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Rotational Constant for Vibrational State Calculator

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Important formulae on Vibrational Spectroscopy Vibrational energy levels

✖Rotational Constant Equilibrium is the rotational constant corresponding to the equilibrium geometry of the molecule.ⓘ Rotational Constant Equilibrium [B_e]			+10% -10%
✖Anharmonic Potential Constant is a constant determined by the shape of the Anharmonic potential of a molecule in vibrational state.ⓘ Anharmonic Potential Constant [α_e]			+10% -10%
✖Vibrational quantum number describes values of conserved quantities in the dynamics of a quantum system in a diatomic molecule.ⓘ Vibrational Quantum Number [v]			+10% -10%

✖Rotational Constant vib is the rotational constant for a given vibrational state of a diatomic molecule.ⓘ Rotational Constant for Vibrational State [B_v]

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Formula

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Rotational Constant for Vibrational State

Formula

B v = B e + (α e \cdot (v + \frac{1}{2}))

Example

35 /m = 20 m⁻¹ + (6 \cdot (2 + \frac{1}{2}))

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Rotational Constant for Vibrational State Solution

STEP 0: Pre-Calculation Summary

Formula Used

Rotational Constant vib = Rotational Constant Equilibrium+(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))
B_v = B_e+(α_e*(v+1/2))
This formula uses 4 Variables

Variables Used

Rotational Constant vib - (Measured in Diopter) - Rotational Constant vib is the rotational constant for a given vibrational state of a diatomic molecule.
Rotational Constant Equilibrium - (Measured in Per Meter) - Rotational Constant Equilibrium is the rotational constant corresponding to the equilibrium geometry of the molecule.
Anharmonic Potential Constant - Anharmonic Potential Constant is a constant determined by the shape of the Anharmonic potential of a molecule in vibrational state.
Vibrational Quantum Number - Vibrational quantum number describes values of conserved quantities in the dynamics of a quantum system in a diatomic molecule.

STEP 1: Convert Input(s) to Base Unit

Rotational Constant Equilibrium: 20 Per Meter --> 20 Per Meter No Conversion Required
Anharmonic Potential Constant: 6 --> No Conversion Required
Vibrational Quantum Number: 2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

B_v = B_e+(α_e*(v+1/2)) --> 20+(6*(2+1/2))

Evaluating ... ...

B_v = 35

STEP 3: Convert Result to Output's Unit

35 Diopter -->35 1 per Meter (Check conversion here)

FINAL ANSWER

35 1 per Meter <-- Rotational Constant vib

(Calculation completed in 00.004 seconds)

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Created by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

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< Vibrational Spectroscopy Calculators

Anharmonic Potential Constant

Go Anharmonic Potential Constant = (Rotational Constant vib-Rotational Constant Equilibrium)/(Vibrational Quantum Number+1/2)

Anharmonicity Constant given Fundamental Frequency

Go Anharmonicity Constant = (Vibration Frequency-Fundamental Frequency)/(2*Vibration Frequency)

Anharmonicity Constant given Second Overtone Frequency

Go Anharmonicity Constant = 1/4*(1-(Second Overtone Frequency/(3*Vibrational Frequency)))

Anharmonicity Constant given First Overtone Frequency

Go Anharmonicity Constant = 1/3*(1-(First Overtone Frequency/(2*Vibrational Frequency)))

< Important formulae on Vibrational Spectroscopy Calculators

Rotational Constant for Vibrational State

Go Rotational Constant vib = Rotational Constant Equilibrium+(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))

Anharmonicity Constant given First Overtone Frequency

Go Anharmonicity Constant = 1/3*(1-(First Overtone Frequency/(2*Vibrational Frequency)))

First Overtone Frequency

Go First Overtone Frequency = (2*Vibrational Frequency)*(1-3*Anharmonicity Constant)

Fundamental Frequency of Vibrational Transitions

Go Fundamental Frequency = Vibrational Frequency*(1-2*Anharmonicity Constant)

< Important Calculators of Vibrational Spectroscopy Calculators

Rotational Constant Related to Equilibrium

Go Rotational Constant Equilibrium = Rotational Constant vib-(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))

Rotational Constant for Vibrational State

Go Rotational Constant vib = Rotational Constant Equilibrium+(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))

Vibrational Quantum Number using Vibrational Frequency

Go Vibrational Quantum Number = (Vibrational Energy/([hP]*Vibrational Frequency))-1/2

Vibrational Quantum Number using Vibrational Wavenumber

Go Vibrational Quantum Number = (Vibrational Energy/[hP]*Vibrational Wavenumber)-1/2

Rotational Constant for Vibrational State Formula

Rotational Constant vib = Rotational Constant Equilibrium+(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))
B_v = B_e+(α_e*(v+1/2))

How do we obtain Rotational constant for vibrational state?

When changing the energy of the vibrational levels, anharmonicity has another, less obvious effect: for a molecule with an Anharmonic potential, the rotational constant changes slightly with vibrational state. The rotational constant for a given vibrational state can be described by the obtained expression, where Be is the rotational constant corresponding to the equilibrium geometry of the molecule, αe is a constant determined by the shape of the Anharmonic potential, and v is the vibrational quantum number.

How to Calculate Rotational Constant for Vibrational State?

Rotational Constant for Vibrational State calculator uses Rotational Constant vib = Rotational Constant Equilibrium+(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2)) to calculate the Rotational Constant vib, The Rotational constant for vibrational state formula is defined for relating in energy and vibrational energy levels in diatomic molecules. Rotational Constant vib is denoted by B_v symbol.

How to calculate Rotational Constant for Vibrational State using this online calculator? To use this online calculator for Rotational Constant for Vibrational State, enter Rotational Constant Equilibrium (B_e), Anharmonic Potential Constant (α_e) & Vibrational Quantum Number (v) and hit the calculate button. Here is how the Rotational Constant for Vibrational State calculation can be explained with given input values -> 35 = 20+(6*(2+1/2)).

FAQ

What is Rotational Constant for Vibrational State?

The Rotational constant for vibrational state formula is defined for relating in energy and vibrational energy levels in diatomic molecules and is represented as B_v = B_e+(α_e*(v+1/2)) or Rotational Constant vib = Rotational Constant Equilibrium+(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2)). Rotational Constant Equilibrium is the rotational constant corresponding to the equilibrium geometry of the molecule, Anharmonic Potential Constant is a constant determined by the shape of the Anharmonic potential of a molecule in vibrational state & Vibrational quantum number describes values of conserved quantities in the dynamics of a quantum system in a diatomic molecule.

How to calculate Rotational Constant for Vibrational State?

The Rotational constant for vibrational state formula is defined for relating in energy and vibrational energy levels in diatomic molecules is calculated using Rotational Constant vib = Rotational Constant Equilibrium+(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2)). To calculate Rotational Constant for Vibrational State, you need Rotational Constant Equilibrium (B_e), Anharmonic Potential Constant (α_e) & Vibrational Quantum Number (v). With our tool, you need to enter the respective value for Rotational Constant Equilibrium, Anharmonic Potential Constant & Vibrational Quantum Number and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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