there are three half-filled 2p orbitals and the valency should be 3 and it is three. These three ‘p’ orbitals are perpendicular to each other and if they form bonds, the angle between them should be 90°. But the actual angle between bonding orbitals in ammonia is 107°. To explain this difference in the angle the concept of hybridization is required.

Electron Configuration:

The Atomic number of Nitrogen is 7.  Its configuration in ground state is 1s², 2s², 2p³

Hybridization:

In the formation of ammonia one 2s orbital and three 2p orbitals of nitrogen mix up forming four hybrid orbitals of equivalent energy. These four new equivalent orbitals are called sp³ hybrid orbitals. They are identical in all respect. One hybrid orbital has paired electrons (lone pair) and it is nonbonding orbital. The other three orbitals are half-filled and they are bonding orbitals. The nonbonding pair of hybridized orbitals is called as a lone pair. These hybridized orbitals are in the directions of four corners of a regular tetrahedron.

Angle and Geometry:

Four sp³ hybridized orbitals formed, repel each other and they should be directed towards the four corners of a regular tetrahedron and the angle between them should be 109.5°. One hybrid orbital has paired electrons and it is nonbonding orbital. The other three orbitals are half-filled and they are bonding orbitals. But due to greater repulsion exerted by lone pair on bonding orbitals, the angle is reduced to 107°. Thus ammonia has distorted tetrahedral shape.

The three half-filled (containing unpaired electron) sp3 hybrid orbitals of nitrogen overlap axially with three half-filled 1s orbitals of three hydrogen atoms separately to form three covalent N-H bonds Hence geometry is tetrahedral pyramidal in which the nitrogen lies at the centre, three hydrogen atoms form the base and one pair of electrons forms the apex of the pyramid. H-N-H angle is 107°.

Bonds:

The three half-filled (containing unpaired electron) sp3 hybrid orbitals of nitrogen overlap axially with three half-filled 1s orbitals of three hydrogen atoms separately to form three covalent N-H bonds (sigma bonds). The fourth hybrid orbital containing lone pair of the electron remains non bonded. The bonds between Nitrogen and hydrogen are sp3- s. H – N – H bond angles are 107°. All N-H bonds in ammonia are of equal strength.

Type and Geometry:

Formation of Water Molecule:

Need of Hybridization:

In oxygen atom there are two half-filled 2p orbitals and valency should be 2 and it is two.  These three ‘p’ orbitals are perpendicular to each other and if they form bonds, the angle between them should be 90°.  But the actual angle between bonding orbitals in water is 104.5°.  To explain this variation the concept of hybridization is required.

Electron Configuration:

The atomic number of Oxygen is 8.  Its configuration in ground state is 1s², 2s², 2p⁴

Hybridization :

In the formation of water molecule one 2s orbital and three 2p orbitals of Oxygen mix up forming four hybrid orbitals of equivalent energy. These four new equivalent orbitals are called sp³ hybrid orbitals. They are identical in all respect. The two hybrid orbitals have paired electrons and they are non – bonding orbitals.  Other two orbitals are half-filled and they are bonding orbitals. The nonbonding pairs of hybridized orbitals are called lone pairs. These hybridized orbitals are in the directions of four corners of a regular tetrahedron.

Angle and Geometry:

Four sp3hybridised orbitals formed, repel each other and they should be directed towards the four corners of a regular tetrahedron and the angle between them should be 109.5°. But due to greater repulsion exerted by lone pair on bonding orbitals, the angle is reduced to 104.5⁰. Thus water has distorted the tetrahedral shape.

The two half-filled (containing unpaired electron) sp³ hybrid orbitals of oxygen overlap axially with two half-filled 1s orbitals of two hydrogen atoms separately to form three O-H bonds. Thus geometry is angular or V-shaped, in which the oxygen lies at the centre, two hydrogen atoms occupy two corners of the tetrahedron and lone pair of electrons occupy remaining two corners of the tetrahedron. H-O-H angle is 104.5⁰.

Bonds:

The two half-filled (containing unpaired electron) sp3 hybrid orbitals of oxygen overlap axially with two half-filled 1s orbitals of two hydrogen atoms separately to form two O-H bonds (sigma bond).  The remaining two hybrid orbitals containing a lone pair of the electron remains nonbonded.

Type and Geometry:

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In this article, we shall study the concept of hybridization of orbitals. This concept overcomes the limitations of valence bond theory.

Need for Hybridization Concept:

A simple approach based on the overlap of s and p orbitals can be applied to many molecules, but it fails to explain the formation of compounds of Beryllium (Be), Boron (B), and carbon (C). The electronic configurations of Be, B, and C in the ground state are as follows.

The atoms of Beryllium Be (Z = 4)  Electronic configuration is 1s² 2s² (With no unpaired electrons).

The atom of Boron B (Z = 5)   Electronic configuration is 1s² 2s² 2p¹ (With one unpaired electron).

The atom of Carbon C (Z = 6)   Electronic configuration is 1s² 2s² 2p² (With two unpaired electrons).

According to valence bond theory valency of an element depends on a number of unpaired electrons in the orbitals. Thus Beryllium, Boron, and Carbon should be zero-valent, monovalent and divalent respectively.  However, these elements form the compounds having valency 2, 3, and 4 respectively. Valence bond theory fails to explain this phenomenon. This is explained by hybridization.

