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Considering x–axis as the internuclear axis which out of the following will not form a sigma bond and why? (a) 1 s and 1 s (b) 1 s and 2px : (c) 2py and 2py (d) 1s and 2s. 

Sigma bond is always formed between two half-filled atomic orbitals along their internuclear axis.i.e the line joining the centres of the nuclei of two atoms(axial overlapping). 2py and 2py will not form a sigma bond because taking x-axis as the internuclear axis, there will be lateral (sideway) overlap between the two 2pv orbitals forming a  bond.
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Write the important conditions required for the linear combination of atomic orbitals to form molecular orbitals.


The following are the conditions for the linear combination of atomic orbitals:
(i) The combining atomic orbitals should have comparable energies.

(ii) The combining atomic orbitals must have proper orientations (same symmetry) so that they are able to overlap to a considerable extent. For example, assuming 2-axis as molecular (or internuclear axis), allowed the combination of atomic orbitals are 2pz orbital of one atom can combine with 2pz orbital of another atom. On the other hand, 2pz orbital of one atom cannot combine with 2px or 2py orbital of another atom or 2px can not combine with 2py. Similarly, 2s orbital of one atom can combine with 2pz orbital but cannot combine with 2lpx or 2py orbital of another atom because they do not have proper orientation for the overlap.

(iii) The extent of overlapping should be large. Greater the overlap, greater will be the electron density.

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Discuss in brief sp2 hybridization (hybridization in C = C bond). Discuss the molecular orbital structure of ethylene (first member of alkene).
Or
Draw diagrams showing the formation of a double bond between carbon atoms in C2H4.

 


sp2 hybridisation. The electronic configuration of carbon (Z = 6) in the excited state is
.
In this type of hybridization one- s and two P-orbitals of the valence shell of carbon atom take part in hybridization go give three new sp2 hybrid orbitals. These sp2 hybrid orbitals lie in a plane and are directed towards the corners of an equilateral triangle with a carbon atom in the centre. The unhybridized 2p1 orbital lies perpendicular to the three hybridised orbitals.



Representation of sp2 hybridization sp2 hybridization is also known as trigonal hybridisation. Each sp1 hybrid orbital has  s-character and 
The molecular orbital structure of ethylene: In ethene molecule, each carbon atom undergoes sp2 hybridisation. One sp2 hybrid orbital of one carbon atom overlaps axially with one sp2 hybrid orbital of the other carbon atom to form sigma (σ) C - C bond. The other two sp2 hybrid orbitals of each carbon atom overlap axially with its orbital of the hydrogen atom to form sigma (σ) C - H bonds. The unhybridized p-orbitals of the two carbon atoms overlap sidewise with each other to form weak pi () bond. The  bond consists of two  electron clouds which lie above and below the plane of carbon and hydrogen atoms.


(a) Formation of ethylene     (b) Molecular orbital structure molecule of ethylene

Thus, ethylene molecule consists of four sigma C – H bonds, one sigma C - C bond and one  bond between carbon-carbon atom. The bond length of carbon-carbon double bond of ethylene is 134pm (1–34 A).
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Which hybrid orbitals are used by carbon atoms in the following molecules ?
(a) CH3 – CH3
(b) CH3 – CH = CH2
(c) CH3 – CH2 - OH
(d) CH3 - CHO
(e) CH3COOH



Both carbon atoms use sp3 hybrid orbitals. 




Both carbon atoms (C1, C2) use a sp3 hybrid orbital.

(d) CH3CHO


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Write the significance of a plus and minus sign shown in representing the orbitals.


The orbital is the maximum probability of finding an electron around the nucleus. This probability is measured in terms of the wave function. The wave function can be positive or negative values.
Since orbitals are represented by wave functions, therefore a plus sign in an orbital represents a positive wave function and a minus sign represents a negative wave function. Further the wave functions of two 1s atomic orbitals can combine in two different ways:
(i) When both have the same signs.
(ii) When they have different signs.

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