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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.

Short Answer

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

Step by step solution

01

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.
02

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.
03

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.

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Key Concepts

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

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.

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Most popular questions from this chapter

A hypothetical diatomic molecule of oxygen (mass =\( 2.656 \times 10^{-26} \mathrm{kg} ) \quad \text { and } \quad \text { hydrogen } \quad\left(\text { mass }=1.67 \times 10^{-27} \mathrm{kg}\right)\) emits a photon of wavelength 2.39\(\mu \mathrm{m}\) when it makes a transition from one vibrational state to the next lower state. If we model this molecule as two point masses at opposite ends of a massless spring, (a) what is the force constant of this spring, and (b) how many vibrations per second is the molecule making?

A hypothetical \(\mathrm{NH}\) molecule makes a rotational-level transition from \(l=3\) to \(I=1\) and gives off a photon of wavelength 1.780 \(\mathrm{nm}\) in doing so. What is the separation between the two atoms in this molecule if we model them as point masses? The mass of hydrogen is \(1.67 \times 10^{-27} \mathrm{kg},\) and the mass of nitrogen is \(2.33 \times 10^{-26} \mathrm{kg} .\)

(a) Suppose a piece of very pure germanium is to be used as a light detector by observing, through the absorption of photons, the increase in conductivity resulting from generation of electron-hole pairs. If each pair requires 0.67 \(\mathrm{eV}\) of energy, what is the maximum wavelength that can be detected? In what portion of the spectrum does it lie? (b) What are the answers to part (a) if the material is silicon, with an energy requirement of 1.14 eV per pair, corresponding to the gap between valence and conduction bands in that element?

(a) A molecule decreases its vibrational energy by 0.250 \(\mathrm{eV}\) by giving up a photon of light. What wavelength of light does it give up during this process, and in what part of the electromagnetic spectrum does that wavelength of light lie? (b) An atom decreases its energy by 8.50 eV by giving up a photon of light. What wavelength of light does it give up during this process, and in what part of the electromagnetic spectrum does that wavelength of light lie? (c) A molecule decreases its rotational energy by \(3.20 \times 10^{-3} \mathrm{eV}\) by giving up a photon of light. What wavelength of light does it give up during this process, and in what part of the electromagnetic spectrum does that wavelength of light lie?

Compute the Fermi energy of potassium by making the simple approximation that each atom contributes one free electron. The density of potassium is \(851 \mathrm{kg} / \mathrm{m}^{3},\) and the mass of a single potassium atom is \(6.49 \times 10^{-26} \mathrm{kg}\) .

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