Anharmonicity Constant given Fundamental Frequency Calculator

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Important formulae on Vibrational Spectroscopy

Vibrational energy levels

✖Vibration Frequency is the frequency of photons on the excited state.ⓘ Vibration Frequency [v₀]			+10% -10%
✖Fundamental Frequency is the frequency of photons on the fundamental excited state/ overtone band of a diatomic molecule.ⓘ Fundamental Frequency [v_0->1]			+10% -10%

✖Anharmonicity Constant is the deviation of a system from being a harmonic oscillator which is related to the vibrational energy levels of diatomic molecule.ⓘ Anharmonicity Constant given Fundamental Frequency [x_e]

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Formula

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Anharmonicity Constant given Fundamental Frequency

Formula

`"x"_{"e"} = ("v"_{"0"}-"v"_{"0->1"})/(2*"v"_{"0"})`

Example

`"0.497308"=("130Hz"-"0.7Hz")/(2*"130Hz")`

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Anharmonicity Constant given Fundamental Frequency Solution

STEP 0: Pre-Calculation Summary

Formula Used

Anharmonicity Constant = (Vibration Frequency-Fundamental Frequency)/(2*Vibration Frequency)
x_e = (v₀-v_0->1)/(2*v₀)
This formula uses 3 Variables

Variables Used

Anharmonicity Constant - Anharmonicity Constant is the deviation of a system from being a harmonic oscillator which is related to the vibrational energy levels of diatomic molecule.
Vibration Frequency - (Measured in Hertz) - Vibration Frequency is the frequency of photons on the excited state.
Fundamental Frequency - (Measured in Hertz) - Fundamental Frequency is the frequency of photons on the fundamental excited state/ overtone band of a diatomic molecule.

STEP 1: Convert Input(s) to Base Unit

Vibration Frequency: 130 Hertz --> 130 Hertz No Conversion Required
Fundamental Frequency: 0.7 Hertz --> 0.7 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x_e = (v₀-v_0->1)/(2*v₀) --> (130-0.7)/(2*130)

Evaluating ... ...

x_e = 0.497307692307692

STEP 3: Convert Result to Output's Unit

0.497307692307692 --> No Conversion Required

FINAL ANSWER

0.497307692307692 ≈ 0.497308 <-- Anharmonicity Constant

(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 Prashant Singh

K J Somaiya College of science (K J Somaiya), Mumbai

Prashant Singh has verified this Calculator and 500+ 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

Anharmonicity Constant given Fundamental Frequency Formula

Anharmonicity Constant = (Vibration Frequency-Fundamental Frequency)/(2*Vibration Frequency)
x_e = (v₀-v_0->1)/(2*v₀)

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 Anharmonicity Constant given Fundamental Frequency?

Anharmonicity Constant given Fundamental Frequency calculator uses Anharmonicity Constant = (Vibration Frequency-Fundamental Frequency)/(2*Vibration Frequency) to calculate the Anharmonicity Constant, The Anharmonicity constant given fundamental frequency formula is defined as the deviation of a system from being a harmonic oscillator in relation to the vibrational energy levels of a diatomic molecule. Anharmonicity Constant is denoted by x_e symbol.

How to calculate Anharmonicity Constant given Fundamental Frequency using this online calculator? To use this online calculator for Anharmonicity Constant given Fundamental Frequency, enter Vibration Frequency (v₀) & Fundamental Frequency (v_0->1) and hit the calculate button. Here is how the Anharmonicity Constant given Fundamental Frequency calculation can be explained with given input values -> 0.497308 = (130-0.7)/(2*130).

FAQ

What is Anharmonicity Constant given Fundamental Frequency?

The Anharmonicity constant given fundamental frequency formula is defined as the deviation of a system from being a harmonic oscillator in relation to the vibrational energy levels of a diatomic molecule and is represented as x_e = (v₀-v_0->1)/(2*v₀) or Anharmonicity Constant = (Vibration Frequency-Fundamental Frequency)/(2*Vibration Frequency). Vibration Frequency is the frequency of photons on the excited state & Fundamental Frequency is the frequency of photons on the fundamental excited state/ overtone band of a diatomic molecule.

How to calculate Anharmonicity Constant given Fundamental Frequency?

The Anharmonicity constant given fundamental frequency formula is defined as the deviation of a system from being a harmonic oscillator in relation to the vibrational energy levels of a diatomic molecule is calculated using Anharmonicity Constant = (Vibration Frequency-Fundamental Frequency)/(2*Vibration Frequency). To calculate Anharmonicity Constant given Fundamental Frequency, you need Vibration Frequency (v₀) & Fundamental Frequency (v_0->1). With our tool, you need to enter the respective value for Vibration Frequency & Fundamental Frequency 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 Anharmonicity Constant?

In this formula, Anharmonicity Constant uses Vibration Frequency & Fundamental Frequency. We can use 4 other way(s) to calculate the same, which is/are as follows -

Anharmonicity Constant = 1/3*(1-(First Overtone Frequency/(2*Vibrational Frequency)))
Anharmonicity Constant = 1/4*(1-(Second Overtone Frequency/(3*Vibrational Frequency)))
Anharmonicity Constant = 1/3*(1-(First Overtone Frequency/(2*Vibrational Frequency)))
Anharmonicity Constant = 1/4*(1-(Second Overtone Frequency/(3*Vibrational Frequency)))

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