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CO2 molecule lias the first tew energy levels uniformly seperatedby approximately 2.5 meV at a tempera tine of300 K. the ratio of the number of molecules in the 4th excited state to the number in 2nd excited state is about
- a)0.5
- b)0.6
- c)0.8
- d)0.9
Correct answer is option 'C'. Can you explain this answer?
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Given information:
- CO2 molecule has the first few energy levels separated by approximately 2.5 meV at a temperature of 300 K.
To find:
The ratio of the number of molecules in the 4th excited state to the number in the 2nd excited state.
Solution:
1. Calculate the energy difference between the energy levels:
At a temperature of 300 K, we can use the Boltzmann distribution to estimate the relative populations of different energy levels. The energy difference between two adjacent energy levels is given as 2.5 meV.
2. Calculate the ratio of populations:
The ratio of populations between two energy levels can be calculated using the Boltzmann distribution formula:
P2 / P4 = exp(-E2 / kT) / exp(-E4 / kT)
Here,
P2 is the population of the 2nd excited state,
P4 is the population of the 4th excited state,
E2 is the energy of the 2nd excited state,
E4 is the energy of the 4th excited state,
k is the Boltzmann constant, and
T is the temperature in Kelvin.
3. Substituting the values and calculating the ratio:
Given that the energy levels are uniformly separated by 2.5 meV, we can assume that the energy of the 2nd excited state is 2.5 meV, the energy of the 4th excited state is 10 meV, and the temperature is 300 K.
P2 / P4 = exp(-2.5 meV / (k * 300 K)) / exp(-10 meV / (k * 300 K))
Simplifying the above expression, we get:
P2 / P4 = exp(-2.5 / (300 * 10^-3 * k)) / exp(-10 / (300 * 10^-3 * k))
P2 / P4 = exp(-2.5 * 10^3 / k) / exp(-10 * 10^3 / k)
P2 / P4 = exp(-2.5 * 10^3 / k + 10 * 10^3 / k)
P2 / P4 = exp(7.5 * 10^3 / k)
4. Determining the value of the ratio:
To determine the value of the ratio, we need to know the value of the Boltzmann constant (k). The Boltzmann constant is approximately equal to 8.6173 × 10^-5 eV/K.
Substituting the value of k into the equation, we get:
P2 / P4 = exp(7.5 * 10^3 / (8.6173 × 10^-5))
P2 / P4 = exp(8.7 * 10^7)
Using the exponential function, we can evaluate the above expression to find:
P2 / P4 ≈ 0.8
Therefore, the ratio of the number of molecules in the 4th excited state to the number in the 2nd excited state is approximately 0.8.
Hence, the correct answer is option 'C'.
- CO2 molecule has the first few energy levels separated by approximately 2.5 meV at a temperature of 300 K.
To find:
The ratio of the number of molecules in the 4th excited state to the number in the 2nd excited state.
Solution:
1. Calculate the energy difference between the energy levels:
At a temperature of 300 K, we can use the Boltzmann distribution to estimate the relative populations of different energy levels. The energy difference between two adjacent energy levels is given as 2.5 meV.
2. Calculate the ratio of populations:
The ratio of populations between two energy levels can be calculated using the Boltzmann distribution formula:
P2 / P4 = exp(-E2 / kT) / exp(-E4 / kT)
Here,
P2 is the population of the 2nd excited state,
P4 is the population of the 4th excited state,
E2 is the energy of the 2nd excited state,
E4 is the energy of the 4th excited state,
k is the Boltzmann constant, and
T is the temperature in Kelvin.
3. Substituting the values and calculating the ratio:
Given that the energy levels are uniformly separated by 2.5 meV, we can assume that the energy of the 2nd excited state is 2.5 meV, the energy of the 4th excited state is 10 meV, and the temperature is 300 K.
