Note on Bonding forces and energies

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Bonding forces and energies

When two isolated atoms are brought together then two types of force comes into play. Attractive force (\(F_A\)) between apposite nature of charge in atoms and repulsive force (\(F_R\)) between same nature of charge . The net force between two atoms is given by,

$$F_N=F_A+F_R\dotsm(1)$$If the magnitude of attractive force and repulsive force becomes equal then the net force between atoms is zero i.e.

For,\(|F_A|=|F_R| \Rightarrow F_N=0 \dotsm(2)\)

If net force in a molecule of a system becomes zero then states of equilibrium exists. The center of two atoms will remains separated by equilibrium separation.

If \(r<r_\circ \Rightarrow F_N=0\), repulsive net force

If \(r>r_\circ \Rightarrow F_N=0\), attractive net force

Fig: Bonding force and energies
Fig: Bonding force and energies(

For many atoms the equilibrium separation is almost o.3 nm (i.e. 3\( A^\circ\)).

In the terms of energy, the force between two atoms is related as,


$$dU=F dr$$

$$U_N=\int F dr$$

$$U_N=\int F_A dr + \int F_R dR$$

$$U_N=U_A+U_R \dotsm(3)$$Where\(U_A\) & \(U_R\) represents attractive and repulsive energy for two isolated atoms.

The bonding energy between two atoms corresponds to energy of the molecule of system at equilibrium separation and is represented by \(U_\circ\) or \(E_\circ\) at \(r= r_\circ\). This energy is the amount of total energy required to completely dissociate to atoms from equilibrium separation. The force between two atoms is responsible for the formation of molecule and materials. The three primary types of bonds in solids are :-

  • Ionic bonding
  • Covalent bonding
  • Metallic bonding
  1. Ionic bonding

In ionic bonding, there is a force between positive ion i.e. cation formed due to the transfer of valence electrons from one atom to another atom and anion negatively charge particle formed due to gain of electron. The nature of the force is electrostatic ( coulomb force ).

For example, The force between \(Na^+\) &\( cl^-\) is ionic bonding.

In terms of energy, the total energy of a molecule in ionic bonding is given by


$$E=\frac{-A}{R}+\frac{B}{R^n} \dotsm (4)$$Here, negative sign indicate the force is attractive amd positive sign indicate the some part of force repulsive and A & B are constant.


  1. Ionic bond is non-directional. The magnitude of bond is equal in all direction.
  2. The attractive force in ionic bond is coloumbic bond.
  3. The material having ionic bonds are hard and brittle.
  4. In the absence of polar solvent ionic compounds are electrically and thermally insulative.
  5. The range of bonding energy is between 3 to 8 ev per atom or 600 to 1500 KJ per mole Example:Nacl,Mgo and some ceramic material.
  6. Ionic compounds are crystalline solid.

2.Covalent bonding

The simplest covalent compound is \(H_2\) gas.

Fig: Covalent bond
Fig: Covalent bond

In generally, the covalent bond is formed between nonmetallic elements in periodic table. The covalent bond is formed due to mutual sharing of electrons. It can also be described as the overlapping of orbital from different atoms.

  1. The covalent bonds are highly directional. It is formed in the direction of maximum overlap of orbitals.
  2. If N be the number of valence electrons in an atom then he atom can be covalently bonded with maximum number of 8-N atoms.

For example: In the case of carbon atom total number of valence electrons (N)=4. So, carbon atom almost be covalently bonded with 8-N=4 atoms.

  1. The strength of covalent bond may be very strong as in diamond. Which is very hard and has very high melting point (greater than \(3550^\circ c\)).
  2. The strength of covalent bond may be very weak as in Bismuth which melts at \(270^\circ c\).
  3. Some of the polythene molecules are covalently bonded as shown in figure

Fig: polythene structure
Fig: polythene structure

  1. Some of the covalent compounds covalently bonded by forming polar covalent bond and the dipole moment of the molecule is non-zero. This indicates covalent compounds have some degree of ionic character. The percentage ionic character of a bond between two atoms A and B is approximately by the expression,

% ionic character =\(\biggl[1-e^\frac{(X_A-X_B)^2}{4}\biggr]\times 100\)%

Where, \(X_A\) and \(X_B\) represents the electronegativity of elements A and B.

  1. Some of the covalent compounds are non conductive lattice both in solid and in molten stage.

Example: Diamond, Boron nitride, Quartz, silicon dioxid.


Callister, W.D and D.G Rethwisch. Material Science and Engineering. 2nd. New Delhi: Wiley India, 2014.

Lindsay, S.M. Introduction of Nanoscience . New York : Oxford University Press, 2010.

Patton, W.J. Materials in industry . New Delhi : Prentice hall of India, 1975.

Poole, C.P. and F.J. Owens. Introduction To Nanotechnology. New Delhi: Wiley India , 2006.

Raghavan, V. Material Science and Engineering. 4th . New Delhi: Pretence-Hall of India, 2003.

Tiley, R.J.D. Understanding solids: The science of Materials. Engalnd : John wiley & Sons , 2004.

1. \(F_N=F_A+F_R\)

2.\(|F_A|=|F_R| \Rightarrow F_N=0\)

3.If \(r<r_\circ \Rightarrow F_N=0\), repulsive net force

If \(r>r_\circ \Rightarrow F_N=0\), attractive net force

4.\(U_N=U_A+U_R \)


  • Ionic bonding
  • Covalent bonding
  • Metallic bonding



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