Solving for sp Hybrid Orbital: \Psi_{sp1}

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To find the other sp hybrid orbital given \Psi_{sp1} = 3\Psi_{2s} + 4\Psi_{2pz}, one must utilize the orthonormal relationships between the orbitals. The key is to ensure that the new hybrid orbital, \Psi_{sp2}, is orthogonal to \Psi_{sp1}. This typically involves applying the Gram-Schmidt process to construct \Psi_{sp2} from the existing orbitals while maintaining orthonormality. Understanding the coefficients and their contributions to the hybridization is crucial for solving the problem. The discussion emphasizes the need for a clear approach to hybrid orbital calculations.
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Homework Statement



Find the other sp hybrid orbital given \Psi_{sp1} = 3\Psi_{2s} + 4\Psi_{2pz} using the orthonormal relationships.


I do not know how to start the problem. if someone could help get me pointed in the right direction or help me through it I would greatly appreciate it : )
 
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If anyone could help, I would greatly appreciate it.
 
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