Problem 4 - University Physics with Modern Physics

Question

Light of wavelength 3.10 \(\mathrm{mm}\) strikes and is absorbed by a molecule. Is this process most likely to alter the rotational, vibrational, or atomic energy levels of the molecule? Explain your reasoning. (b) If the light in part (a) had a wavelength of 207 \(\mathrm{nm}\) , which energy levels would it most likely affect? Explain.

Step-by-Step Solution

Answer

(a) Rotational levels; (b) Electronic levels.

Step 1: Understand Energy Levels and Wavelength

Molecules can have different types of energy levels: rotational, vibrational, and electronic. Rotational transitions occur at longer wavelengths in the microwave region (about centimeters to millimeters), vibrational transitions occur at shorter wavelengths in the infrared region, and electronic transitions occur at even shorter wavelengths in the visible or ultraviolet region.

Step 2: Analyze 3.10 mm Wavelength of Light

The given wavelength of 3.10 mm is in the microwave region of the electromagnetic spectrum. This region is typically associated with rotational transitions. Therefore, light of this wavelength will most likely affect the rotational energy levels of a molecule.

Step 3: Analyze 207 nm Wavelength of Light

The wavelength of 207 nm is in the ultraviolet region of the electromagnetic spectrum. This region corresponds to the energy required for electronic transitions. Thus, light of this wavelength is most likely to affect the electronic energy levels of a molecule.

Key Concepts

Rotational Energy

Rotational energy in molecules corresponds to the energy associated with the molecule's rotation around its center of mass. This type of energy is often influenced by electromagnetic radiation in the microwave region, with wavelengths usually in centimeters to millimeters.
When molecules absorb such microwave radiation, they undergo rotational transitions, altering their rotational energy levels. It's important to understand that the energy required for these rotations is quite low, hence the longer wavelength regions like microwaves are most effective. Microwaves induce changes in the way a molecule spins around its axis, which can be visualized as tiny, spinning tops changing speeds or directions when energy is added or removed. Thus, when a molecule absorbs light with a 3.10 mm wavelength, it most likely undergoes changes in its rotational energy, as this corresponds to the energy required to excite these specific transitions. This process affects how fast or slow the molecule rotates, which can have implications for its physical properties as well.

Vibrational Energy

Vibrational energy denotes the energy resulting from the vibrational motion of the atoms within a molecule. Vibrational transitions typically occur at shorter wavelengths than rotational transitions and are often found in the infrared region of the electromagnetic spectrum.
Atoms in a molecule are bonded and feel forces of attraction which act like springs. When a molecule absorbs the appropriate amount of energy, these atoms oscillate around their equilibrium positions. This oscillatory motion is what defines vibrational energy changes. The different vibrational modes include stretching (where bond lengths change) and bending (where bond angles change). Infrared radiation, which lies between the microwave and visible regions of the spectrum, offers the right amount of energy to cause vibrational transitions. Unlike rotational transitions, these are generally higher in energy and thus require shorter wavelengths to occur. This makes infrared spectroscopy particularly useful in studying these transitions.

Electronic Energy

Electronic energy levels pertain to the energy states of electrons within an atom or molecule. Unlike rotational and vibrational energy changes, electronic transitions require much shorter wavelengths, typically in the visible or ultraviolet part of the spectrum.
When a molecule absorbs electromagnetic radiation at these shorter wavelengths, electrons are excited from one energy level to a higher energy state. This transition involves more energy than both rotational and vibrational transitions. The absorbed energy is usually sufficient to alter the configuration of electrons around the atomic nuclei, thereby changing the electronic energy levels of the molecule. In specific terms, for a 207 nm wavelength light, the energy is in the ultraviolet region, which is suitable for electronic transitions. This means absorbing light at this wavelength is likely to excite electrons to higher energy levels, possibly resulting in phenomena such as fluorescence or phosphorescence. This type of transition is essential in understanding chemical reactivity, color, and other electronic properties of molecules.