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construct wavefunction for the sp hybrid orbitals

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter13: Introduction To Symmetry In Quantum Mechanics

Section: Chapter Questions

Problem 13.75E

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Question

construct wavefunction for the sp hybrid orbitals

Expert Solution

Step 1

In sp-hybridization, two sp-orbitals are involved. Equation for the 1^st orbital and 2^nd orbital are shown below in which z-axis is considered as internuclear axis where ψ₁ and ψ₂ are wavefunction for the 1^st and 2^nd sp-orbital. Also, a₁ and a₂ are the coefficient for the s-orbital in ψ₁ and ψ₂ respectively and λ₁ and λ₂ are the coefficient for the p-orbital in ψ₁ and ψ₂ respectively.

Step 2

Since the s-orbital is equally distributed due to its spherical shape. Thus, a₁ and a₂ are equal to each other and the number of hybrid orbital is two.

Step 3

Under normalized condition, the sum of square of the coefficient of the wave function is 1

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