Valence Bond Theory fails to explain the observed geometry of the molecules of water and ammonia e.g. in the formation of H₂O molecule, the H – O – H bond angle should be 90°. But the measured bond angle is 104.3° and the molecule is V-Shaped. Valence bond theory failed to explain this change. To explain The equivalence of bonds we have to use the concept of a process of mixing and recasting of atomic orbitals. For e.g. all the four C-H bonds in methane molecule are equivalent in terms of strength, energy, etc. It can be explained on the basis of hybridization.

Note: The above paragraphs give limitations of the valence bond theory.

Hybridization:

Mixing and recasting or orbitals of an atom (same atom) with nearly equal energy to form new equivalent orbitals with maximum symmetry and definite orientation in space is called hybridization.

Steps Involved in Hybridization:

Step -1: Formation of excited state:

The atom in the ground state takes up some energy and goes to the excited state.  In this process, usually, a pair of electrons in lower energy orbital is split up and one of the electron from this pair is transferred to some empty slightly higher but almost equal energy orbital.  Thus the excited state has a larger number of half-filled orbitals. This new number of half-filled orbitals decides the number of covalent bonds an atom can form.

Step = 2: Mixing and recasting of atomic orbitals:

The orbitals of nearly the same energy in an excited state now hybridize i.e. unite and redistribute themselves giving hybrid orbitals of the same energy and definite orientation in space. Mixing and recasting or orbitals of an atom(same atom) with nearly equal energy to form new equivalent orbitals with maximum symmetry and definite orientation in space is called hybridization.

One 2-s orbital and three p- orbitals mix together and recast themselves to form new four sp³ hybridized orbitals.

Step – 3: Proper Orientation of the Hybrid Orbitals in Space:

The hybrid orbitals then get arranged in space in such a way to minimize mutual repulsion. Each hybrid orbital is more concentrated on one side of the nucleus. Due to this greater overlap is achieved and a stronger bond is formed.

Thus in carbon, the four hybrid sp3 orbitals arrange themselves at four corners of a tetrahedron to minimize mutual repulsion.

Essential Condition for Hybridization:

The orbitals participating in hybridization should have nearly the same energy. Thus in the formation of methane, the 2s and 2p orbitals of carbon have nearly the same energies, so that the recasting of orbitals is possible.  But hybridization of 2s and 3p is not possible because there is much difference between their energies.

Characteristics or Rules of hybridization:

• Atomic orbitals undergoing hybridization should belong to the same atom or ion.
• Atomic orbitals participating in hybridization should have nearly the same energy. Thus 2s and 2p can hybridize, 3s and 3p can also hybridize, but 2s and 3p cannot.
• The total number of hybrid orbitals formed is equal to the number of atomic orbitals involved in the hybridization process.
• All hybrid orbitals are identical with respect to energy and directional character.
• The hybrid orbitals may differ from one other in their orientations.
• The shape of the hybrid orbitals is different from that of the original atomic orbital.
• Similar to atomic orbitals, each hybrid orbital can have a maximum of two electrons.
• The hybrid orbitals are concentrated in one particular direction to achieve greater overlapping.
• The hybrid orbitals have maximum symmetry and definite orientation in space so that the mutual force of repulsion of electrons is avoided.

Types of Hybridization and Geometry of Molecules:

The hybridization involving s and p orbitals are of the following three types:

• Tetrahedral or sp³ hybridization e.g. CH₄, NH₃, H₂O
• Trigonal or sp² e.g. BF₃, C₂H₄.
• Diagonal or sp hybridization e.g. BeF₂, C₂H₂

Their names indicate the orientation of the orbitals in space and the designation (sp², sp³, etc) indicates the number and types of atomic orbitals involved in hybridization.

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According to Valence Bond Theory, covalent bonds are of two types a) Sigma bond (σ) and b) Pi bond (π)

Sigma bond (σ):

The covalent bond formed as a result of an end to end overlap i.e. head-on collision of atomic orbitals Or A covalent bond formed by collinear or coaxial i.e. in a line of internuclear axis overlapping of an atomic orbital is known as a sigma bond. Example: In hydrogen molecule, there is a sigma bond between two overlapping ‘s’ orbitals.

Formation of Sigma Bond:

A covalent bond formed by collinear or coaxial i.e. in a line of internuclear axis overlapping of an atomic orbital is known as a sigma bond. S orbitals are non-directional hence they can overlap in any side. Thus s-s overlap always forms a sigma bond. In order to form sigma bond p orbitals must lie along the internuclear axis. They are formed by s-s overlap e.g. H-H, s-p overlap e.g. H-F, p-p overlap e.g. F-F

Characteristics of Sigma Bond:

• It is a covalent bond formed by a coaxial overlap of bonding orbitals.
• It is a very strong bond, due to a greater extent of overlapping.
• It is possible between any two orbitals s-s, p-p or s-p and also hybrid orbitals.
• Bond energy is more.

Pi Bond (π):

A covalent bond is formed by lateral or sideway or collateral overlapping of pure orbitals is known as a pi bond. Example: Ethylene has one pz – pz  π bond. Acetylene has two π bonds.

Formation of pi Bond:

A covalent bond is formed by lateral or sideway or collateral overlapping of pure orbitals is known as a pi bond. A pi bond is formed by a lateral overlap of two p orbitals oriented mutually parallel but perpendicular to the internuclear axis.

Characteristics of Pi Bond:

• It is a covalent bond formed by a lateral or sideways overlap of atomic orbitals.
• It is a weak bond due to the lower extent of overlapping.
• It is possible between two ‘p’ orbitals only.
• Bond energy is less.
• It is to be noted that the pi bond is formed when the sigma bond already exists. The formation of only a pi bond is not possible.

