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The fundamental vibration frequency and rotational constant of carbon monoxide molecule are 6.5 * 10 ^ 13 * s ^ - 1 and 1.743 * 10 ^ 11 * s ^ - 1 respectively. The rotational will have the same energy as ir would have in its first vibrational states with no rotational energy is:?
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The fundamental vibration frequency and rotational constant of carbon ...
Fundamental Vibration Frequency
The fundamental vibration frequency of the carbon monoxide molecule is given as 6.5 * 10^13 s^-1. This frequency corresponds to the energy associated with the vibrational motion of the molecule.
Rotational Constant
The rotational constant is provided as 1.743 * 10^11 s^-1. This constant relates to the energy levels associated with the rotational motion of the molecule.
Energy Calculation
To find the rotational energy that matches the vibrational energy in the first vibrational state, we use the following relationships:
- Vibrational Energy: The energy for the first vibrational state (n=1) is given by:
- E_v = h * ν, where h is Planck's constant and ν is the frequency.
- Rotational Energy: The energy for the rotational level is given by:
- E_r = B * J * (J + 1), where B is the rotational constant and J is the rotational quantum number.
For the first vibrational state, we consider J = 0, thus:
- E_r = B * 0 * (0 + 1) = 0.
However, for J = 1 (the first rotational state), substituting J=1 gives:
- E_r = B * 1 * (1 + 1) = 2B.
Equating Energies
Setting the vibrational energy equal to the first rotational energy, we have:
- E_v = E_r (for J=1).
This means the rotational energy will be equal to the vibrational energy when we consider the first excited state of rotation, giving us an understanding of energy quantization in molecular systems.
Conclusion
The rotational energy in the first vibrational state without any rotational energy is effectively zero. The first vibrational state’s energy can be compared to the first rotational state (J=1) to understand molecular dynamics more comprehensively.
The fundamental vibration frequency of the carbon monoxide molecule is given as 6.5 * 10^13 s^-1. This frequency corresponds to the energy associated with the vibrational motion of the molecule.
Rotational Constant
The rotational constant is provided as 1.743 * 10^11 s^-1. This constant relates to the energy levels associated with the rotational motion of the molecule.
Energy Calculation
To find the rotational energy that matches the vibrational energy in the first vibrational state, we use the following relationships:
- Vibrational Energy: The energy for the first vibrational state (n=1) is given by:
- E_v = h * ν, where h is Planck's constant and ν is the frequency.
- Rotational Energy: The energy for the rotational level is given by:
- E_r = B * J * (J + 1), where B is the rotational constant and J is the rotational quantum number.
For the first vibrational state, we consider J = 0, thus:
- E_r = B * 0 * (0 + 1) = 0.
However, for J = 1 (the first rotational state), substituting J=1 gives:
- E_r = B * 1 * (1 + 1) = 2B.
Equating Energies
Setting the vibrational energy equal to the first rotational energy, we have:
- E_v = E_r (for J=1).
This means the rotational energy will be equal to the vibrational energy when we consider the first excited state of rotation, giving us an understanding of energy quantization in molecular systems.
Conclusion
The rotational energy in the first vibrational state without any rotational energy is effectively zero. The first vibrational state’s energy can be compared to the first rotational state (J=1) to understand molecular dynamics more comprehensively.
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The fundamental vibration frequency and rotational constant of carbon monoxide molecule are 6.5 * 10 ^ 13 * s ^ - 1 and 1.743 * 10 ^ 11 * s ^ - 1 respectively. The rotational will have the same energy as ir would have in its first vibrational states with no rotational energy is:?
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The fundamental vibration frequency and rotational constant of carbon monoxide molecule are 6.5 * 10 ^ 13 * s ^ - 1 and 1.743 * 10 ^ 11 * s ^ - 1 respectively. The rotational will have the same energy as ir would have in its first vibrational states with no rotational energy is:? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about The fundamental vibration frequency and rotational constant of carbon monoxide molecule are 6.5 * 10 ^ 13 * s ^ - 1 and 1.743 * 10 ^ 11 * s ^ - 1 respectively. The rotational will have the same energy as ir would have in its first vibrational states with no rotational energy is:? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The fundamental vibration frequency and rotational constant of carbon monoxide molecule are 6.5 * 10 ^ 13 * s ^ - 1 and 1.743 * 10 ^ 11 * s ^ - 1 respectively. The rotational will have the same energy as ir would have in its first vibrational states with no rotational energy is:?.
The fundamental vibration frequency and rotational constant of carbon monoxide molecule are 6.5 * 10 ^ 13 * s ^ - 1 and 1.743 * 10 ^ 11 * s ^ - 1 respectively. The rotational will have the same energy as ir would have in its first vibrational states with no rotational energy is:? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about The fundamental vibration frequency and rotational constant of carbon monoxide molecule are 6.5 * 10 ^ 13 * s ^ - 1 and 1.743 * 10 ^ 11 * s ^ - 1 respectively. The rotational will have the same energy as ir would have in its first vibrational states with no rotational energy is:? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The fundamental vibration frequency and rotational constant of carbon monoxide molecule are 6.5 * 10 ^ 13 * s ^ - 1 and 1.743 * 10 ^ 11 * s ^ - 1 respectively. The rotational will have the same energy as ir would have in its first vibrational states with no rotational energy is:?.
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The fundamental vibration frequency and rotational constant of carbon monoxide molecule are 6.5 * 10 ^ 13 * s ^ - 1 and 1.743 * 10 ^ 11 * s ^ - 1 respectively. The rotational will have the same energy as ir would have in its first vibrational states with no rotational energy is:?, a detailed solution for The fundamental vibration frequency and rotational constant of carbon monoxide molecule are 6.5 * 10 ^ 13 * s ^ - 1 and 1.743 * 10 ^ 11 * s ^ - 1 respectively. The rotational will have the same energy as ir would have in its first vibrational states with no rotational energy is:? has been provided alongside types of The fundamental vibration frequency and rotational constant of carbon monoxide molecule are 6.5 * 10 ^ 13 * s ^ - 1 and 1.743 * 10 ^ 11 * s ^ - 1 respectively. The rotational will have the same energy as ir would have in its first vibrational states with no rotational energy is:? theory, EduRev gives you an
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