Which of the following linear combinations of atomic orbitals will lead to the formation of molecular orbitals in homonuclear diatomic molecules (internuclear axis in z-direction)?
(1) \( 2p_z \) and \( 2p_x \)
(2) \( 2s \) and \( 2p_x \)
(3) \( 3d_{xy} \) and \( 3d_{x^2-y^2} \)
(4) \( 2s \) and \( 2p_z \)
(5) \( 2p_z \) and \( 3d_{x^2-y^2} \)
Which of the following linear combinations of atomic orbitals will lead to the formation of molecular orbitals in homonuclear diatomic molecules (internuclear axis in z-direction)?
(1) \( 2p_z \) and \( 2p_x \)
(2) \( 2s \) and \( 2p_x \)
(3) \( 3d_{xy} \) and \( 3d_{x^2-y^2} \)
(4) \( 2s \) and \( 2p_z \)
(5) \( 2p_z \) and \( 3d_{x^2-y^2} \)
Show Hint
- E only
- A and B only
- D only
- C and D only
The Correct Option is C
Approach Solution - 1
To determine which linear combinations of atomic orbitals will lead to the formation of molecular orbitals in homonuclear diatomic molecules with the internuclear axis in the z-direction, we need to consider the symmetry and orientation of the atomic orbitals involved.
- \( 2p_z \) and \( 2p_x \): \(2p_z\) orbitals are aligned along the z-axis, while \(2p_x\) orbitals are aligned along the x-axis. Due to their differing orientations, these orbitals cannot effectively overlap to form a molecular orbital. Hence, this combination is not possible.
- \( 2s \) and \( 2p_x \): The \(2s\) orbital is spherically symmetric, while \(2p_x\) is oriented along the x-axis. The lack of proper orientation means they cannot combine to form a molecular orbital. Thus, this combination is not feasible.
- \( 3d_{xy} \) and \( 3d_{x^2-y^2} \): Both these d-orbitals lie in the xy-plane and have symmetry that does not match the z-axis orientation necessary for forming bonds in diatomic molecules with the internuclear axis in the z-direction. Therefore, they cannot form molecular orbitals.
- \( 2s \) and \( 2p_z \): The spherical symmetry of \(2s\) and the z-orientation of \(2p_z\) allow them to combine effectively since the orientation along the z-axis is appropriate for bonding in homonuclear diatomic molecules. Thus, this combination will form molecular orbitals.
- \( 2p_z \) and \( 3d_{x^2-y^2} \): Similar to the point above, the \(2p_z\) orbital is in the z-direction, whereas the \(3d_{x^2-y^2}\) orbital lies in the xy-plane, making it inappropriate for forming molecular orbitals along the z-axis. Hence, this combination is not possible.
Therefore, the correct choice is "D only," as only the combination of \(2s\) and \(2p_z\) leads to molecular orbital formation in the context described.
Approach Solution -2
For molecular orbital formation along the z-direction, the atomic orbitals must have components along the z-axis.
The correct combination involves: - \( 2s \) and \( 2p_z \), both of which have components along the z-axis, and can combine effectively to form bonding and antibonding molecular orbitals.
Thus, the correct answer is \( \boxed{(3) D Only} \).
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