Sigma Bond is Stronger Than a pi Bond:

The extent of overlapping of orbitals along the same axes is always greater than the extent of overlapping at an angle. Also, the larger the overlapping of orbitals, the stronger is the covalent bond.

A sigma bond is formed by co-axial overlapping of atomic orbitals. Due to the large overlap of atomic orbitals, the bond involves more evolution of energy than Pi bond. Due to the large overlap of atomic orbitals, the bond involves more evolution of energy than Pi bond. In this bond, the electron density between two nuclei on the internuclear axis is very high.

A pi bond is formed by collateral or sidewise overlapping of atomic orbitals. Due to the less overlap of atomic orbitals, the bond involves less evolution of energy than the sigma bond. In the case of a pi bond, the electron density is higher above and below the internuclear axis and not on the nuclear axis.

Hence the sigma bond in which overlapping of orbitals take place along the same axis is stronger than the pi bond in which overlapping of orbitals takes place at an angle (laterally).

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In this article, we shall study the formation of bonds by overlapping of orbitals and different types of overlaps.

Formation of Hydrogen Molecule on The Basis Of Orbital Overlap:

The electronic configuration of a hydrogen atom is 1s¹. It contains one unpaired electron in its valence shell. Therefore 1s orbital in the hydrogen atom is bonding orbital. When the two hydrogen atoms having valence electrons with opposite spins approach each other, the attractive force dominates the repulsive force between the electrons in the initial stage. Thus, as the distance between two hydrogen atoms decreases the potential energy of the system gradually decreases.

A state of minimum potential energy is reached when the forces of attraction are balanced by the forces of repulsion between two hydrogen atoms. At this point the energy of the system is minimum and the stability is maximum. At this stage orbital of two hydrogen atoms, overlap and spins of electrons are neutralized and a stable covalent bond is formed between hydrogen atoms, forming H₂, molecule. In this case, the overlap of orbitals is maximum. This overlap is called s-s overlap and bond formed are coaxial overlapping of two s orbital is called s-s sigma (σ) bond.

In the formation of a molecule, the release of energy comes from two sources. The neutralization of spin magnetic moments of the two electrons and the accumulation of electron density between two nuclei.

Diagram :

1 S Orbital          1 S Orbital         S-S overlap

Reason: Helium does not form a diatomic molecule:

Helium with atomic number 2 has electron configuration 1s2. Thus helium contains two paired electrons in its 1s orbital. The pairing of electrons in 1s orbital neutralizes the spin magnetic moments of each other. This gives stability to the helium atom. There are no empty orbitals in the first shell for unpairing and promoting these paired electrons to higher energy orbital. Thus helium has no unpaired electron i.e. no bonding orbital. Therefore according to valence bond theory, it cannot form a covalent bond with another helium atom.

Each helium atom has paired electrons in 1s is orbital.  If two such orbitals come close to each other, there is net repulsion between them because repulsive forces are stronger than the attractive forces.  If they do so it increases the potential energy of the system and it becomes unstable.  Thus overlapping of orbitals cannot take place. Therefore helium cannot form a diatomic molecule. It exists as a monoatomic gas.

Types of Overlap of Atomic Orbitals:

The term overlap refers to the overlap of the atomic orbitals of the two approaching atoms as they enter into the bond formation stage. In the case of s and p orbitals, there can be three types of overlap.

s – s orbital overlap ( formation of H₂ molecule):

The mutual overlap between the half-filled s orbitals of two atoms is called s – s overlap and the covalent bond formed is known as sigma (s) bond. e.g. formation of a hydrogen molecule from two hydrogen atoms.

s – orbital is spherical in shape and overlapping takes place to some extent in all directions.  Hence s -s bond is non – directional.

Hydrogen (1s¹) atom has 1s orbital containing a single electron i.e. it is half-filled.  Two such 1s orbitals from the two hydrogen atoms having electrons with opposite spins approach each other, then the potential energy of the system decreases. The two ‘s’ orbitals overlap each other when they acquire minimum potential energy, forming H-H sigma bond or s-s overlap. H-H bond is a nonpolar covalent bond.

As the two orbitals are overlapping such that the overlapped region lies on the line joining the two nuclei of the overlapping orbitals (axial overlapping) bond formed is sigma bond.

Diagram :

1 S Orbital          1 S Orbital         S-S overlap

p – p orbital overlap (Formation of Fluorine F₂ molecule):

The mutual overlap between two half-filled p – orbitals of two atoms is called p – p overlap and the covalent bond formed is known as p – p bond.  If the overlapping takes place along the internuclear axis the bond is called sigma bond and if the overlapping takes place literally the bond is known as pi bond. e.g. formation of fluorine molecule from two fluorine atoms. CI₂, Br₂and I₂ are also formed by p – p overlap.

The atomic number of fluorine is 9. The electronic configuration of the fluorine atom is 1s². 2s². 2p_x², 2p_y², 2p_z¹. Each F atom has one unpaired electron in p – orbital (p_z orbital). When two fluorine atoms each containing unpaired electron with opposite spins approach each other, then the potential energy of the system decreases. The two ‘p’ orbitals overlap each other when they acquire minimum potential energy.

