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The absorption lines arising from pure rotational effects of HCl are observed at 83.03 cm−1, 103.73 cm−1, 124.30 cm−1, 145.03 cm−1 and 165.51 cm−1. The moment of inertia of the HCl molecule is: (h=6.626×10−34Js, c=3×1010cm/s)

  • a)
    1.1 × 10−48 kg-m2

  • b)
    2.8 × 10−47 kg-m2

  • c)
    2.8 × 10−48 kg-m2

  • d)
    1.1 × 10−42 kg-m2

Correct answer is option 'B'. Can you explain this answer?
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The absorption lines arising from pure rotational effects of HCl are o...
Concept:
Pure Roatational Motion - The rigid body in such a motion rotates about a fixed axis that is perpendicular to a fixed plane. In other words, the axis is fixed and does not move or change its direction relative to an inertial frame of reference. 2.
Calculation:
2B = 103.73 - 83.03 cm-1 
= 20.70 cm-1
2B = 124.30 - 103.73 cm-1
= 20.57 cm-1
2B = 145.03 - 124.30 cm-1
= 20.73 cm-1
2B = 165.51 - 145.03 cm-1
= 20.48 cm-1
Average value 2B = 62.00/3 = 20.67 cm-1
B = 10.33 cm-1
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The absorption lines arising from pure rotational effects of HCl are o...
Understanding Rotational Spectroscopy
Rotational absorption lines in a molecule provide crucial information about its moment of inertia. For a diatomic molecule like HCl, the energy levels of pure rotational motion can be described by the formula:
E(J) = hB * J(J + 1)
where:
- E(J) is the energy of the rotational level,
- J is the rotational quantum number (0, 1, 2,...),
- B is the rotational constant, and
- h is Planck's constant.
Calculating Rotational Constant (B)
The observed spectral lines correspond to different J values:
- For J = 0: E(0) = 0
- For J = 1: E(1) = hB * 1(1 + 1) = 2hB
- For J = 2: E(2) = hB * 2(2 + 1) = 6hB
- For J = 3: E(3) = hB * 3(3 + 1) = 12hB
- For J = 4: E(4) = hB * 4(4 + 1) = 20hB
The difference between energy levels gives us the rotational constant:
- ΔE(1→2) = E(2) - E(1) = 4hB
- ΔE(2→3) = E(3) - E(2) = 6hB
- ΔE(3→4) = E(4) - E(3) = 8hB
From the given absorption lines, you can find the differences in wavenumbers:
Observed Absorption Lines
- 103.73 cm-1 - 83.03 cm-1 = 20.70 cm-1
- 124.30 cm-1 - 103.73 cm-1 = 20.57 cm-1
- 145.03 cm-1 - 124.30 cm-1 = 20.73 cm-1
- 165.51 cm-1 - 145.03 cm-1 = 20.48 cm-1
Taking an average gives an approximate value for B.
Calculating Moment of Inertia (I)
The rotational constant B is related to the moment of inertia I by the formula:
B = h / (4πcI)
Rearranging gives:
I = h / (4πcB)
Using the average value of B obtained from the differences, you can calculate I. After performing the necessary calculations, you will find that:
Final Result
The moment of inertia I is approximately 2.8 × 10^-47 kg-m², confirming that option B is the correct answer.
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The absorption lines arising from pure rotational effects of HCl are observed at 83.03 cm−1, 103.73 cm−1, 124.30 cm−1, 145.03 cm−1and 165.51 cm−1. The moment of inertia of the HCl molecule is: (h=6.626×10−34Js,c=3×1010cm/s)a)1.1 × 10−48kg-m2b)2.8 × 10−47kg-m2c)2.8 × 10−48kg-m2d)1.1 × 10−42kg-m2Correct answer is option 'B'. Can you explain this answer?
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The absorption lines arising from pure rotational effects of HCl are observed at 83.03 cm−1, 103.73 cm−1, 124.30 cm−1, 145.03 cm−1and 165.51 cm−1. The moment of inertia of the HCl molecule is: (h=6.626×10−34Js,c=3×1010cm/s)a)1.1 × 10−48kg-m2b)2.8 × 10−47kg-m2c)2.8 × 10−48kg-m2d)1.1 × 10−42kg-m2Correct answer is option 'B'. Can you explain this answer? for UGC NET 2025 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about The absorption lines arising from pure rotational effects of HCl are observed at 83.03 cm−1, 103.73 cm−1, 124.30 cm−1, 145.03 cm−1and 165.51 cm−1. The moment of inertia of the HCl molecule is: (h=6.626×10−34Js,c=3×1010cm/s)a)1.1 × 10−48kg-m2b)2.8 × 10−47kg-m2c)2.8 × 10−48kg-m2d)1.1 × 10−42kg-m2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UGC NET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The absorption lines arising from pure rotational effects of HCl are observed at 83.03 cm−1, 103.73 cm−1, 124.30 cm−1, 145.03 cm−1and 165.51 cm−1. The moment of inertia of the HCl molecule is: (h=6.626×10−34Js,c=3×1010cm/s)a)1.1 × 10−48kg-m2b)2.8 × 10−47kg-m2c)2.8 × 10−48kg-m2d)1.1 × 10−42kg-m2Correct answer is option 'B'. Can you explain this answer?.
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