Vibrational Quantum Number using Vibrational Wavenumber Calculator

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Physical spectroscopy

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Vibrational Spectroscopy

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Important formulae on Vibrational Spectroscopy

Vibrational energy levels

✖Vibrational Energy is the total energy of the respective rotation-vibration levels of a diatomic molecule.ⓘ Vibrational Energy [E_vf]			+10% -10%
✖Vibrational Wavenumber is simply the harmonic vibrational frequency or energy expressed in units of cm inverse.ⓘ Vibrational Wavenumber [ω']			+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 Vibrational Wavenumber [v]

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Formula

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Vibrational Quantum Number using Vibrational Wavenumber

Formula

`"v" = ("E"_{"vf"}/"[hP]"*"ω'")-1/2`

Example

`"2.3E^36"=("100J"/"[hP]"*"15/m")-1/2`

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Vibrational Quantum Number using Vibrational Wavenumber Solution

STEP 0: Pre-Calculation Summary

Formula Used

Vibrational Quantum Number = (Vibrational Energy/[hP]*Vibrational Wavenumber)-1/2
v = (E_vf/[hP]*ω')-1/2
This formula uses 1 Constants, 3 Variables

Constants Used

[hP] - Planck constant Value Taken As 6.626070040E-34

Variables Used

Vibrational Quantum Number - Vibrational quantum number describes values of conserved quantities in the dynamics of a quantum system in a diatomic molecule.
Vibrational Energy - (Measured in Joule) - Vibrational Energy is the total energy of the respective rotation-vibration levels of a diatomic molecule.
Vibrational Wavenumber - (Measured in Diopter) - Vibrational Wavenumber is simply the harmonic vibrational frequency or energy expressed in units of cm inverse.

STEP 1: Convert Input(s) to Base Unit

Vibrational Energy: 100 Joule --> 100 Joule No Conversion Required
Vibrational Wavenumber: 15 1 per Meter --> 15 Diopter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v = (E_vf/[hP]*ω')-1/2 --> (100/[hP]*15)-1/2

Evaluating ... ...

v = 2.26378530704454E+36

STEP 3: Convert Result to Output's Unit

2.26378530704454E+36 --> No Conversion Required

FINAL ANSWER

2.26378530704454E+36 ≈ 2.3E+36 <-- Vibrational Quantum Number

(Calculation completed in 00.004 seconds)

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Credits

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

Pragati Jaju has verified this Calculator and 300+ more calculators!

< 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

< 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 Vibrational Wavenumber Formula

Vibrational Quantum Number = (Vibrational Energy/[hP]*Vibrational Wavenumber)-1/2
v = (E_vf/[hP]*ω')-1/2

What is vibrational energy?

Vibrational spectroscopy looks at the differences in energy between the vibrational modes of a molecule. These are larger than the rotational energy states. This spectroscopy can provide a direct measure of bond strength. The vibration energy levels can be explained using diatomic molecules.
To a first approximation, molecular vibrations can be approximated as simple harmonic oscillators, with an associated energy known as vibrational energy.

How to Calculate Vibrational Quantum Number using Vibrational Wavenumber?

Vibrational Quantum Number using Vibrational Wavenumber calculator uses Vibrational Quantum Number = (Vibrational Energy/[hP]*Vibrational Wavenumber)-1/2 to calculate the Vibrational Quantum Number, The Vibrational quantum number using vibrational wavenumber 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 Vibrational Wavenumber using this online calculator? To use this online calculator for Vibrational Quantum Number using Vibrational Wavenumber, enter Vibrational Energy (E_vf) & Vibrational Wavenumber (ω') and hit the calculate button. Here is how the Vibrational Quantum Number using Vibrational Wavenumber calculation can be explained with given input values -> 2.3E+36 = (100/[hP]*15)-1/2.

FAQ

What is Vibrational Quantum Number using Vibrational Wavenumber?

The Vibrational quantum number using vibrational wavenumber 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 = (E_vf/[hP]*ω')-1/2 or Vibrational Quantum Number = (Vibrational Energy/[hP]*Vibrational Wavenumber)-1/2. Vibrational Energy is the total energy of the respective rotation-vibration levels of a diatomic molecule & Vibrational Wavenumber is simply the harmonic vibrational frequency or energy expressed in units of cm inverse.

How to calculate Vibrational Quantum Number using Vibrational Wavenumber?

The Vibrational quantum number using vibrational wavenumber 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 = (Vibrational Energy/[hP]*Vibrational Wavenumber)-1/2. To calculate Vibrational Quantum Number using Vibrational Wavenumber, you need Vibrational Energy (E_vf) & Vibrational Wavenumber (ω'). With our tool, you need to enter the respective value for Vibrational Energy & Vibrational Wavenumber 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 Vibrational Energy & Vibrational Wavenumber. We can use 4 other way(s) to calculate the same, which is/are as follows -

Vibrational Quantum Number = ((Rotational Constant vib-Rotational Constant Equilibrium)/Anharmonic Potential Constant)-1/2
Vibrational Quantum Number = (Vibrational Energy/([hP]*Vibrational Frequency))-1/2
Vibrational Quantum Number = (Vibrational Energy/([hP]*Vibrational Frequency))-1/2
Vibrational Quantum Number = ((Rotational Constant vib-Rotational Constant Equilibrium)/Anharmonic Potential Constant)-1/2

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