As the two orbitals are overlapping such that the overlapped region lies on the line joining the two nuclei of the overlapping orbitals (axial overlapping) bond formed is sigma bond. As p orbitals are dumbbell-shaped they overlap in a particular direction. Therefore the p-p bond is directional. The back lobe of the overlapping p orbital is distorted and its size is reduced. This is due to the tendency of the electron to remain in the overlapping region.

F-F bond is a non-polar, as shared pair of electrons is attracted by both the atoms.

Diagram :

1 P Orbital                    1 P Orbital                          P-P overlap

s – p orbital overlap (Formation of Hydrogen Fluoride Molecule):

The overlap between the half-filled s – orbital of one atom and the half-filled p – orbital of another atom is called s – p overlap and the covalent bond formed is known as s – p sigma bond. E.g.: Formation of HF molecule, H – X bond in HCI, HBr, and HI are also formed by s-p overlap.

The electronic configuration of a hydrogen atom is 1s1, while that of fluorine atom is 1s2. 2s2. 2px2, 2py2, 2pz1. Thus 1s orbital of a hydrogen atom and the 2p orbital of fluorine atom containing unpaired electron can overlap and the bond formation is possible provided the spin of electrons in overlapping orbitals is opposite. The bond in hydrogen fluoride is a s – p bond. As the two orbitals are overlapping such that the overlapped region lies on the line joining the two nuclei of the overlapping orbitals (axial overlapping) bond formed is sigma bond. The back lobe of the overlapping p orbital is distorted and its size is reduced. This is due to the tendency of the electron to remain in the overlapping region.

Fluorine is more electronegative than hydrogen, hence H-F bond is polar.

Diagram :                                

Reason: H – F bond is polar.

HF molecule is formed by the s-p overlap of orbitals. On Pauling scale, the electronegativity of H is 2.1 and that of F is 4. Thus fluorine is more electronegative than H, the electronic cloud in this bond is displaced more towards fluorine.  In other words, the electron pair shared between the two atoms is attracted more towards fluorine. This gives fluorine atom a partial negative charge (δ -) and hydrogen atom a partial charge   (δ +).

Thus the H – F bond is not purely covalent.  It possesses a partial ionic character and is said to be a polar bond.  The bond has 43% ionic character. H – X bond in HCI, HBr, and HI are also polar since CI, Br and I are more electronegative than H.

Science > Chemistry > Physical Chemistry > Nature of Chemical Bond > Overlapping of Orbitals

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Valence bond theory was proposed by Heitler and London in (1927) and it was extended by Pauling and Slater (1931). It is based on the following concepts.

• The pairing of electrons.
• Neutralization of opposite electron spins.
• Overlapping of orbitals containing unpaired electrons to give a region of common electron density to the combining atoms.

Postulates of Valence Bond Theory:

 Condition of bond formation: 

A covalent bond is formed when the atomic orbital of one atom overlaps the atomic orbital of the other atom. The sharing of electrons takes place due to the overlapping of half-filled orbitals of the outermost shell of the two atoms. Only atomic orbital with unpaired electrons with opposite spin can participate in overlapping or bonding.  They are known as Bonding Orbitals.

Binding force of covalent bond: 

During the overlapping of half-filled orbitals, spins get neutralized and electron density between the two nuclei increases. As a result of this, the force of repulsion between the two nuclei decreases, while the force of attraction between the nucleus of one and the electron of other increases.

Strength of a bond:

Bond is formed when the system attains a stable lowest energy level.  This occurs at a certain minimum equilibrium distance between two nuclei known as bond length. The strength of the covalent bond depends upon the extent of overlapping between two atoms.  Greater the overlap, stronger is the bond. Complete overlapping is not possible as there are repulsive forces between two nuclei.

Number of covalent bonds:

One bonding orbital can form only one covalent bond.  Hence the number of bonding orbitals restricts the number of covalent bonds that can be formed by an atom. The number of unpaired electrons possessed by an atom determines its valency.

Directional nature of covalent bond:

S- orbitals are non-directional but p, d, and f  – orbitals have a particular direction. Due to their directional nature, the geometry of the molecule depends upon the orientation of the overlapping of the orbitals.

Geometry of a Molecule on the Basis of Valence Bond Theory:

A covalent bond is formed when the atomic orbital of one atom overlaps the atomic orbital of the other atom. The bond has maximum electron density in the region of overlap. The line joining the nuclei of two atoms determines the direction of the bond.

‘S’ orbitals are spherical and non – directional, but p, d, f orbitals are directionally oriented and produce overlap in the internuclear axis resulting in a bond formation having s a specific direction. The geometry of molecules and bond angles therein are determined by the directional orientation of orbitals involved in the overlap. The electron pairs in the valence shell of the central atom arrange themselves symmetrically so as to get as far apart as possible due to repulsion between them.

e.g. Methane has tetrahedral geometry, Boron trifluoride has planar geometry while Beryllium difluoride has linear geometry, etc.

Energy Changes in Covalent Bond Formation on the Basis of Valence Bond Theory:

Interactive Force Between Approaching Molecules:

It must be realized that when any two atoms approach close to each other new forces of attraction and repulsion set in.

The forces of attraction are between the nucleus of one atom and the electron of the other and vice – versa. The forces of repulsion are between two nuclei amongst themselves as well as between the electrons of the two atoms amongst themselves.  The force of attraction and repulsion are represented in the figure.

If the net result is attraction i.e. attractive forces are stronger than the repulsive forces the total energy of the system decreases and a chemical bond results.   If the net result is repulsion i.e. the repulsive forces are stronger than attractive forces, the total energy of the system increases and no chemical bonding is not possible.

