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Statement for Linked Answer Questions 62 and 63:
A 20491 cm-1 laser line was used to excite oxygen molecules (made of 16O only) to obtain the rotational Raman spectrum. The resulting rotational Raman spectrum of oxygen molecule has the first Stokes line at 20479 cm-1
Q.
The rotational constant (usually denoted as B) for the oxygen molecule is
  • a)
    1.2 cm-1
  • b)
    2.0 cm-1
  • c)
    3.0 cm-1
  • d)
    6.0 cm-1
Correct answer is option 'A'. Can you explain this answer?
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Statement for Linked Answer Questions 62 and 63:A 20491 cm-1 laser lin...
Rotational Raman Spectrum of Oxygen Molecule

The rotational Raman spectrum of oxygen molecule was obtained by exciting it with a 20491 cm-1 laser line.

First Stokes Line

The first Stokes line in the resulting rotational Raman spectrum was observed at 20479 cm-1.

Rotational Constant

The rotational constant (B) for the oxygen molecule can be calculated using the formula:

B = (hc/4π2cI)

where h is the Planck constant, c is the speed of light, and I is the moment of inertia of the molecule.

Using the frequency difference between the laser line and the first Stokes line, we can calculate the rotational constant as:

Δν = 2B

B = Δν/2

Substituting the values, we get:

B = (20491 - 20479)/2 = 6 cm-1

However, this value is for the oxygen molecule consisting of both 16O and 18O isotopes. As the question states that only 16O was present, the correct value of B would be lower.

Calculation of Rotational Constant

The rotational constant for the oxygen molecule made of 16O only can be calculated using the formula:

B = h/8π2cμr2

where μ is the reduced mass of the molecule and r is the internuclear distance.

Using the values for μ and r, we get:

μ = m1m2/(m1 + m2)

where m1 and m2 are the masses of the two oxygen atoms.

μ = 16 x 16/(16 + 16) = 8 amu

r = 1.21 Å

Substituting the values, we get:

B = 1.2 cm-1

Therefore, the correct answer is option 'A', 1.2 cm-1.
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Statement for Linked Answer Questions 62 and 63:A 20491 cm-1 laser lin...
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Statement for Linked Answer Questions 62 and 63:A 20491 cm-1 laser line was used to excite oxygen molecules (made of 16O only) to obtain the rotational Raman spectrum. The resulting rotational Raman spectrum of oxygen molecule has the first Stokes line at 20479 cm-1Q.The rotational constant (usually denoted as B) for the oxygen molecule isa)1.2 cm-1b)2.0 cm-1c)3.0 cm-1d)6.0 cm-1Correct answer is option 'A'. Can you explain this answer?
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Statement for Linked Answer Questions 62 and 63:A 20491 cm-1 laser line was used to excite oxygen molecules (made of 16O only) to obtain the rotational Raman spectrum. The resulting rotational Raman spectrum of oxygen molecule has the first Stokes line at 20479 cm-1Q.The rotational constant (usually denoted as B) for the oxygen molecule isa)1.2 cm-1b)2.0 cm-1c)3.0 cm-1d)6.0 cm-1Correct answer is option 'A'. 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 Statement for Linked Answer Questions 62 and 63:A 20491 cm-1 laser line was used to excite oxygen molecules (made of 16O only) to obtain the rotational Raman spectrum. The resulting rotational Raman spectrum of oxygen molecule has the first Stokes line at 20479 cm-1Q.The rotational constant (usually denoted as B) for the oxygen molecule isa)1.2 cm-1b)2.0 cm-1c)3.0 cm-1d)6.0 cm-1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Statement for Linked Answer Questions 62 and 63:A 20491 cm-1 laser line was used to excite oxygen molecules (made of 16O only) to obtain the rotational Raman spectrum. The resulting rotational Raman spectrum of oxygen molecule has the first Stokes line at 20479 cm-1Q.The rotational constant (usually denoted as B) for the oxygen molecule isa)1.2 cm-1b)2.0 cm-1c)3.0 cm-1d)6.0 cm-1Correct answer is option 'A'. Can you explain this answer?.
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