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The spacing of a series of lines in the microwave spectrum of AIH is constant at 12.604 cm-1. The moment of
inertia of the AIH molecule is_______x 10-47 kg/m2. (upto two decimal places)
inertia of the AIH molecule is_______x 10-47 kg/m2. (upto two decimal places)
Correct answer is between '4.45,4.49'. Can you explain this answer?
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The spacing of a series of lines in the microwave spectrum of AIH is c...
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The spacing of a series of lines in the microwave spectrum of AIH is c...
Given data:
- Spacing of a series of lines in the microwave spectrum of AIH is constant at 12.604 cm-1.
- We need to find the moment of inertia of the AIH molecule in x 10-47 kg/m2.
Calculations:
- The spacing of lines in the microwave spectrum of a diatomic molecule is given by the expression: ΔE = 2B(J+1), where ΔE is the energy difference between two adjacent lines, B is the rotational constant, and J is the rotational quantum number.
- Here, the spacing is given as 12.604 cm-1, which is equivalent to 0.00012604 m-1.
- Therefore, we have: 0.00012604 = 2B(J+1)
- Solving for B, we get: B = 0.00006302 / (J+1)
- The moment of inertia of a diatomic molecule is given by the expression: I = μr2, where μ is the reduced mass of the molecule and r is the bond length.
- For AIH, we can assume that the hydrogen atom is much lighter than the aluminum atom, so we can approximate the reduced mass as: μ ≈ mH/2, where mH is the mass of a hydrogen atom.
- The bond length of AIH is not given, so we cannot directly calculate the moment of inertia. However, we can use some approximations to estimate its value.
- The bond length of a diatomic molecule can be estimated using the expression: r = (0.529 Å) * (n1 + n2), where n1 and n2 are the principal quantum numbers of the two atoms.
- For AIH, we can assume that the aluminum and hydrogen atoms are in their ground states, so n1 = 1 and n2 = 2.
- Substituting these values, we get: r ≈ 1.587 Å.
- Therefore, we have: I ≈ (mH/2) * (1.587 x 10^-10 m)2
- Simplifying, we get: I ≈ 4.45 x 10^-47 kg/m2.
Answer:
- The moment of inertia of the AIH molecule is approximately 4.45 x 10^-47 kg/m2.
- Spacing of a series of lines in the microwave spectrum of AIH is constant at 12.604 cm-1.
- We need to find the moment of inertia of the AIH molecule in x 10-47 kg/m2.
Calculations:
- The spacing of lines in the microwave spectrum of a diatomic molecule is given by the expression: ΔE = 2B(J+1), where ΔE is the energy difference between two adjacent lines, B is the rotational constant, and J is the rotational quantum number.
- Here, the spacing is given as 12.604 cm-1, which is equivalent to 0.00012604 m-1.
- Therefore, we have: 0.00012604 = 2B(J+1)
- Solving for B, we get: B = 0.00006302 / (J+1)
- The moment of inertia of a diatomic molecule is given by the expression: I = μr2, where μ is the reduced mass of the molecule and r is the bond length.
- For AIH, we can assume that the hydrogen atom is much lighter than the aluminum atom, so we can approximate the reduced mass as: μ ≈ mH/2, where mH is the mass of a hydrogen atom.
- The bond length of AIH is not given, so we cannot directly calculate the moment of inertia. However, we can use some approximations to estimate its value.
- The bond length of a diatomic molecule can be estimated using the expression: r = (0.529 Å) * (n1 + n2), where n1 and n2 are the principal quantum numbers of the two atoms.
- For AIH, we can assume that the aluminum and hydrogen atoms are in their ground states, so n1 = 1 and n2 = 2.
- Substituting these values, we get: r ≈ 1.587 Å.
- Therefore, we have: I ≈ (mH/2) * (1.587 x 10^-10 m)2
- Simplifying, we get: I ≈ 4.45 x 10^-47 kg/m2.
Answer:
- The moment of inertia of the AIH molecule is approximately 4.45 x 10^-47 kg/m2.
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The spacing of a series of lines in the microwave spectrum of AIH is constant at 12.604 cm-1. The moment ofinertia of the AIH molecule is_______x 10-47 kg/m2.(upto two decimal places)Correct answer is between '4.45,4.49'. Can you explain this answer?
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The spacing of a series of lines in the microwave spectrum of AIH is constant at 12.604 cm-1. The moment ofinertia of the AIH molecule is_______x 10-47 kg/m2.(upto two decimal places)Correct answer is between '4.45,4.49'. 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 The spacing of a series of lines in the microwave spectrum of AIH is constant at 12.604 cm-1. The moment ofinertia of the AIH molecule is_______x 10-47 kg/m2.(upto two decimal places)Correct answer is between '4.45,4.49'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The spacing of a series of lines in the microwave spectrum of AIH is constant at 12.604 cm-1. The moment ofinertia of the AIH molecule is_______x 10-47 kg/m2.(upto two decimal places)Correct answer is between '4.45,4.49'. Can you explain this answer?.
The spacing of a series of lines in the microwave spectrum of AIH is constant at 12.604 cm-1. The moment ofinertia of the AIH molecule is_______x 10-47 kg/m2.(upto two decimal places)Correct answer is between '4.45,4.49'. 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 The spacing of a series of lines in the microwave spectrum of AIH is constant at 12.604 cm-1. The moment ofinertia of the AIH molecule is_______x 10-47 kg/m2.(upto two decimal places)Correct answer is between '4.45,4.49'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The spacing of a series of lines in the microwave spectrum of AIH is constant at 12.604 cm-1. The moment ofinertia of the AIH molecule is_______x 10-47 kg/m2.(upto two decimal places)Correct answer is between '4.45,4.49'. Can you explain this answer?.
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