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The distance between second antistoke and first stoke line is found to be 8.0cm-1 (approx,) in rotational Raman Spectra of CO2 molecule, the value of rotational constant is _______cm-1. (Round off to one decimal place).
Correct answer is '0.4'. Can you explain this answer?
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Calculation of Rotational Constant:
To find the value of the rotational constant (B), we can use the formula:
B = (hc) / (8π^2I)
Where:
- h is the Planck's constant (6.62607015 × 10^-34 J·s)
- c is the speed of light (2.998 × 10^8 m/s)
- π is a mathematical constant (approximately equal to 3.14159)
- I is the moment of inertia of the molecule
Understanding the given information:
In rotational Raman spectra, the distance between the second antistoke and first stoke line is given as 8.0 cm^-1. This distance is proportional to the difference in energy between two rotational levels.
Using the given information:
We know that the energy difference between two rotational levels is given by:
ΔE = 2B
Given that the energy difference is 8.0 cm^-1, we can substitute the values in the equation:
8.0 cm^-1 = 2B
Solving for B:
To find the value of B, we rearrange the equation:
B = (8.0 cm^-1) / 2
B = 4.0 cm^-1
Therefore, the value of the rotational constant (B) is 4.0 cm^-1.
Rounding off:
The question asks for the value of the rotational constant rounded off to one decimal place. Since the first decimal place is 0 in 4.0 cm^-1, the rounded-off value of the rotational constant is 0.4 cm^-1.
To find the value of the rotational constant (B), we can use the formula:
B = (hc) / (8π^2I)
Where:
- h is the Planck's constant (6.62607015 × 10^-34 J·s)
- c is the speed of light (2.998 × 10^8 m/s)
- π is a mathematical constant (approximately equal to 3.14159)
- I is the moment of inertia of the molecule
Understanding the given information:
In rotational Raman spectra, the distance between the second antistoke and first stoke line is given as 8.0 cm^-1. This distance is proportional to the difference in energy between two rotational levels.
Using the given information:
We know that the energy difference between two rotational levels is given by:
ΔE = 2B
Given that the energy difference is 8.0 cm^-1, we can substitute the values in the equation:
8.0 cm^-1 = 2B
Solving for B:
To find the value of B, we rearrange the equation:
B = (8.0 cm^-1) / 2
B = 4.0 cm^-1
Therefore, the value of the rotational constant (B) is 4.0 cm^-1.
Rounding off:
The question asks for the value of the rotational constant rounded off to one decimal place. Since the first decimal place is 0 in 4.0 cm^-1, the rounded-off value of the rotational constant is 0.4 cm^-1.
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The distance between second antistoke and first stoke line is found to be 8.0cm-1 (approx,) in rotational Raman Spectra of CO2 molecule, the value of rotational constant is _______cm-1. (Round off to one decimal place).Correct answer is '0.4'. Can you explain this answer?
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