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The rotational spectrum of gaseous CN consist of series of equally?
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The rotational spectrum of gaseous CN consist of series of equally?
Answer :
The pure rotational (microwave) spectrum of the gaseous molecule CN consists of a series of equally spaced line separated by
3.7978 cm–
1
. The inter nuclear distance of the molecule is [Molar masses are
12
C=12.011 and
14
N=14.007 g mol
–
1
]:
This question is part of UPSC exam. View all Chemistry courses
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The rotational spectrum of gaseous CN consist of series of equally?
The rotational spectrum of gaseous CN consists of a series of equally spaced lines. This can be explained by the principles of quantum mechanics and the quantization of energy levels in a molecule.
Quantization of Rotational Energy:
In a molecule, the rotation of the molecule around its axis is quantized, meaning that it can only have certain discrete energy values. The rotational energy levels are given by the equation E = J(J + 1)h^2/8π^2I, where J is the rotational quantum number, h is Planck's constant, and I is the moment of inertia of the molecule.
Equally Spaced Energy Levels:
The energy levels for rotational motion in a diatomic molecule like CN are equally spaced. This is because the moment of inertia (I) is proportional to the reduced mass of the molecule, which is nearly constant for a diatomic molecule. As a result, the energy difference between adjacent rotational levels is constant, leading to equally spaced lines in the rotational spectrum.
Transition Frequencies:
The transition frequencies between rotational energy levels can be determined using the equation ΔE = E(J+1) - E(J) = 2BJ, where B is the rotational constant. Since the energy difference between adjacent levels is constant, the transition frequencies between these levels will also be constant.
Spectral Lines:
When a molecule undergoes a transition from one rotational energy level to another, it emits or absorbs radiation at a specific frequency. These frequencies correspond to the rotational transition lines in the spectrum. The equally spaced energy levels result in equally spaced spectral lines in the rotational spectrum of gaseous CN.
Conclusion:
In summary, the rotational spectrum of gaseous CN consists of a series of equally spaced lines due to the quantization of rotational energy levels in the molecule. The equally spaced energy levels and transition frequencies between them result in equally spaced spectral lines. This phenomenon can be explained by the principles of quantum mechanics and is a fundamental characteristic of diatomic molecules.
Quantization of Rotational Energy:
In a molecule, the rotation of the molecule around its axis is quantized, meaning that it can only have certain discrete energy values. The rotational energy levels are given by the equation E = J(J + 1)h^2/8π^2I, where J is the rotational quantum number, h is Planck's constant, and I is the moment of inertia of the molecule.
Equally Spaced Energy Levels:
The energy levels for rotational motion in a diatomic molecule like CN are equally spaced. This is because the moment of inertia (I) is proportional to the reduced mass of the molecule, which is nearly constant for a diatomic molecule. As a result, the energy difference between adjacent rotational levels is constant, leading to equally spaced lines in the rotational spectrum.
Transition Frequencies:
The transition frequencies between rotational energy levels can be determined using the equation ΔE = E(J+1) - E(J) = 2BJ, where B is the rotational constant. Since the energy difference between adjacent levels is constant, the transition frequencies between these levels will also be constant.
Spectral Lines:
When a molecule undergoes a transition from one rotational energy level to another, it emits or absorbs radiation at a specific frequency. These frequencies correspond to the rotational transition lines in the spectrum. The equally spaced energy levels result in equally spaced spectral lines in the rotational spectrum of gaseous CN.
Conclusion:
In summary, the rotational spectrum of gaseous CN consists of a series of equally spaced lines due to the quantization of rotational energy levels in the molecule. The equally spaced energy levels and transition frequencies between them result in equally spaced spectral lines. This phenomenon can be explained by the principles of quantum mechanics and is a fundamental characteristic of diatomic molecules.
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The rotational spectrum of gaseous CN consist of series of equally? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about The rotational spectrum of gaseous CN consist of series of equally? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The rotational spectrum of gaseous CN consist of series of equally?.
The rotational spectrum of gaseous CN consist of series of equally? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about The rotational spectrum of gaseous CN consist of series of equally? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The rotational spectrum of gaseous CN consist of series of equally?.
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