P2 / P4 = exp(-2.5 meV / (k * 300 K)) / exp(-10 meV / (k * 300 K))
Simplifying the above expression, we get:
P2 / P4 = exp(-2.5 / (300 * 10^-3 * k)) / exp(-10 / (300 * 10^-3 * k))
P2 / P4 = exp(-2.5 * 10^3 / k) / exp(-10 * 10^3 / k)
P2 / P4 = exp(-2.5 * 10^3 / k + 10 * 10^3 / k)
P2 / P4 = exp(7.5 * 10^3 / k)
4. Determining the value of the ratio:
To determine the value of the ratio, we need to know the value of the Boltzmann constant (k). The Boltzmann constant is approximately equal to 8.6173 × 10^-5 eV/K.
Substituting the value of k into the equation, we get:
P2 / P4 = exp(7.5 * 10^3 / (8.6173 × 10^-5))
P2 / P4 = exp(8.7 * 10^7)
Using the exponential function, we can evaluate the above expression to find:
P2 / P4 ≈ 0.8
Therefore, the ratio of the number of molecules in the 4th excited state to the number in the 2nd excited state is approximately 0.8.
Hence, the correct answer is option 'C'.
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CO2molecule lias the first tew energy levels uniformly seperatedby approximately 2.5 meV at a tempera tine of300 K. the ratio of the number of molecules in the 4th excited state to the number in 2nd excited state is abouta)0.5b)0.6c)0.8d)0.9Correct answer is option 'C'. Can you explain this answer?
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CO2molecule lias the first tew energy levels uniformly seperatedby approximately 2.5 meV at a tempera tine of300 K. the ratio of the number of molecules in the 4th excited state to the number in 2nd excited state is abouta)0.5b)0.6c)0.8d)0.9Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about CO2molecule lias the first tew energy levels uniformly seperatedby approximately 2.5 meV at a tempera tine of300 K. the ratio of the number of molecules in the 4th excited state to the number in 2nd excited state is abouta)0.5b)0.6c)0.8d)0.9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for CO2molecule lias the first tew energy levels uniformly seperatedby approximately 2.5 meV at a tempera tine of300 K. the ratio of the number of molecules in the 4th excited state to the number in 2nd excited state is abouta)0.5b)0.6c)0.8d)0.9Correct answer is option 'C'. Can you explain this answer?.
CO2molecule lias the first tew energy levels uniformly seperatedby approximately 2.5 meV at a tempera tine of300 K. the ratio of the number of molecules in the 4th excited state to the number in 2nd excited state is abouta)0.5b)0.6c)0.8d)0.9Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about CO2molecule lias the first tew energy levels uniformly seperatedby approximately 2.5 meV at a tempera tine of300 K. the ratio of the number of molecules in the 4th excited state to the number in 2nd excited state is abouta)0.5b)0.6c)0.8d)0.9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for CO2molecule lias the first tew energy levels uniformly seperatedby approximately 2.5 meV at a tempera tine of300 K. the ratio of the number of molecules in the 4th excited state to the number in 2nd excited state is abouta)0.5b)0.6c)0.8d)0.9Correct answer is option 'C'. Can you explain this answer?.
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CO2molecule lias the first tew energy levels uniformly seperatedby approximately 2.5 meV at a tempera tine of300 K. the ratio of the number of molecules in the 4th excited state to the number in 2nd excited state is abouta)0.5b)0.6c)0.8d)0.9Correct answer is option 'C'. Can you explain this answer?, a detailed solution for CO2molecule lias the first tew energy levels uniformly seperatedby approximately 2.5 meV at a tempera tine of300 K. the ratio of the number of molecules in the 4th excited state to the number in 2nd excited state is abouta)0.5b)0.6c)0.8d)0.9Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of CO2molecule lias the first tew energy levels uniformly seperatedby approximately 2.5 meV at a tempera tine of300 K. the ratio of the number of molecules in the 4th excited state to the number in 2nd excited state is abouta)0.5b)0.6c)0.8d)0.9Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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