Bonding in the BH3 molecule is covalent and can be described by sp2 hybrid orbitals of the form Show that two hybrid orbitals φa andφb are orthogonal.
Bonding in the BH3 molecule is covalent and can be described by sp2 hybrid orbitals of the form Show that two hybrid orbitals φa andφb are orthogonal.
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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Bonding in the BH3 molecule is covalent and can be described by sp2 hybrid orbitals of
the form
Show that two hybrid orbitals φa andφb are orthogonal.
![### Molecular Orbital Expressions
#### Orbital \( \phi_a \)
\[
\phi_a = \sqrt{\frac{1}{3}} (2s) + \sqrt{\frac{2}{3}} (2p_x)
\]
#### Orbital \( \phi_b \)
\[
\phi_b = \sqrt{\frac{1}{3}} (2s) - \sqrt{\frac{1}{6}} (2p_x) + \sqrt{\frac{1}{2}} (2p_y)
\]
#### Orbital \( \phi_c \)
\[
\phi_c = ?
\]
These expressions represent molecular orbitals, which are combinations of atomic orbitals used to describe the wave-like behavior of electrons in a molecule. The coefficients (such as \(\sqrt{\frac{1}{3}}\), \(\sqrt{\frac{2}{3}}\), etc.) reflect the contribution of each atomic orbital (e.g., \(2s\), \(2p_x\), \(2p_y\)) to the molecular orbital. In the expressions, the \(2s\) and \(2p_x\), \(2p_y\) are atomic orbitals from an atom, likely involved in bonding.
Understanding these molecular orbitals helps in explaining the geometry, bonding properties, and other characteristics of molecules. The question mark under \(\phi_c\) suggests exploring or deriving this particular orbital expression further.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc5a50dc1-17fe-4f06-9b54-35228343592d%2F45ca2a0b-09b3-4dac-beb2-2a9eba4f3a25%2Fh4konq9_processed.png&w=3840&q=75)
Transcribed Image Text:### Molecular Orbital Expressions
#### Orbital \( \phi_a \)
\[
\phi_a = \sqrt{\frac{1}{3}} (2s) + \sqrt{\frac{2}{3}} (2p_x)
\]
#### Orbital \( \phi_b \)
\[
\phi_b = \sqrt{\frac{1}{3}} (2s) - \sqrt{\frac{1}{6}} (2p_x) + \sqrt{\frac{1}{2}} (2p_y)
\]
#### Orbital \( \phi_c \)
\[
\phi_c = ?
\]
These expressions represent molecular orbitals, which are combinations of atomic orbitals used to describe the wave-like behavior of electrons in a molecule. The coefficients (such as \(\sqrt{\frac{1}{3}}\), \(\sqrt{\frac{2}{3}}\), etc.) reflect the contribution of each atomic orbital (e.g., \(2s\), \(2p_x\), \(2p_y\)) to the molecular orbital. In the expressions, the \(2s\) and \(2p_x\), \(2p_y\) are atomic orbitals from an atom, likely involved in bonding.
Understanding these molecular orbitals helps in explaining the geometry, bonding properties, and other characteristics of molecules. The question mark under \(\phi_c\) suggests exploring or deriving this particular orbital expression further.
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