Question

Explain the relationship between the frequency of vibrations in a molecule and the frequencies of light it will absorb.

Short answer

Molecules absorb light at frequencies matching their vibrational frequencies, following resonance and selection rules.

Step-by-step solution

Understanding Molecular Vibrations

Molecular vibrations refer to the periodic motion of atoms within a molecule. These vibrations occur because the atoms in a molecule are constantly moving, stretching and bending at specific frequencies. The frequency at which a molecule vibrates depends on the masses of the atoms and the strength of the bonds between them.

The Concept of Light Absorption

When light encounters a molecule, it can be absorbed if its frequency matches the frequency of the molecular vibration. This happens because the energy from the light can be used to increase the amplitude of the vibration (or excitation) of the molecule.

Matching Frequencies

For a molecule to absorb light, the frequency of the light must match the natural frequency of vibration of the molecule. This is due to the resonance condition, where the energy transition between states is possible only if energies match perfectly. Thus, absorption occurs when the photon's energy bridges the gap between two vibrational energy levels.

Using Selection Rules

Not all vibrations will correspond to absorbable frequencies. Selection rules (derived from quantum mechanics) dictate which vibrational transitions are allowed. These rules are based on the symmetry properties of the molecules and dictate which changes in molecular vibrations can lead to absorption.

Key concepts

Light Absorption

Light absorption is a fundamental concept in understanding how molecules interact with electromagnetic radiation. When light, which is made up of photons, encounters a molecule, it can be absorbed if certain conditions are met. This absorption happens when the energy of the light precisely matches the energy required to change the vibrational state of the molecule.

Think of it as a lock and key mechanism where the light's frequency needs to fit into the "energy gap" between two vibrational states. The molecule can only absorb the light if this fit is perfect. Therefore, understanding light absorption is about knowing how this energy conversion allows molecules to "grab" light and use it to increase their vibrational activity.

Vibrational Frequency

Vibrational frequency refers to the rate at which atoms in a molecule vibrate. Each molecule has its "voice", a specific set of frequencies at which its atoms stretch, bend, or twist. The vibrational frequency is determined by two main factors:

• The masses of the atoms
• The strength of the bonds

Heavier atoms and stronger bonds typically result in lower vibrational frequencies, while lighter atoms and weaker bonds often lead to higher ones.

Vibrational frequencies are crucial because they directly influence whether or not a molecule can absorb a particular frequency of light. In simpler terms, the vibrational frequency tells us what "tune" of light can make the molecule "dance".

Selection Rules

Selection rules are like guidelines that dictate which vibrational transitions in a molecule are allowed when it absorbs light. These rules are derived from the principles of quantum mechanics and are crucial for understanding why only certain vibrations lead to absorption.

Selection rules take into account the symmetry properties of the molecule. These symmetry properties determine whether a vibration can cause a change in the molecule's dipole moment, which is essential for light absorption. In other words:

• Only those molecular vibrations that change the dipole moment can interact with light

Selection rules help us predict and understand which vibrational modes can indeed be excited by light, filtering out those that cannot.

Resonance Condition

The resonance condition is the principle that the frequency of the incoming light must match the natural vibrational frequency of the molecule for absorption to occur. This matching requirement is a direct consequence of energy conservation principles.

When the resonance condition is met, the energy of the photon (light particle) precisely equals the energy needed to move from one vibrational level to another. This is like hitting the right note on a musical instrument to produce a sound. Only when this precise energy alignment happens will the molecule absorb the light, resulting in an increased amplitude of its vibrational motion.

Understanding the resonance condition is crucial because it explains why only certain frequencies of light can be absorbed relative to a molecule's specific vibrations.