Variation in Energy of System Due to Approach of Orbitals for Overlapping:

When two Hydrogen atoms with unpaired electrons with parallel spin approach each other, repulsion is greater than attraction and energy of system increases and bonding does not take place. In this case, the energy goes on increasing as inter-nuclear distance starts decreasing.

When two Hydrogen atoms with unpaired electrons with opposite spin approach each other, the attraction is greater than repulsion and energy of system continuously decreases till it becomes minimum at equilibrium distance between the two nuclei. There is overlap and leads to covalent bond formation between two hydrogens.

Formation of Hydrogen Molecule in terms of Decrease of Potential Energy:

The way in which the potential energy of the system changes as two hydrogen atoms having electrons with opposite spins approaches each other to form a covalent bond is represented in the potential energy curve. Graphical representation of the change in potential energy as a function of internuclear distance is known as the Potential Energy Curve. The electronic configuration o the hydrogen atom is 1s¹.  It contains one unpaired electron in its valence shell.

Explanation of Curve – 1

• State A: When two hydrogen atoms are far apart from each other, then the potential energy of one atom is independent of the other.  This potential energy is taken arbitrarily as zero
• State B: As the two hydrogen atoms having electrons with opposite spins approach each other, the electrons of one atom begin to feel the attractive forces of the nucleus of the other atom.  The attractive force dominates the repulsive force between the electrons.  Thus, as the distance between two hydrogen atoms decreases the potential energy of the system gradually decreases.
• State C: A state of minimum potential energy is reached when the forces of attraction are balanced by the forces of repulsion between two hydrogen atoms.  At this stage orbital of two hydrogen atoms, overlap and spins of electrons are neutralized and a stable covalent bond is formed between hydrogen atoms, forming a hydrogen molecule. In this case, the overlap of orbitals is maximum. The minimum equilibrium distance between the two hydrogen nuclei at this stage is called bond length which is 74 picometer. The amount of energy released at this stage is called bond energy and it is equal to 431.8 kJ/mole.8.
• State D:  When two hydrogen atoms are forced to come still closer, then the potential energy of the system shows a sharp rise.  This is due to the increases of repulsive forces between the two nuclei at such small inter-nuclear distance and hence bond formed becomes unstable.

Explanation of Curve – 2

• State E: It two hydrogen atoms having electrons with parallel spins approach each other, potential energy of system increases and no bond is formed between the two hydrogen atoms.

Science > Chemistry > Physical Chemistry > Nature of Chemical Bond > Valence Bond Theory

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Mendel performed his experiments with garden pea plant, which has traits or alleles having complete dominance and hence the laws of inheritance were proved. Other scientists performed their experiments on different plants and animals and found deviations to Mendelian ratios. Depending upon these experiments and observations, a different pattern of inheritance called gene interactions was discovered. This study is known as Post – Mendelian genetics or Neo-Mendelian genetics. In this article, we shall study the concept of polygenic inheritance.

Polygenic Inheritance or Quantitative Inheritance:

These characters are determined by two or more gene pairs and they have an additive or cumulative effect. These genes are called cumulative genes or polygenes or multiple factors. Polygenes are two or more different pairs of nonallelic genes, present on different loci, which influence a single phenotypic character and have an additive or cumulative effect. They are also called quantitative genes or cumulative genes or multiple factors.

A single phenotypic character governed by more than one pair of genes is called polygenic character or quantitative character. Polygenic characters or quantitative character show continuous variation. Galton (1883) predicted that in human population characters such as height, skin colour and intelligence show continuous variations in expression and not only two contrasting expressions.

In cumulative or polygenic inheritance each gene has a certain amount of effect. So more is the number of dominant genes, the greater is the expression of the character. It is generally believed that during evolution there was a duplication of chromosome or chromosome parts. This resulted in multiple copies of the same gene. Note that Mendel studied qualitative inheritance, where complete dominance is observed.

Polygenic Inheritance in Wheat Kernel Colour:

Swedish geneticist H. Nilsson-Ehle discovered polygenic inheritance. He crossed a red kernelled variety of wheat with white kernelled variety. In F₁ generation all plants have grains with intermediate colour between red and white. In F₂ generation five different phenotypic expressions (the darkest red, medium red, intermediate red, light red, white) appeared in the ratio 1:4:6:4:1. Nilson Ehle suggested that the kernel colour in wheat is controlled by two pairs of genes, Aa and Bb. Genes A and B determine the red colour. a and b which do not produce red colour pigment and their expression is a white colour of the kernel.

Polygenic Inheritance in Human Skin Colour:

The presence of melanin pigment is responsible for the colour of the skin in a human being. Each dominant gene is responsible for the synthesis of a fixed amount of melanin. The amount of melanin synthesized is directly proportional to the number of dominant genes.

The amount of melanin developing in persons is determined by three pars of genes A, B, C. These are present on three different loci and each dominant gene is responsible for the synthesis of a fixed amount of melanin. A genotype of a pure black parent in which melanin is produced is the highest is AABBCC, while that of pure white also called albino no melanin is formed is aabbcc.

Mulattoes i.e. F₁ offspring produce (2³ = 8) different types of gametes. Let us consider mulatto intermediate whose genotype is AaBbCc. By doing cross among two mulatto intermediate we get (2⁶ = 64) combinations in F₂ generation. But there only 7 phenotypes due to a cumulative effect of each dominant gene.

