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Fundamental Frequency of Vibrational Transitions Calculator

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Important formulae on Vibrational Spectroscopy Vibrational energy levels

✖The Vibrational Frequency is the frequency of photons on the excited state.ⓘ Vibrational Frequency [v_vib]			+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 [x_e]			+10% -10%

✖Fundamental Frequency is the frequency of photons on the fundamental excited state/ overtone band of a diatomic molecule.ⓘ Fundamental Frequency of Vibrational Transitions [v_0->1]

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Fundamental Frequency of Vibrational Transitions Solution

STEP 0: Pre-Calculation Summary

Formula Used

Fundamental Frequency = Vibrational Frequency*(1-2*Anharmonicity Constant)
v_0->1 = v_vib*(1-2*x_e)
This formula uses 3 Variables

Variables Used

Fundamental Frequency - (Measured in Hertz) - Fundamental Frequency is the frequency of photons on the fundamental excited state/ overtone band of a diatomic molecule.
Vibrational Frequency - (Measured in Hertz) - The Vibrational Frequency is the frequency of photons on the excited state.
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.

STEP 1: Convert Input(s) to Base Unit

Vibrational Frequency: 1.3 Hertz --> 1.3 Hertz No Conversion Required
Anharmonicity Constant: 0.24 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v_0->1 = v_vib*(1-2*x_e) --> 1.3*(1-2*0.24)

Evaluating ... ...

v_0->1 = 0.676

STEP 3: Convert Result to Output's Unit

0.676 Hertz --> No Conversion Required

FINAL ANSWER

0.676 Hertz <-- Fundamental Frequency

(Calculation completed in 00.020 seconds)

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Created by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

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

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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

Fundamental Frequency of Vibrational Transitions Formula

LaTeX Go

Fundamental Frequency = Vibrational Frequency*(1-2*Anharmonicity Constant)
v_0->1 = v_vib*(1-2*x_e)

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 Fundamental Frequency of Vibrational Transitions?

Fundamental Frequency of Vibrational Transitions calculator uses Fundamental Frequency = Vibrational Frequency*(1-2*Anharmonicity Constant) to calculate the Fundamental Frequency, The Fundamental frequency of vibrational transitions formula is defined as the frequency of photons on the fundamental excited state of a diatomic molecule. Fundamental Frequency is denoted by v_0->1 symbol.

How to calculate Fundamental Frequency of Vibrational Transitions using this online calculator? To use this online calculator for Fundamental Frequency of Vibrational Transitions, enter Vibrational Frequency (v_vib) & Anharmonicity Constant (x_e) and hit the calculate button. Here is how the Fundamental Frequency of Vibrational Transitions calculation can be explained with given input values -> 0.676 = 1.3*(1-2*0.24).

FAQ

What is Fundamental Frequency of Vibrational Transitions?

The Fundamental frequency of vibrational transitions formula is defined as the frequency of photons on the fundamental excited state of a diatomic molecule and is represented as v_0->1 = v_vib*(1-2*x_e) or Fundamental Frequency = Vibrational Frequency*(1-2*Anharmonicity Constant). The Vibrational Frequency is the frequency of photons on the excited state & Anharmonicity Constant is the deviation of a system from being a harmonic oscillator which is related to the vibrational energy levels of diatomic molecule.

How to calculate Fundamental Frequency of Vibrational Transitions?

The Fundamental frequency of vibrational transitions formula is defined as the frequency of photons on the fundamental excited state of a diatomic molecule is calculated using Fundamental Frequency = Vibrational Frequency*(1-2*Anharmonicity Constant). To calculate Fundamental Frequency of Vibrational Transitions, you need Vibrational Frequency (v_vib) & Anharmonicity Constant (x_e). With our tool, you need to enter the respective value for Vibrational Frequency & Anharmonicity Constant 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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