LCM of two numbers

Vibrational Quantum Number using Rotational Constant Calculator

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Important formulae on Vibrational Spectroscopy Vibrational energy levels

✖Rotational Constant vib is the rotational constant for a given vibrational state of a diatomic molecule.ⓘ Rotational Constant vib [B_v]			+10% -10%
✖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 using Rotational Constant [v]

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Vibrational Quantum Number using Rotational Constant Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Vibrational Quantum Number - Vibrational quantum number describes values of conserved quantities in the dynamics of a quantum system in a diatomic molecule.
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.

STEP 1: Convert Input(s) to Base Unit

Rotational Constant vib: 35 1 per Meter --> 35 Diopter (Check conversion here)
Rotational Constant Equilibrium: 20 Per Meter --> 20 Per Meter No Conversion Required
Anharmonic Potential Constant: 6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v = ((B_v-B_e)/α_e)-1/2 --> ((35-20)/6)-1/2

Evaluating ... ...

v = 2

STEP 3: Convert Result to Output's Unit

2 --> No Conversion Required

FINAL ANSWER

2 <-- Vibrational Quantum Number

(Calculation completed in 00.004 seconds)

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National Institute of Information Technology (NIIT), Neemrana

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< Vibrational Spectroscopy Calculators

Anharmonic Potential Constant

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

Anharmonicity Constant given Fundamental Frequency

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

Anharmonicity Constant given Second Overtone Frequency

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

Anharmonicity Constant given First Overtone Frequency

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

< Important formulae on Vibrational Spectroscopy Calculators

Rotational Constant for Vibrational State

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

Anharmonicity Constant given First Overtone Frequency

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

First Overtone Frequency

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

Fundamental Frequency of Vibrational Transitions

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

< Important Calculators of Vibrational Spectroscopy Calculators

Rotational Constant Related to Equilibrium

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

Rotational Constant for Vibrational State

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

Vibrational Quantum Number using Vibrational Frequency

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

Vibrational Quantum Number using Vibrational Wavenumber

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

Vibrational Quantum Number using Rotational Constant Formula

LaTeX Go

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

How do you obtain Vibrational quantum number using rotational constant?

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.
Vibrational quantum number is obtained when we reframe the expression to obtain the desired output.

How to Calculate Vibrational Quantum Number using Rotational Constant?

Vibrational Quantum Number using Rotational Constant calculator uses Vibrational Quantum Number = ((Rotational Constant vib-Rotational Constant Equilibrium)/Anharmonic Potential Constant)-1/2 to calculate the Vibrational Quantum Number, The Vibrational quantum number using rotational constant formula is defined as a scalar quantum number that defines the energy state of a harmonic or approximately harmonic vibrating diatomic molecule. Vibrational Quantum Number is denoted by v symbol.

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

FAQ

What is Vibrational Quantum Number using Rotational Constant?

The Vibrational quantum number using rotational constant formula is defined as a scalar quantum number that defines the energy state of a harmonic or approximately harmonic vibrating diatomic molecule and is represented as v = ((B_v-B_e)/α_e)-1/2 or Vibrational Quantum Number = ((Rotational Constant vib-Rotational Constant Equilibrium)/Anharmonic Potential Constant)-1/2. Rotational Constant vib is the rotational constant for a given vibrational state of a diatomic molecule, 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.

How to calculate Vibrational Quantum Number using Rotational Constant?

The Vibrational quantum number using rotational constant formula is defined as a scalar quantum number that defines the energy state of a harmonic or approximately harmonic vibrating diatomic molecule is calculated using Vibrational Quantum Number = ((Rotational Constant vib-Rotational Constant Equilibrium)/Anharmonic Potential Constant)-1/2. To calculate Vibrational Quantum Number using Rotational Constant, you need Rotational Constant vib (B_v), Rotational Constant Equilibrium (B_e) & Anharmonic Potential Constant (α_e). With our tool, you need to enter the respective value for Rotational Constant vib, Rotational Constant Equilibrium & Anharmonic Potential Constant and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Vibrational Quantum Number?

In this formula, Vibrational Quantum Number uses Rotational Constant vib, Rotational Constant Equilibrium & Anharmonic Potential Constant. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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