When we analyze all possible combinations and plot the probability graph by taking frequency distribution of colour, the number of dominant genes in various shades on the x-axis and the frequency of different shades onthe y-axis. In Polygenic inheritance often we get a bell-shaped curve as shown below.

This means that most people fall in the middle of the phenotypic range, such as skin colour, while very few people are at the extremes, such as pure white or pure dark. At one end of the curve will be individuals who are recessive for all the alleles (for example, aabbcc). They are rare; at the other end will be individuals who are dominant for all the alleles (for example, AABBCC) they are rare. In the middle of the curve will be individuals who have a combination of dominant and recessive alleles (for example, AaBbCc or AaBBcc). The graph also shows that the expression level of the phenotype is dependent on the number of contributive alleles and hence more quantitative.

Other examples are the height of human being, cob length of maize.

Comparative Study of Qualitative and Quantitative Inheritance:

Qualitative Inheritance:

• Qualitative characters are classical Mendelian traits which have two contrasting expressions and are controlled by a single pair of genes. e.g. tall and dwarf pea plants. A qualitative character can be expressed by a single pair of the gene. Hence the traits are called monogenic traits. The inheritance of monogenic traits (monogene) or qualitative characters is called qualitative or monogenic inheritance.
• A qualitative trait is expressed qualitatively, which means that the phenotype falls into different categories. These categories do not necessarily have a certain order.
• Qualitative inheritance was first studied by Mendel.

Characteristics of Qualitative Inheritance:

• A quantitative inheritance or monogenic inheritance deals with the inheritances of qualitative characters which have two contrasting expressions e.g. tall and dwarf pea plants.
• Each character is controlled by a single pair of contrasting alleles.
• There is no intermediate type.
• Each character has two distinct contrasting expressions i.e. they exhibit two distinct phenotypes.
• The degree of expression remains the same whether the character is controlled by one or both the dominant genes.
• Single effect genes are seen.
• It is not influenced by environmental factors.
• It shows a discontinuous pattern of inheritance.
• Individuals of F1 generation resembles the dominant parent.
• Individuals of the F2 generation are in the ratio 3:1. An intermediate expression is absent.
• It concerns with individual matings and their progeny.
• Analysis of this inheritance can be done by counting and finding ratios.
• Examples: Inheritances of qualitative characters like height, seed coat and seed colour of the pea plant.

Quantitative Inheritance:

A quantitative inheritance or polygenic inheritance deals with the inheritances of quantitative characters like height, weight, skin colour, intelligence, etc in the human population and exhibits continuous variation. Few characters in plants like height, the size, shape, number of seeds and fruits also exhibit quantitative inheritance.

In quantitative inheritance each gene has a certain amount of effect and the more number of dominant genes, the more is the degree of expression of the character. The gradation in the expression of the characters is determined by the number of gene pairs and all the gene pairs have an additive or cumulative effect.

Quantitative or polygenic inheritance was first studied by J. Kolreuter (1760) in case of height in tobacco and F. Galton (1883) in case of height and intelligence in human beings. Nilsson-Ehle (1908) obtained the first experimental proof of polygenic inheritance in case of kernel colour in wheat. The possible origin of polygenic inheritance is due to the duplication of a chromosome or its part, the increase in chromosomes number (Polyploidy) or the mutations producing genes having the similar effect.

Characteristics of Quantitative Inheritance:

• A quantitative inheritance or polygenic inheritance deals with the inheritances of quantitative characters.
• Each character is controlled by more than one pair of nonallelic genes (polygenes)
• In the case of one polygene pair, the number of phenotypes is 3 (1: 2: 1). In the case of two polygene pairs, the number of phenotypes is 5 (1: 4: 6: 4: 1). In the case of three polygene pairs,  the number of phenotypes is 7 (1 : 6: 15: 20: 15: 6: 1). Thus the number of intermediate types increases with the increase in the number of polygenes but the number of parental types remains the same
• Each character has an intergrading range of phenotypes.
• The degree of expression depends on the number of dominant genes.
• Single effect gene cannot be seen.
• It is influenced by environmental factors.
• It shows a continuous pattern of inheritance.
• F1 generation shows intermediate expression between the two parents.
• In F2 generation individuals with intermediate genotype and phenotype are maximum.
• It concerns with a population of organisms consisting of all possible kinds of matings.
• Analysis of this inheritance needs an appropriate statistical method and is complicated.
• Examples: Inheritances of quantitative characters like height, weight, skin colour, intelligence, etc in the human population. Few characters in plants like height, the size, shape, number of seeds and fruits also exhibit quantitative inheritance.

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Mendel performed his experiments with garden pea plant, which has traits or alleles having complete dominance and hence the laws of inheritance were proved. Other scientists performed their experiments on different plants and animals and found deviations to Mendelian ratios. Depending upon these experiments and observations, a different pattern of inheritance called gene interactions was discovered. This study is known as Post – Mendelian genetics or Neo-Mendelian genetics. In this article, we shall study the concept of pleiotropy and its effects.

The phenomenon of controlling more than one character at the same time is called pleiotropy or pleiotropism. Such genes are called pleiotropic genes. These genes produce more than one phenotypic effect which is totally unrelated. The pleiotropic effect is produced by a gene owing to a cascade (succession) of reactions during some metabolic pathway which is influenced by the original gene product and contributes to different phenotypic effects. The ratio is 2:1 instead of 3:1

Examples: In the pea plant, the same gene that affects the colour of the flower also influences the colour of the seed coat and the colour of the leaf axil. The gene that determines the size of the wings in Drosophila also affects its eye colour, the position of dorsal bristles, the shape of the spermatheca, fertility and length of life.

