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- https://chem.libretexts.org/Courses/Western_Washington_University/Biophysical_Chemistry_(Smirnov_and_McCarty)/01%3A_Biochemical_Thermodynamics/1.05%3A_The_Boltzmann_Distribution_and_the_Statistical_Definition_of_EntropyIn this chapter we introduce the statistical definition of entropy as formulated by Boltzmann. This allows us to consider entropy from the perspective of the probabilities of different configurations ...In this chapter we introduce the statistical definition of entropy as formulated by Boltzmann. This allows us to consider entropy from the perspective of the probabilities of different configurations of the constituent interacting particles in an ensemble. This conception of entropy led to the development of modern statistical thermodynamics. For systems that can exchange thermal energy with the surroundings, the equilibrium probability distribution will be the Boltzmann distribution.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/17%3A_Boltzmann_Factor_and_Partition_Functions/17.02%3A_The_Boltzmann_Distribution_represents_a_Thermally_Equilibrated_DistributionThis page explores the relationship between energy states and the total number of systems in an ensemble, highlighting the Boltzmann distribution's role in predicting system occupancy based on energy ...This page explores the relationship between energy states and the total number of systems in an ensemble, highlighting the Boltzmann distribution's role in predicting system occupancy based on energy levels. It introduces the molecular partition function, q, showing its dependence on temperature for determining thermally accessible states.
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Instrumental_Analysis_(LibreTexts)/14%3A_Applications_of_Ultraviolet_Visible_Molecular_Absorption_Spectrometry/14.02%3A_Absorbing_SpeciesThere are two general requirements for an analyte’s absorption of electromagnetic radiation. First, there must be a mechanism by which the radiation’s electric field or magnetic field can interact wit...There are two general requirements for an analyte’s absorption of electromagnetic radiation. First, there must be a mechanism by which the radiation’s electric field or magnetic field can interact with the analyte. For ultraviolet and visible radiation, absorption of a photon changes the energy of the analyte’s valence electrons. The second requirement is that the photon’s energy must exactly equal the difference in energy between two of the analyte’s quantized energy states.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/18%3A_Partition_Functions_and_Ideal_Gases/18.03%3A_The_Energy_of_a_Diatomic_Polyatomic_Molecule_Can_Be_Approximated_as_a_Sum_of_Separate_TermsThis page explains the differences in degrees of freedom between monatomic and polyatomic gases, highlighting that polyatomic gases, including diatomic ones, have additional rotational and vibrational...This page explains the differences in degrees of freedom between monatomic and polyatomic gases, highlighting that polyatomic gases, including diatomic ones, have additional rotational and vibrational energy storage capabilities. It discusses the overall partition function for polyatomic gases, which includes contributions from translational, vibrational, rotational, and electronic states, with the electronic partition function typically equating to one at room temperature.
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Instrumental_Analysis_(LibreTexts)/06%3A_An_Introduction_to_Spectrophotometric_Methods/6.04%3A_SpectraWhen an atom, ion, or molecule absorbs a photon it undergoes a transition from a lower-energy state to a higher-energy, or excited state, we obtain an absorbance spectrum. The result of the reverse pr...When an atom, ion, or molecule absorbs a photon it undergoes a transition from a lower-energy state to a higher-energy, or excited state, we obtain an absorbance spectrum. The result of the reverse process, in which an atom, ion, or molecule emits a photon as it moves from a higher-energy state to a lower energy state, is an emission spectrum. In this section we consider the characteristics of each.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/15%3A_Lasers_Laser_Spectroscopy_and_Photochemistry/15.03%3A_A_Two-Level_System_Cannot_Achieve_a_Population_InversionThis page explains lasing in two-level atomic systems, highlighting key conditions for laser operation: coherence, monochromatic output, collimation, and efficiency. Coherence relies on stimulated emi...This page explains lasing in two-level atomic systems, highlighting key conditions for laser operation: coherence, monochromatic output, collimation, and efficiency. Coherence relies on stimulated emission and requires a population inversion, which is difficult to achieve in two-level systems due to high energy demands. As a result, these systems are mostly limited to pulsed operation, making three-level systems more favorable for continuous lasing.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/17%3A_Boltzmann_Factor_and_Partition_Functions/17.06%3A_The_Partition_Function_of_Distinguishable_Independent_Molecules_is_the_Product_of_the_Molecular_Partition_FunctionsThis page discusses the derivation of the partition function for a system of distinguishable subsystems, such as gas molecules. It highlights that energy is additive, allowing the total energy to be e...This page discusses the derivation of the partition function for a system of distinguishable subsystems, such as gas molecules. It highlights that energy is additive, allowing the total energy to be expressed as the sum of individual molecule energies. For distinguishable, independent molecules, the overall partition function is the product of individual partition functions.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/01%3A_The_Dawn_of_the_Quantum_Theory/1.05%3A_The_Rydberg_Formula_and_the_Hydrogen_Atomic_SpectrumThis page discusses Rydberg's theory and Balmer's formula for predicting hydrogen spectrum wavelengths, highlighting Balmer's 1885 formula for visible wavelengths and Rydberg's generalization for all ...This page discusses Rydberg's theory and Balmer's formula for predicting hydrogen spectrum wavelengths, highlighting Balmer's 1885 formula for visible wavelengths and Rydberg's generalization for all atomic spectra, including the Lyman series in the ultraviolet. The Lyman series corresponds to transitions to the n=1 orbit, with relevant formulas and values mentioned. Various sequentially named series are outlined, emphasizing that atomic spectra provide insights into atomic structure.
- https://chem.libretexts.org/Courses/University_of_Wisconsin_Oshkosh/Chem_370%3A_Physical_Chemistry_1_-_Thermodynamics_(Gutow)/01%3A_Thermodynamics/1.06%3A_The_Boltzmann_Distribution_and_the_Statistical_Definition_of_EntropyIn this chapter we introduce the statistical definition of entropy as formulated by Boltzmann. This allows us to consider entropy from the perspective of the probabilities of different configurations ...In this chapter we introduce the statistical definition of entropy as formulated by Boltzmann. This allows us to consider entropy from the perspective of the probabilities of different configurations of the constituent interacting particles in an ensemble. This conception of entropy led to the development of modern statistical thermodynamics. For systems that can exchange thermal energy with the surroundings, the equilibrium probability distribution will be the Boltzmann distribution.
