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# Bond Length

Atoms are not stable because of the presence of unpaired electrons. They become more stable by forming molecules. Molecules that are more stable can be with similar atoms or different atoms.

Stability is inversely related to energy that is if the molecule is more stable it has less energy and more at rest. Formation of molecules involves bond formation. Formation of stable bonds, the energies involved is explained by molecular orbital theory proposed by Hund and Mullikan. In this topic we will be discussing various aspects of these theories and how they explain various bond formation.

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## Bond Length Table

The distance between the nuclei of the two bonded atoms is called the bond distance. The bond distance can be obtained by adding the atomic radii of the bonded atoms. Covalent radius of an atom is considered the atomic radius of an atom.

 Atom Covalent radius in Å Atom Covalent radius in Å H 0.28 F 0.64 C 0.77 Cl 0.99 N 0.70 Br 1.14 P 1.10 I 1.33 O 0.66 S 1.04

C = 0.67
C ≡ 0.61
N = 0.63
N ≡ 0.55

## Carbon Carbon Bond Length

Carbon shows two different bond lengths when forming covalent bond between another atom of carbon and when it forms a bond with atom of other element. Generally the bond is much stronger when it is formed between same atoms due to the balance of electronegativities.

Carbon atom undergoes hybridization. Its electronic configuration is 1s2,2s1 and 2px1,2py1,2pz1. Carbon forms three types of bonds- single, double and triple bonds. In single bond all the 4 hybridized electrons participate and form 4 head on ‘$\sigma$’bonds and it is called sp3 hybridization.

In double bond formation there will be 3 ‘$\sigma$’bonds and one lateral ‘$pi$’ bond and the hybridization is called sp2 hybridization. In the triple bond formation there will be 2 ‘$\sigma$’bonds and 2 ‘$\pi$’ bonds and is called sp hybridization. The bond lengths of these bonds differ. Triple bond is shorter than the double which is in turn shorter than the single bond.

The values of covalent radii are given in the table shown above. The bond lengths are double the covalent radius and are as given below.

C - C1.54 Å
C = C → 1.34 Å
C ≡ C → 1.22 Å

## Hydrogen Bond Length

Hydrogen atom with its lone electron forms a covalent bond with another atom of hydrogen to stabilize itself as a molecule H2. The bond length is O.56 Å.

## CO Bond Length

The atoms of carbon and oxygen are bonded together by a triple bond in the formation of carbon monoxide (:C ≡ O:)The covalent radius of triple bonded carbon atom is 0.61 and the covalent radius of oxygen atom is 0.66. Thus, the bond length is 0.61+ 0.66 = 1.27Å.

## HCl Bond Length

Hydrogen atom has a single electron and chlorine has 7 electrons in their valence shells. Both hydrogen and chlorine atoms share the electrons and become a stable molecule of HCl.

The bond formed in this union is a single covalent bond. The covalent radius of hydrogen atom is 0.28Å and that of chlorine atom is 0.99Å.