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For a diatomic vibrating rotor, in vibrational level u = 3 and rotational level J, the sum of the rotational and vibrational energies is 11493.6 cm–1. Its equilibrium oscillation frequency is 2998.3 cm–1, anharmonicity constant is 0.0124 and rotational constant under rigid rotor approximation is 9.716 cm–1. The value of J is ___________. (Up to nearest integer)
Correct answer is '12 to 12'. Can you explain this answer?
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For a diatomic vibrating rotor, in vibrational level u = 3 and rotatio...
-1.
To solve this problem, we need to use the expression for the total energy of a diatomic vibrating rotor:
E = (J + 1/2)hBarω + (u + 1/2)hBarωe
where J is the rotational quantum number, u is the vibrational quantum number, hBar is the reduced Planck constant, ω is the rotational constant, and ωe is the vibrational constant.
We are given that u = 3 and the sum of the rotational and vibrational energies is 11493.6 cm-1. We can rewrite the expression above as:
E = JhBarω + (1/2)hBarω + 3hBarωe + (1/2)hBarωe
Substituting the given values and solving for J, we get:
11493.6 cm-1 = J(1.98630 x 10^-23 J·s) + (9.4426 x 10^-21 J) + 3(498.30 cm-1) + (1241.4 cm-1)
J = 19.78
Therefore, the rotational quantum number is J = 19.78.
To solve this problem, we need to use the expression for the total energy of a diatomic vibrating rotor:
E = (J + 1/2)hBarω + (u + 1/2)hBarωe
where J is the rotational quantum number, u is the vibrational quantum number, hBar is the reduced Planck constant, ω is the rotational constant, and ωe is the vibrational constant.
We are given that u = 3 and the sum of the rotational and vibrational energies is 11493.6 cm-1. We can rewrite the expression above as:
E = JhBarω + (1/2)hBarω + 3hBarωe + (1/2)hBarωe
Substituting the given values and solving for J, we get:
11493.6 cm-1 = J(1.98630 x 10^-23 J·s) + (9.4426 x 10^-21 J) + 3(498.30 cm-1) + (1241.4 cm-1)
J = 19.78
Therefore, the rotational quantum number is J = 19.78.
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For a diatomic vibrating rotor, in vibrational level u = 3 and rotational level J, the sum of the rotational and vibrational energies is 11493.6 cm–1. Its equilibrium oscillation frequency is 2998.3 cm–1, anharmonicity constant is 0.0124 and rotational constant under rigid rotor approximation is 9.716 cm–1. The value of J is ___________. (Up to nearest integer)Correct answer is '12 to 12'. Can you explain this answer?
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For a diatomic vibrating rotor, in vibrational level u = 3 and rotational level J, the sum of the rotational and vibrational energies is 11493.6 cm–1. Its equilibrium oscillation frequency is 2998.3 cm–1, anharmonicity constant is 0.0124 and rotational constant under rigid rotor approximation is 9.716 cm–1. The value of J is ___________. (Up to nearest integer)Correct answer is '12 to 12'. 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 For a diatomic vibrating rotor, in vibrational level u = 3 and rotational level J, the sum of the rotational and vibrational energies is 11493.6 cm–1. Its equilibrium oscillation frequency is 2998.3 cm–1, anharmonicity constant is 0.0124 and rotational constant under rigid rotor approximation is 9.716 cm–1. The value of J is ___________. (Up to nearest integer)Correct answer is '12 to 12'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a diatomic vibrating rotor, in vibrational level u = 3 and rotational level J, the sum of the rotational and vibrational energies is 11493.6 cm–1. Its equilibrium oscillation frequency is 2998.3 cm–1, anharmonicity constant is 0.0124 and rotational constant under rigid rotor approximation is 9.716 cm–1. The value of J is ___________. (Up to nearest integer)Correct answer is '12 to 12'. Can you explain this answer?.
For a diatomic vibrating rotor, in vibrational level u = 3 and rotational level J, the sum of the rotational and vibrational energies is 11493.6 cm–1. Its equilibrium oscillation frequency is 2998.3 cm–1, anharmonicity constant is 0.0124 and rotational constant under rigid rotor approximation is 9.716 cm–1. The value of J is ___________. (Up to nearest integer)Correct answer is '12 to 12'. 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 For a diatomic vibrating rotor, in vibrational level u = 3 and rotational level J, the sum of the rotational and vibrational energies is 11493.6 cm–1. Its equilibrium oscillation frequency is 2998.3 cm–1, anharmonicity constant is 0.0124 and rotational constant under rigid rotor approximation is 9.716 cm–1. The value of J is ___________. (Up to nearest integer)Correct answer is '12 to 12'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a diatomic vibrating rotor, in vibrational level u = 3 and rotational level J, the sum of the rotational and vibrational energies is 11493.6 cm–1. Its equilibrium oscillation frequency is 2998.3 cm–1, anharmonicity constant is 0.0124 and rotational constant under rigid rotor approximation is 9.716 cm–1. The value of J is ___________. (Up to nearest integer)Correct answer is '12 to 12'. Can you explain this answer?.
Solutions for For a diatomic vibrating rotor, in vibrational level u = 3 and rotational level J, the sum of the rotational and vibrational energies is 11493.6 cm–1. Its equilibrium oscillation frequency is 2998.3 cm–1, anharmonicity constant is 0.0124 and rotational constant under rigid rotor approximation is 9.716 cm–1. The value of J is ___________. (Up to nearest integer)Correct answer is '12 to 12'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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