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Use the Boltzmann equation to find the relative number of atoms or molecules in the excited state for each of the following transitions at room temperature (Assume that gi/ go is 1 for all transitions). a. Electronic transition with an emission of 280 nm (UV) b. Electronic transitions with an emission of 6700 A (red visible light) c. Vibrational transition with a frequency of 2500 waves/cm (Mid IR) d. A rotational transition with a 2.45 GHz (microwave oven frequency) e. An NMR transition with a frequency of 60 MHz

Use the Boltzmann equation to find the relative number of atoms or molecules in the excited state for each of the following transitions at room temperature (Assume that gi/ go is 1 for all transitions). a. Electronic transition with an emission of 280 nm (UV) b. Electronic transitions with an emission of 6700 A (red visible light) c. Vibrational transition with a frequency of 2500 waves/cm (Mid IR) d. A rotational transition with a 2.45 GHz (microwave oven frequency) e. An NMR transition with a frequency of 60 MHz

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Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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**Title: Understanding Transitions Using the Boltzmann Equation** **Introduction:** The Boltzmann equation is essential in determining the relative number of atoms or molecules in different energy states. This equation helps us understand how atoms or molecules populate various energy levels, especially when they transition between states. Here, we will apply the equation to several types of transitions at room temperature, assuming that the degeneracy factors (\(g_i/g_o\)) are equal to 1 for all transitions. **Types of Transitions:** 1. **Electronic Transitions** - **Emission at 280 nm (UV)** - Ultraviolet (UV) light emission involves transitions between electronic energy levels. The given wavelength is 280 nm. 2. **Electronic Transitions** - **Emission at 6700 Å (Red Visible Light)** - Visible light emissions occur in the red spectrum. The wavelength provided here is 6700 Å (Angstrom). 3. **Vibrational Transitions** - **Frequency of 2500 waves/cm (Mid Infrared)** - Vibrational transitions occur when molecules change their vibrational states. The given frequency is 2500 waves per centimeter in the mid-infrared spectrum. 4. **Rotational Transitions** - **Frequency of 2.45 GHz (Microwave Oven Frequency)** - Rotational transitions involve changes in the rotational energy levels of molecules. The specified frequency is 2.45 GHz, commonly used in microwave ovens. 5. **Nuclear Magnetic Resonance (NMR) Transitions** - **Frequency of 60 MHz** - NMR transitions are used to study the magnetic properties of atomic nuclei. The given frequency is 60 MHz. **Conclusion:** The Boltzmann equation allows us to quantify and predict the distribution of atoms or molecules among different energy states. By applying it to these transitions, we gain insights into various physical and chemical processes occurring at room temperature. Each type of transition—electronic, vibrational, rotational, and NMR—plays a critical role in scientific and technological applications.
Transcribed Image Text:**Title: Understanding Transitions Using the Boltzmann Equation** **Introduction:** The Boltzmann equation is essential in determining the relative number of atoms or molecules in different energy states. This equation helps us understand how atoms or molecules populate various energy levels, especially when they transition between states. Here, we will apply the equation to several types of transitions at room temperature, assuming that the degeneracy factors (\(g_i/g_o\)) are equal to 1 for all transitions. **Types of Transitions:** 1. **Electronic Transitions** - **Emission at 280 nm (UV)** - Ultraviolet (UV) light emission involves transitions between electronic energy levels. The given wavelength is 280 nm. 2. **Electronic Transitions** - **Emission at 6700 Å (Red Visible Light)** - Visible light emissions occur in the red spectrum. The wavelength provided here is 6700 Å (Angstrom). 3. **Vibrational Transitions** - **Frequency of 2500 waves/cm (Mid Infrared)** - Vibrational transitions occur when molecules change their vibrational states. The given frequency is 2500 waves per centimeter in the mid-infrared spectrum. 4. **Rotational Transitions** - **Frequency of 2.45 GHz (Microwave Oven Frequency)** - Rotational transitions involve changes in the rotational energy levels of molecules. The specified frequency is 2.45 GHz, commonly used in microwave ovens. 5. **Nuclear Magnetic Resonance (NMR) Transitions** - **Frequency of 60 MHz** - NMR transitions are used to study the magnetic properties of atomic nuclei. The given frequency is 60 MHz. **Conclusion:** The Boltzmann equation allows us to quantify and predict the distribution of atoms or molecules among different energy states. By applying it to these transitions, we gain insights into various physical and chemical processes occurring at room temperature. Each type of transition—electronic, vibrational, rotational, and NMR—plays a critical role in scientific and technological applications.
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Concept:

Boltzmann Equation 

 

NiNo=gigo e-EKTWhere,NiNo= Relative number of atoms/moleculesgigo = 1 (Given)E= Energy of the TranstionK= Boltzmann ConstantT=Temperature

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