Please explain how to use Boltzmann equation for these problems. **Title: Understanding Atomic and Molecular Transitions Using the Boltzmann Equation****Introduction:**Explore how the Boltzmann equation is used to determine the relative number of atoms or molecules in the excited state for various transitions at room temperature. Assume that the statistical weight factor \( g_i/g_0 \) is 1 for all transitions.**Transitions and Corresponding Parameters:**1. **Electronic Transition in the Ultraviolet Range** - **Wavelength:** 280 nm (UV) - Description: This transition involves the movement of electrons and occurs in the ultraviolet spectrum.2. **Electronic Transitions with Visible Light Emission** - **Wavelength:** 6700 Å (red visible light) - Description: Involves electron transitions resulting in emission in the red region of the visible spectrum.3. **Vibrational Transition in the Mid Infrared Range** - **Frequency:** 2500 waves/cm (Mid IR) - Description: This involves the vibrational modes of molecules, commonly observed in the mid-infrared spectrum.4. **Rotational Transition at Microwave Frequencies** - **Frequency:** 2.45 GHz (microwave oven frequency) - Description: Rotational transitions pertinent to microwave frequencies, similar to those used in microwave ovens.5. **NMR Transition at Radio Frequencies** - **Frequency:** 60 MHz - Description: Nuclear Magnetic Resonance (NMR) transitions observed at radio frequencies, useful in structural determination of compounds.**Conclusion:**These parameters highlight the variety of electronic, vibrational, rotational, and nuclear transitions that can be analyzed using the Boltzmann equation. Understanding these transitions at room temperature allows for practical applications in spectroscopy and molecular analysis.

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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

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

Please explain how to use Boltzmann equation for these problems.

**Title: Understanding Atomic and Molecular Transitions Using the Boltzmann Equation**

**Introduction:**
Explore how the Boltzmann equation is used to determine the relative number of atoms or molecules in the excited state for various transitions at room temperature. Assume that the statistical weight factor \( g_i/g_0 \) is 1 for all transitions.

**Transitions and Corresponding Parameters:**

1. **Electronic Transition in the Ultraviolet Range**
- **Wavelength:** 280 nm (UV)
- Description: This transition involves the movement of electrons and occurs in the ultraviolet spectrum.

2. **Electronic Transitions with Visible Light Emission**
- **Wavelength:** 6700 Å (red visible light)
- Description: Involves electron transitions resulting in emission in the red region of the visible spectrum.

3. **Vibrational Transition in the Mid Infrared Range**
- **Frequency:** 2500 waves/cm (Mid IR)
- Description: This involves the vibrational modes of molecules, commonly observed in the mid-infrared spectrum.

4. **Rotational Transition at Microwave Frequencies**
- **Frequency:** 2.45 GHz (microwave oven frequency)
- Description: Rotational transitions pertinent to microwave frequencies, similar to those used in microwave ovens.

5. **NMR Transition at Radio Frequencies**
- **Frequency:** 60 MHz
- Description: Nuclear Magnetic Resonance (NMR) transitions observed at radio frequencies, useful in structural determination of compounds.

**Conclusion:**
These parameters highlight the variety of electronic, vibrational, rotational, and nuclear transitions that can be analyzed using the Boltzmann equation. Understanding these transitions at room temperature allows for practical applications in spectroscopy and molecular analysis.

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