Calculate the ratio between the population of state 1 and state 2 two for the following two systems at 300 K: a. b. ΔΕ=10:21 J ΔΕ=10:20 J E₁ Eo E₁ Eo c. For which of the two systems, a. or b., do you expect a higher absorption intensity? Explain your reasoning.
Calculate the ratio between the population of state 1 and state 2 two for the following two systems at 300 K: a. b. ΔΕ=10:21 J ΔΕ=10:20 J E₁ Eo E₁ Eo c. For which of the two systems, a. or b., do you expect a higher absorption intensity? Explain your reasoning.
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Transcribed Image Text:**Title: Population Ratio and Absorption Intensity in Excited States**
**Description:**
*Calculate the ratio between the population of state 1 and state 2 for the following two systems at 300 K:*
**a.**
A diagram showing two energy levels labeled \(E_0\) and \(E_1\) with an upward arrow between them. The energy difference is given as \(\Delta E = 10^{-21}\) J.
**b.**
A diagram similar to the first, with energy levels labeled \(E_0\) and \(E_1\), and an energy difference of \(\Delta E = 10^{-20}\) J.
**c.**
*For which of the two systems, a. or b., do you expect a higher absorption intensity? Explain your reasoning.*
**Analysis:**
- The diagrams depict two systems with different energy gaps between their ground (\(E_0\)) and excited states (\(E_1\)).
- The exponential dependence of population ratio on energy difference and temperature, via the Boltzmann distribution, implies smaller \(\Delta E\) will favor a higher population in the excited state.
- Therefore, in system a., with a smaller \(\Delta E\), one would expect a greater proportion of particles to be in the excited state compared to system b.
**Discussion:**
In terms of absorption intensity:
- System a. may exhibit higher absorption intensity at equilibrium if a significant number of particles reside in the ground state that can transition upward, as the higher population in excited states in system a. increases potential for absorption from ground state to excited state.
- The larger energy gap in system b. reduces thermal occupation of the excited state at the same temperature, possibly resulting in lower absorption intensity compared to system a.
**Conclusion:**
The investigation of these systems' energy transitions provides insight into the thermal population of states and associated spectroscopic characteristics, important for practical applications in fields like spectroscopy and quantum mechanics.
Expert Solution
Given:
Energy difference in system a,
Energy difference in system b,
Temperature,
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