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 13.89E
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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 1st orbital and 2nd orbital are shown below in which z-axis is considered as internuclear axis where ψ1 and ψ2 are wavefunction for the 1st and 2nd 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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