Concept explainers
(a)
Interpretation:
The below two-hybrid orbital are orthogonal has to be determined.
Concept Introduction:
Hybrid orbitals are formed by the mixture of atomic orbitals overlapped on each other of different proportions. The four hybrid orbitals of
The two orbitals are orthogonal when there is no interaction between the atomic electrons and another atom.
(a)
Explanation of Solution
The two-hybrid orbitals are normalized and for the orbitals to be orthogonal the integral of the wave function should be equal to zero that is the value of I is equal to zero.
For the orbitals,
Substitute
The integral value of product of different orbitals that are hybridized is zero, that is expressed as follows:
Further, integral value of product of different orbitals that are hybridized is zero and it is as follows:
Equation (2) can be modified as follows:
Substitute 1 for
Since the value of I is zero, therefore the two-hybrid orbitals that are
(b)
Interpretation:
The hybrid orbitals those are orthogonal to below hybrid orbitals have to be determined.
Concept Introduction:
Refer to part (a).
(b)
Explanation of Solution
For the hybrid orbitals
The other two hybrid orbitals are normalized and orthogonal so the integral of the wave function should be equal to zero that is value of I is equal to zero.
For the orbitals,
Substitute
The integral value of product of different orbitals that are hybridized is zero, that is expressed as follows:
Further, integral value of product of different orbitals that are hybridized is zero and it is as follows:
Equation (5) can be modified as follows:
Substitute 1 for
Since the value of I is zero, therefore the two-hybrid orbitals that are
For the hybrid orbitals
The other two hybrid orbitals are normalized and orthogonal so the integral of the wave function should be equal to zero that is value of I is equal to zero.
For the orbitals,
Substitute
The integral value of product of different orbitals that are hybridized is zero, that is expressed as follows:
Further, integral value of product of different orbitals that are hybridized is zero and it is as follows:
Equation (8) can be modified as follows:
Substitute 1 for
Since, the value of I is zero, therefore the two-hybrid orbitals that are
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Chapter 2 Solutions
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