construct wavefunction for the sp hybrid orbitals

Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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construct wavefunction for the sp hybrid orbitals

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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.

Chemistry homework question answer, step 1, image 1

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.

Chemistry homework question answer, step 2, image 1

Step 3

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

Chemistry homework question answer, step 3, image 1

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