Multiple Choice
Which statement best explains how the bands in the crystal of a metal are analogous to atomic orbitals?
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12. Molecular Shapes & Valence Bond Theory
Molecular Orbital Theory
Multiple Choice
Which of the following correctly describes the molecular orbital energy diagram for the diatomic molecule He_2?
A
Only the bonding (σ_{1s}) orbital is filled, resulting in a bond order of 1.
B
Both bonding (σ_{1s}) and antibonding (σ^*_{1s}) orbitals are filled, resulting in a bond order of 0.
C
Neither bonding nor antibonding orbitals are filled, resulting in a bond order of 0.
D
Only the antibonding (σ^*_{1s}) orbital is filled, resulting in a bond order of -1.
Verified step by step guidance1
Step 1: Determine the total number of electrons in the He_2 molecule. Each helium atom has 2 electrons, so He_2 has a total of 4 electrons.
Step 2: Recall the order of molecular orbitals for diatomic molecules formed from 1s atomic orbitals: the bonding orbital is \( \sigma_{1s} \) and the antibonding orbital is \( \sigma^*_{1s} \).
Step 3: Fill the molecular orbitals with the 4 electrons following the Aufbau principle and Pauli exclusion principle: first fill the bonding \( \sigma_{1s} \) orbital with 2 electrons, then fill the antibonding \( \sigma^*_{1s} \) orbital with the remaining 2 electrons.
Step 4: Calculate the bond order using the formula: \[ \text{Bond order} = \frac{(\text{number of electrons in bonding orbitals}) - (\text{number of electrons in antibonding orbitals})}{2} \]. Substitute the values: 2 electrons in bonding and 2 in antibonding orbitals.
Step 5: Interpret the bond order result. A bond order of 0 means no net bond is formed, which explains why He_2 is not a stable molecule.
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