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For a diatomic molecule AB, the energy for the rotational transition from J = 0 to J = 1 state is 3.9 cm-1. The energy for rotational transition from J = 3 to J = 4 state would be (a) 3,9 cm-1 (b) 7.8 cm-1 (15.6 cm-1 (d) 11.7 cm-1?
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For a diatomic molecule AB, the energy for the rotational transition f...
Rotational Transitions in Diatomic Molecules
Rotational transitions in diatomic molecules occur when the molecule changes its rotational energy level. These transitions are quantized, meaning that the energy difference between two rotational states is discrete and can be measured in units of cm-1.
Given Information
- Initial state: J = 0
- Final state: J = 1
- Energy for rotational transition from J = 0 to J = 1: 3.9 cm-1
Determining the Energy for the J = 3 to J = 4 Transition
To determine the energy for the rotational transition from J = 3 to J = 4, we need to understand the relationship between the rotational energy levels in a diatomic molecule.
In a diatomic molecule, the rotational energy levels are given by the expression:
E(J) = B * J * (J + 1)
where E(J) is the energy of the Jth rotational level, B is the rotational constant, and J is the rotational quantum number.
Calculating the Rotational Constant
To calculate the rotational constant (B), we can use the given information about the energy for a transition from J = 0 to J = 1.
Using the expression for the energy levels, we can write:
E(J=1) - E(J=0) = B * (1 * (1 + 1)) - B * (0 * (0 + 1))
3.9 cm-1 = B * (2 - 0)
3.9 cm-1 = 2B
B = 3.9 cm-1 / 2
B = 1.95 cm-1
Calculating the Energy for the J = 3 to J = 4 Transition
Using the rotational constant (B) we calculated, we can now determine the energy for the J = 3 to J = 4 transition.
E(J=4) - E(J=3) = B * (4 * (4 + 1)) - B * (3 * (3 + 1))
E(J=4) - E(J=3) = B * (20 - 9)
E(J=4) - E(J=3) = 11B
E(J=4) - E(J=3) = 11 * 1.95 cm-1
E(J=4) - E(J=3) = 21.45 cm-1
Therefore, the energy for the rotational transition from J = 3 to J = 4 state is 21.45 cm-1.
Answer
The correct option is (d) 11.7 cm-1.
Rotational transitions in diatomic molecules occur when the molecule changes its rotational energy level. These transitions are quantized, meaning that the energy difference between two rotational states is discrete and can be measured in units of cm-1.
Given Information
- Initial state: J = 0
- Final state: J = 1
- Energy for rotational transition from J = 0 to J = 1: 3.9 cm-1
Determining the Energy for the J = 3 to J = 4 Transition
To determine the energy for the rotational transition from J = 3 to J = 4, we need to understand the relationship between the rotational energy levels in a diatomic molecule.
In a diatomic molecule, the rotational energy levels are given by the expression:
E(J) = B * J * (J + 1)
where E(J) is the energy of the Jth rotational level, B is the rotational constant, and J is the rotational quantum number.
Calculating the Rotational Constant
To calculate the rotational constant (B), we can use the given information about the energy for a transition from J = 0 to J = 1.
Using the expression for the energy levels, we can write:
E(J=1) - E(J=0) = B * (1 * (1 + 1)) - B * (0 * (0 + 1))
3.9 cm-1 = B * (2 - 0)
3.9 cm-1 = 2B
B = 3.9 cm-1 / 2
B = 1.95 cm-1
Calculating the Energy for the J = 3 to J = 4 Transition
Using the rotational constant (B) we calculated, we can now determine the energy for the J = 3 to J = 4 transition.
E(J=4) - E(J=3) = B * (4 * (4 + 1)) - B * (3 * (3 + 1))
E(J=4) - E(J=3) = B * (20 - 9)
E(J=4) - E(J=3) = 11B
E(J=4) - E(J=3) = 11 * 1.95 cm-1
E(J=4) - E(J=3) = 21.45 cm-1
Therefore, the energy for the rotational transition from J = 3 to J = 4 state is 21.45 cm-1.
Answer
The correct option is (d) 11.7 cm-1.
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For a diatomic molecule AB, the energy for the rotational transition from J = 0 to J = 1 state is 3.9 cm-1. The energy for rotational transition from J = 3 to J = 4 state would be (a) 3,9 cm-1 (b) 7.8 cm-1 (15.6 cm-1 (d) 11.7 cm-1?
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For a diatomic molecule AB, the energy for the rotational transition from J = 0 to J = 1 state is 3.9 cm-1. The energy for rotational transition from J = 3 to J = 4 state would be (a) 3,9 cm-1 (b) 7.8 cm-1 (15.6 cm-1 (d) 11.7 cm-1? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about For a diatomic molecule AB, the energy for the rotational transition from J = 0 to J = 1 state is 3.9 cm-1. The energy for rotational transition from J = 3 to J = 4 state would be (a) 3,9 cm-1 (b) 7.8 cm-1 (15.6 cm-1 (d) 11.7 cm-1? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a diatomic molecule AB, the energy for the rotational transition from J = 0 to J = 1 state is 3.9 cm-1. The energy for rotational transition from J = 3 to J = 4 state would be (a) 3,9 cm-1 (b) 7.8 cm-1 (15.6 cm-1 (d) 11.7 cm-1?.
For a diatomic molecule AB, the energy for the rotational transition from J = 0 to J = 1 state is 3.9 cm-1. The energy for rotational transition from J = 3 to J = 4 state would be (a) 3,9 cm-1 (b) 7.8 cm-1 (15.6 cm-1 (d) 11.7 cm-1? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about For a diatomic molecule AB, the energy for the rotational transition from J = 0 to J = 1 state is 3.9 cm-1. The energy for rotational transition from J = 3 to J = 4 state would be (a) 3,9 cm-1 (b) 7.8 cm-1 (15.6 cm-1 (d) 11.7 cm-1? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a diatomic molecule AB, the energy for the rotational transition from J = 0 to J = 1 state is 3.9 cm-1. The energy for rotational transition from J = 3 to J = 4 state would be (a) 3,9 cm-1 (b) 7.8 cm-1 (15.6 cm-1 (d) 11.7 cm-1?.
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