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A molecule normally absorbs in the green wavelength (500nm). At some temperature, It is measured that for every 10 molecules in the excited state. There are about 27 molecules in the ground state. The approximate temperature of the molecules is _____ x 104 K. (Round off to nearest integer).
Correct answer is '3'. Can you explain this answer?
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A molecule normally absorbs in the green wavelength (500nm). At some t...
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A molecule normally absorbs in the green wavelength (500nm). At some t...
Explanation:
The given problem involves the concept of Boltzmann distribution, which gives the ratio of the number of molecules in the excited state to the number of molecules in the ground state at a particular temperature T. The Boltzmann distribution is given by the following equation:
)
where N1 and N2 are the number of molecules in the ground and excited states, respectively, g1 and g2 are the degeneracies of the ground and excited states, ΔE is the energy difference between the two states, kB is the Boltzmann constant, and T is the temperature in Kelvin.
Solution:
Given, the molecule absorbs in the green wavelength (500nm), which corresponds to an energy difference of ΔE = hc/λ = (6.626 x 10^-34 J s x 3 x 10^8 m/s)/(500 x 10^-9 m) = 3.97 x 10^-19 J.
We can assume that g1 = 1 (since the ground state is non-degenerate) and g2 = 10 (since there are 10 excited molecules for every 27 ground state molecules).
Substituting these values in the Boltzmann distribution equation and solving for T, we get:
)
Taking natural logarithm on both sides, we get:
Solving for T, we get:
The given problem involves the concept of Boltzmann distribution, which gives the ratio of the number of molecules in the excited state to the number of molecules in the ground state at a particular temperature T. The Boltzmann distribution is given by the following equation:
where N1 and N2 are the number of molecules in the ground and excited states, respectively, g1 and g2 are the degeneracies of the ground and excited states, ΔE is the energy difference between the two states, kB is the Boltzmann constant, and T is the temperature in Kelvin.
Solution:
Given, the molecule absorbs in the green wavelength (500nm), which corresponds to an energy difference of ΔE = hc/λ = (6.626 x 10^-34 J s x 3 x 10^8 m/s)/(500 x 10^-9 m) = 3.97 x 10^-19 J.
We can assume that g1 = 1 (since the ground state is non-degenerate) and g2 = 10 (since there are 10 excited molecules for every 27 ground state molecules).
Substituting these values in the Boltzmann distribution equation and solving for T, we get:
Taking natural logarithm on both sides, we get:
Solving for T, we get:
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A molecule normally absorbs in the green wavelength (500nm). At some temperature, It is measured that for every 10 molecules in the excited state. There are about 27 molecules in the ground state. The approximate temperature of the molecules is _____ x 104 K. (Round off to nearest integer).Correct answer is '3'. Can you explain this answer?
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A molecule normally absorbs in the green wavelength (500nm). At some temperature, It is measured that for every 10 molecules in the excited state. There are about 27 molecules in the ground state. The approximate temperature of the molecules is _____ x 104 K. (Round off to nearest integer).Correct answer is '3'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about A molecule normally absorbs in the green wavelength (500nm). At some temperature, It is measured that for every 10 molecules in the excited state. There are about 27 molecules in the ground state. The approximate temperature of the molecules is _____ x 104 K. (Round off to nearest integer).Correct answer is '3'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A molecule normally absorbs in the green wavelength (500nm). At some temperature, It is measured that for every 10 molecules in the excited state. There are about 27 molecules in the ground state. The approximate temperature of the molecules is _____ x 104 K. (Round off to nearest integer).Correct answer is '3'. Can you explain this answer?.
A molecule normally absorbs in the green wavelength (500nm). At some temperature, It is measured that for every 10 molecules in the excited state. There are about 27 molecules in the ground state. The approximate temperature of the molecules is _____ x 104 K. (Round off to nearest integer).Correct answer is '3'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about A molecule normally absorbs in the green wavelength (500nm). At some temperature, It is measured that for every 10 molecules in the excited state. There are about 27 molecules in the ground state. The approximate temperature of the molecules is _____ x 104 K. (Round off to nearest integer).Correct answer is '3'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A molecule normally absorbs in the green wavelength (500nm). At some temperature, It is measured that for every 10 molecules in the excited state. There are about 27 molecules in the ground state. The approximate temperature of the molecules is _____ x 104 K. (Round off to nearest integer).Correct answer is '3'. Can you explain this answer?.
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