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Vibrational Quantum Number using Rotational Constant Calculator

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✖Rotational Constant vib is the rotational constant for a given vibrational state of a diatomic molecule.ⓘ Rotational Constant vib [Bv]
+10%
-10%
✖Rotational Constant Equilibrium is the rotational constant corresponding to the equilibrium geometry of the molecule.ⓘ Rotational Constant Equilibrium [Be]
+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 [αe]
+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

Formula
`"v" = (("B"_{"v"}-"B"_{"e"})/"α"_{"e"})-1/2`

Example
`"2"=(("35/m"-"20m⁻¹")/"6")-1/2`

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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 = ((Bv-Be)/αe)-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 = ((Bv-Be)/αe)-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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Created by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
Akshada Kulkarni has created this Calculator and 500+ more calculators!
Verified by Pragati Jaju
College Of Engineering (COEP), Pune
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22 Vibrational Spectroscopy Calculators

Maximum Vibrational Number using Anharmonicity Constant
Go Max Vibrational Number = ((Vibrational Wavenumber)^2)/(4*Vibrational Wavenumber*Vibrational Energy*Anharmonicity Constant)
Vibrational Quantum Number using Rotational Constant
Go Vibrational Quantum Number = ((Rotational Constant vib-Rotational Constant Equilibrium)/Anharmonic Potential Constant)-1/2
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))
Anharmonic Potential Constant
Go Anharmonic Potential Constant = (Rotational Constant vib-Rotational Constant Equilibrium)/(Vibrational Quantum Number+1/2)
Maximum Vibrational Quantum Number
Go Max Vibrational Number = (Vibrational Wavenumber/(2*Anharmonicity Constant*Vibrational Wavenumber))-1/2
Anharmonicity Constant given Fundamental Frequency
Go Anharmonicity Constant = (Vibration Frequency-Fundamental Frequency)/(2*Vibration Frequency)
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
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)))
Energy Difference between Two Vibrational States
Go Change in Energy = Equilibrium Vibrational Frequency*(1-(2*Anharmonicity Constant))
Vibrational Frequency given Second Overtone Frequency
Go Vibrational Frequency = Second Overtone Frequency/3*(1-(4*Anharmonicity Constant))
Second Overtone Frequency
Go Second Overtone Frequency = (3*Vibrational Frequency)*(1-4*Anharmonicity Constant)
First Overtone Frequency
Go First Overtone Frequency = (2*Vibrational Frequency)*(1-3*Anharmonicity Constant)
Vibrational Frequency given First Overtone Frequency
Go Vibrational Frequency = First Overtone Frequency/2*(1-3*Anharmonicity Constant)
Vibrational Frequency given Fundamental Frequency
Go Vibrational Frequency = Fundamental Frequency/(1-2*Anharmonicity Constant)
Fundamental Frequency of Vibrational Transitions
Go Fundamental Frequency = Vibrational Frequency*(1-2*Anharmonicity Constant)
Vibrational Degree of Freedom for Nonlinear Molecules
Go Vibrational Degree Nonlinear = (3*Number of Atoms)-6
Vibrational Degree of Freedom for Linear Molecules
Go Vibrational Degree Linear = (3*Number of Atoms)-5
Total Degree of Freedom for Nonlinear Molecules
Go Degree of Freedom Non Linear = 3*Number of Atoms
Total Degree of Freedom for Linear Molecules
Go Degree of Freedom Linear = 3*Number of Atoms

10+ Important formulae on Vibrational Spectroscopy Calculators

Vibrational Quantum Number using Rotational Constant
Go Vibrational Quantum Number = ((Rotational Constant vib-Rotational Constant Equilibrium)/Anharmonic Potential Constant)-1/2
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))
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)
Vibrational Degree of Freedom for Nonlinear Molecules
Go Vibrational Degree Nonlinear = (3*Number of Atoms)-6
Vibrational Degree of Freedom for Linear Molecules
Go Vibrational Degree Linear = (3*Number of Atoms)-5
Total Degree of Freedom for Nonlinear Molecules
Go Degree of Freedom Non Linear = 3*Number of Atoms
Total Degree of Freedom for Linear Molecules
Go Degree of Freedom Linear = 3*Number of Atoms

21 Important Calculators of Vibrational Spectroscopy Calculators

Maximum Vibrational Number using Anharmonicity Constant
Go Max Vibrational Number = ((Vibrational Wavenumber)^2)/(4*Vibrational Wavenumber*Vibrational Energy*Anharmonicity Constant)
Vibrational Quantum Number using Rotational Constant
Go Vibrational Quantum Number = ((Rotational Constant vib-Rotational Constant Equilibrium)/Anharmonic Potential Constant)-1/2
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))
Anharmonic Potential Constant
Go Anharmonic Potential Constant = (Rotational Constant vib-Rotational Constant Equilibrium)/(Vibrational Quantum Number+1/2)
Maximum Vibrational Quantum Number
Go Max Vibrational Number = (Vibrational Wavenumber/(2*Anharmonicity Constant*Vibrational Wavenumber))-1/2
Anharmonicity Constant given Fundamental Frequency
Go Anharmonicity Constant = (Vibration Frequency-Fundamental Frequency)/(2*Vibration Frequency)
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
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)))
Vibrational Frequency given Second Overtone Frequency
Go Vibrational Frequency = Second Overtone Frequency/3*(1-(4*Anharmonicity Constant))
Second Overtone Frequency
Go Second Overtone Frequency = (3*Vibrational Frequency)*(1-4*Anharmonicity Constant)
First Overtone Frequency
Go First Overtone Frequency = (2*Vibrational Frequency)*(1-3*Anharmonicity Constant)
Vibrational Frequency given First Overtone Frequency
Go Vibrational Frequency = First Overtone Frequency/2*(1-3*Anharmonicity Constant)
Vibrational Frequency given Fundamental Frequency
Go Vibrational Frequency = Fundamental Frequency/(1-2*Anharmonicity Constant)
Fundamental Frequency of Vibrational Transitions
Go Fundamental Frequency = Vibrational Frequency*(1-2*Anharmonicity Constant)
Vibrational Degree of Freedom for Nonlinear Molecules
Go Vibrational Degree Nonlinear = (3*Number of Atoms)-6
Vibrational Degree of Freedom for Linear Molecules
Go Vibrational Degree Linear = (3*Number of Atoms)-5
Total Degree of Freedom for Nonlinear Molecules
Go Degree of Freedom Non Linear = 3*Number of Atoms
Total Degree of Freedom for Linear Molecules
Go Degree of Freedom Linear = 3*Number of Atoms

Vibrational Quantum Number using Rotational Constant Formula

Vibrational Quantum Number = ((Rotational Constant vib-Rotational Constant Equilibrium)/Anharmonic Potential Constant)-1/2
v = ((Bv-Be)/αe)-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 (Bv), Rotational Constant Equilibrium (Be) & Anharmonic Potential Constant (αe) 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 = ((Bv-Be)/αe)-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 (Bv), Rotational Constant Equilibrium (Be) & Anharmonic Potential Constant (αe). 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 4 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
  • Vibrational Quantum Number = (Vibrational Energy/[hP]*Vibrational Wavenumber)-1/2
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