Effects of Pleiotropy in Human Beings:

Phenylketonuria (PKU):

Phenylketonuria also called PKU, is a rare inherited disorder that causes an amino acid called phenylalanine to build up in the body. PKU is caused by a defect in the gene that helps create the enzyme needed to break down phenylalanine.

Phenylketonuria is an autosomal recessive character controlled by a mutant gene present on the 12th chromosome. This mutant gene fails to code for the enzyme phenylalanine hydroxylase (PAH) required for normal metabolism of amino acid phenylalanine to tyrosine. Due to this, there is an accumulation of amino acid phenylalanine in the body fluids such as blood, sweat, and cerebrospinal fluid. An abnormal breakdown product phenyl ketone is found in urine. A higher level of phenylalanine and breakdown product phenyl ketone causes severe brain damage leading to mental retardation.

Symptoms: A musty odor in the breath, skin or urine, caused by too much phenylalanine in the body, neurological problems that may include seizures, skin rashes (eczema), fair skin and blue eyes, because phenylalanine can’t transform into melanin — the pigment responsible for hair and skin tone, abnormally small head (microcephaly), hyperactivity, intellectual disability, delayed development, behavioral, emotional and social problems, psychiatric disorders

Inheritance: For a child to inherit PKU, both the mother and father must have and pass on the defective gene. This pattern of inheritance is called autosomal recessive. If only one parent has the defective gene, there’s no risk of passing PKU to a child, but it’s possible for the child to be a carrier. Most often, PKU is passed to children by two parents who are carriers of the disorder but don’t know about it.

Marfan or Morphan’s Syndrome:

Marfan syndrome is a genetic disorder that affects the body’s connective tissue. Connective tissue holds all the body’s cells, organs and tissue together. It also plays an important role in helping the body grow and develop properly.

It is caused by a pleiotropic gene which is characterized by a slender body, limb elongation, hypermobility in joints, lens dislocation and a tendency to develop heart diseases. Marfan syndrome does not affect intelligence.

Marfan syndrome is caused by a defect in the gene that enables your body to produce a protein that helps give connective tissue its elasticity and strength. Most people with Marfan syndrome inherit the abnormal gene from a parent who has the disorder. In about 25 percent of the people who have the Marfan syndrome, the abnormal gene doesn’t come from either parent. In these cases, a new mutation develops spontaneously.

Sickle Cell Anaemia:

The gene Hb^s (recessive) is responsible for disease sickle cell anaemia. A normal or healthy gene is HbA .which is dominant. Thus disease carrier having heterozygotes HbA / Hbs show signs of mild anaemia as their R.B.C.s become sickle-shaped (half-moon) and their oxygen-carrying capacity decreases. But can live a normal life. But the homozygotes with recessive gene Hbs die of fatal anaemia. A gene which causes death of the bearer is called a lethal gene.  Two carrier parents will produce normal, carriers and sickle cell anemic children in 1:2:1 ratio.

Effect of the Pleiotropy in Mice:

Mice were first used for genetics research by the French biologist Lucien Cuénot in 1902. His breeding experiments showed that three mnemons (genes), allowed the production of one chromogen (pigment) and two distases (enzymes). The combination of the chromogen and one of the enzymes produced either a black or yellow colour in the mice. If there was no chromogen the mouse was albino. He showed mice inherited these coat colours in the ratio 3:1 as predicted by Mendel’s inheritance laws.

In 1905 Cuénot discovered the first lethal genetic mutation in the mouse. Lethal gene in mice causes death at an early stage of development, often before birth. The effect of the lethal gene is illustrated by the inheritance of fur (coat) color in mice,

In mice, yellow fur is dominant over non-yellow fur color. A cross was made between two heterozygous yellow fur mice (Yy and Yy) and F₁ generation was obtained. The cross is supposed to produce offsprings like 1 YY genotype, 2 Yy genotype, and 1 yy genotype.

The dominant homozygous organism with yellow fur color (YY) will never survive. The dominant homozygous organism dies in the embryonic stage because of a lethal combination. Hence the ratio 3:1 ratio changes to 2:1. It is a modified monohybrid ratio. Therefore, all living yellow fur mice are heterozygous(Yy). Here, gene ‘Y’ is recessive in relation to its effect on viability but dominant in relation to fur color.

Lethal Genes:

Sometimes, the pleiotropic gene effect may produce various abnormal phenotypic features which are collectively called syndromes.

If the effects of the pleiotropic gene become the cause of the death of an individual, then the pleiotropic gene is called the lethal gene. The lethal genes cause a great deviation from the normal development of an individual. Hence, that individual does not survive.  As a result of the lethal effect, Mendel’s monohybrid ratio of 3:1 gets modified and changed into 2:1. This lethal gene is seen either in the homozygous dominant condition or homozygous recessive condition.

Science > Biology > Genetic Basis of Inheritance > Pleiotropy

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Mendel performed his experiments with garden pea plant, which has traits or alleles having complete dominance and hence the laws of inheritance were proved. Other scientists performed their experiments on different plants and animals and found deviations to Mendelian ratios. Depending upon these experiments and observations, a different pattern of inheritance called gene interactions was discovered. This study is known as Post – Mendelian genetics or Neo-Mendelian genetics. In this article we shall study the concept of complete dominance, partial dominance, and codominance.

