Chapter 11: Problem 14

Discuss the selection rules for vibrational transitions when the two nuclei of a diatomic molecule arc the same and when they are different.

Short Answer

Expert verified

Homonuclear diatomic molecules lack IR active vibrational transitions, but heteronuclear diatomic molecules have IR active transitions following abla v = ±1abla v = ±1.

Step by step solution

Understand Vibrational Transitions

Vibrational transitions occur when a molecule absorbs or emits a photon and transitions between different vibrational energy levels.

Selection Rules Overview

Selection rules determine which transitions are allowed based on specific changes in quantum numbers. For vibrational transitions, the main rule is that the change in the vibrational quantum number (abla v)abla v must equal ±1.

Same Nuclei (Homonuclear Diatomic Molecules)

For homonuclear diatomic molecules (e.g., H2, N2), only vibrational transitions with a change in dipole moment occur. However, these molecules have no permanent dipole moment, so vibrational transitions are typically forbidden in IR spectroscopy. Raman spectroscopy can still be used to observe these transitions.

Different Nuclei (Heteronuclear Diatomic Molecules)

For heteronuclear diatomic molecules (e.g., CO, HCl), there is a permanent dipole moment. Vibrational transitions are allowed under IR spectroscopy following the selection rule abla v = ±1abla v = ±1. These transitions typically appear as peaks in an IR spectrum.

Key Points Summary

Selection rules for vibrational transitions depend on molecular dipole moments. Homonuclear molecules typically don't show IR active vibrational transitions, but heteronuclear molecules do.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Selection Rules

Selection rules are guidelines in quantum mechanics that determine the allowed transitions between energy levels. For vibrational transitions in diatomic molecules, the main selection rule is that the change in the vibrational quantum number (abla v) must equal ±1. This means a molecule can only go from one vibrational level to the next (or previous) by absorbing or emitting a photon. These rules help us understand and predict the behavior of molecules during spectroscopy.

Homonuclear Diatomic Molecules

Homonuclear diatomic molecules consist of two identical atoms (e.g., H₂, N₂). These molecules do not have a permanent dipole moment because their bonding electrons are evenly shared. Since there is no change in dipole moment during vibrational transitions, these molecules are typically IR inactive. This means they do not absorb infrared radiation well and thus do not show up in IR spectroscopy. However, they can still be studied using Raman spectroscopy, which involves scattering of light rather than absorption.

Heteronuclear Diatomic Molecules

Heteronuclear diatomic molecules have two different kinds of atoms (e.g., CO, HCl). Because the atoms are different, these molecules generally have a permanent dipole moment. This means there is an uneven distribution of electron density. During vibrational transitions, there is a change in the dipole moment, making these molecules IR active. This activity means they can absorb infrared light at specific frequencies, and these absorptions appear as peaks in an IR spectrum. This property allows researchers to study these molecules using IR spectroscopy.

Dipole Moment

A dipole moment occurs when there is a separation of electrical charge within a molecule, resulting in a positive and a negative end. This is common in heteronuclear diatomic molecules due to the difference in electronegativity between the two atoms. The dipole moment is crucial for IR spectroscopy because infrared absorption involves changes in the dipole moment. If a molecule has no dipole moment changes during vibration, it will not be IR active. Understanding dipole moments helps us predict which molecules can be analyzed using different types of spectroscopy.

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Discuss the selection rules for vibrational transitions when the two nuclei of a diatomic molecule arc the same and when they are different.

Short Answer

Step by step solution

Understand Vibrational Transitions

Selection Rules Overview

Same Nuclei (Homonuclear Diatomic Molecules)

Different Nuclei (Heteronuclear Diatomic Molecules)

Key Points Summary

Key Concepts

Selection Rules

Homonuclear Diatomic Molecules

Heteronuclear Diatomic Molecules

Dipole Moment

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