Gene Interactions:

It was observed that the phenotypic expression of a gene can be modified or influenced by the other gene. This phenomenon is called gene interaction. There are two types of gene interactions

Intragenic (Interallelic) Interaction:

It occurs between alleles of the same gene e.g. incomplete dominance, co-dominance, and multiple alleles.

Intergenic (nonallelic) Interaction:

It occurs between the alleles of different genes on the same or different chromosomes. e.g. Pleiotropy, polygeny, epistasis, supplementary and complementary genes.

Neo-mendelian genetics includes interaction between alleles of a gene (interallelic interaction or intragenic interaction) and intergenic interaction or multiple genes inheritance.

Incomplete Dominance or Partial Dominance Or Blending Dominance:

In this case, both the genes of an allelomorphic pair express themselves partially. One gene cannot suppress the expression of other completely. e.g. four o’clock plant, snapdragon (Dog flower or Antirrhinum)

When a cross is made between true-breeding red-flowered plants (RR) and true breeding white-flowered plants (rr), the F1 generation is all pink-flowered (Rr) plants.

When pink-flowered plants of F1 generations are self-pollinated i.e. crossed among themselves, the F2 plants with red (RR), pink (Rr) and white (rr) flowers appear in the ratio 1:2:1. Here the phenotype ratio matches the genotype ratio of a monohybrid cross, but the phenotype ratio had changed from Mendelian ratio 3:1. No allele is dominant but the expression is intermediate between the two.

e.g. Andalusian Fowls (Chickens):

Andalusian fowls occur in three colours: black, white and blue. A cross between pure black (BB) and pure white (bb) produces F1 blue hybrid fowls. The genotype ratio of F1 generation is pure black (BB) : hybrid blue (bb) : Pure white (bb) is 1:2:1.

The phenomenon of incomplete dominance can be explained on the basis of Mendelian segregation. In complete dominance, the recessive factor cannot express, but in incomplete dominance both alleles have equal chance to express, hence we get hybrid intermediate in the F₁ generation.

Characteristics of Incomplete Dominance:

• In this case, both the genes of an allelomorphic pair express themselves partially.
• The expression of the hybrid genotype is intermediate to the phenotypes produced by each of the alleles separately.
• One gene can not suppress the expression of others completely.
• The expressed phenotype is new and no allele has its own effect.
• It is the result of the quantitative effect of alleles.
• The mixing of the phenotype effect of alleles is found.

Co-dominance:

In this case, both the genes of an allelomorphic pair express themselves equally in the F₁ generation. Such alleles express themselves independently even if present together in hybrids are called co-dominant alleles e.g. coat colour of cattle.

When red cattle are crossed with white cattle, the F1 generation has a roan coat colour where black and white patches appear separately. When F₁generation is self-crossed, F₂ Generation shows 4 phenotypes with ratio White: Both white and red: red = 1:2:1 and Genotypic ratio WW:RW: RR = 1:2:1. In F2 generation the phenotype ratio matches the genotype ratio.

Characteristics of Codominance:

• In this case, both the genes of an allelomorphic pair express themselves equally in the F₁ generation.
• Both the alleles express equally.
• The expressed phenotype is the combination of two phenotypes of the two alleles.
• No quantitative effect of alleles is found.
• No mixing of phenotype effect of alleles is found.

Complementary Genes:

In this type of interaction, two separate pairs of genes interact to produce the phenotype in such a way that neither dominant is expressive unless another one is present. Thus the effect of one dominant is expressed if and only if another dominant complement it. These types of genes are called complementary genes. This inheritance was discovered by W. Bateson and R. C. Punnett in sweet pea (Lathyrus odoratus).

When two certain white-flowered varieties of sweet pea are crossed with each other. They produced the F1 plant with red flowers. The F2 generation is obtained by self-pollination of the F1 generation, The ratio of red-flowered plants to white-flowered plants is found to be 9:7, which was different than the dihybrid ratio of 9:3:3:1.

The red colour in the flower of a sweet pea plant is produced by a pigment called anthocyanin. Its formation depends on two independent factors (C and P). Both these factors must be present to produce the pigment.

Multiple Alleles:

More than two alternative forms (alleles) of a gene in a population occupying the same locus on a chromosome or its homologue are known as multiple alleles. Thus the multiple alleles are multiple alternatives of the same gene which influence the same character and produce different expressions in different individuals of a species or population.

e.g. In Drosophila, a large number of multiple alleles are known. One of them is the series of wing abnormally ranging in size from normal wings to no wings.

Characteristics of Multiple Alleles:

• Multiple alleles arise by mutation of the wild type of gene.
• They occupy the same locus on homologous chromosomes.
• They regulate the same character but have a different degree of expression.
• They do not undergo crossing over.
• Only one member of the series of multiple alleles is present in a given chromosome and only two members in an individual.
• In multiple alleles, the wild type of expression is dominant while all other expressions are recessive to the wild type. But there may be complete dominance or codominance.

Blood Groups in Human Beings:

The gene I control ABO blood groups it has three alleles; IA, IB and i. The allele IA and IB produce slightly different types of sugar and allele i does not produce any sugar. The letter I is derived from the word Isoagglutinin (antigen)

As humans are diploid organisms, each person possesses any two of the three I genes. IA and IB are co-dominant and completely dominant on i.

Blood Group of Progeny (Children):

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