Energy of Vibrational Transitions Calculator

✖Vibrational quantum number describes values of conserved quantities in the dynamics of a quantum system in a diatomic molecule.ⓘ Vibrational Quantum Number [v]			+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%
✖The Vibrational Frequency is the frequency of photons on the excited state.ⓘ Vibrational Frequency [v_vib]			+10% -10%

✖Vibrational Energy in Transition is the total energy of the respective rotation-vibration levels of a diatomic molecule.ⓘ Energy of Vibrational Transitions [E_t]

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Energy of Vibrational Transitions Solution

STEP 0: Pre-Calculation Summary

Formula Used

Vibrational Energy in Transition = ((Vibrational Quantum Number+1/2)-Anharmonicity Constant*((Vibrational Quantum Number+1/2)^2))*([hP]*Vibrational Frequency)
E_t = ((v+1/2)-x_e*((v+1/2)^2))*([hP]*v_vib)
This formula uses 1 Constants, 4 Variables

Constants Used

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

Variables Used

Vibrational Energy in Transition - (Measured in Joule) - Vibrational Energy in Transition is the total energy of the respective rotation-vibration levels of a diatomic molecule.
Vibrational Quantum Number - Vibrational quantum number describes values of conserved quantities in the dynamics of a quantum system in a diatomic molecule.
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.
Vibrational Frequency - (Measured in Hertz) - The Vibrational Frequency is the frequency of photons on the excited state.

STEP 1: Convert Input(s) to Base Unit

Vibrational Quantum Number: 2 --> No Conversion Required
Anharmonicity Constant: 0.24 --> No Conversion Required
Vibrational Frequency: 1.3 Hertz --> 1.3 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_t = ((v+1/2)-x_e*((v+1/2)^2))*([hP]*v_vib) --> ((2+1/2)-0.24*((2+1/2)^2))*([hP]*1.3)

Evaluating ... ...

E_t = 8.613891052E-34

STEP 3: Convert Result to Output's Unit

8.613891052E-34 Joule --> No Conversion Required

FINAL ANSWER

8.613891052E-34 ≈ 8.6E-34 Joule <-- Vibrational Energy in Transition

(Calculation completed in 00.004 seconds)

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Home » Chemistry » Analytical chemistry » Molecular Spectroscopy » Vibrational spectroscopy » Vibrational Energy Levels » Energy of Vibrational Transitions

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Created by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

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National Institute Of Technology (NIT), Surathkal

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Energy of Vibrational Transitions

LaTeX Go Vibrational Energy in Transition = ((Vibrational Quantum Number+1/2)-Anharmonicity Constant*((Vibrational Quantum Number+1/2)^2))*([hP]*Vibrational Frequency)

Dissociation Energy given Vibrational Wavenumber

LaTeX Go Dissociation Energy of Potential = (Vibrational Wavenumber^2)/(4*Anharmonicity Constant*Vibrational Wavenumber)

Vibrational Energy

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

Dissociation Energy of Potential

LaTeX Go Actual Dissociation Energy of Potential = Vibrational Energy*Max Vibrational Number

< Vibrational energy levels Calculators

Anharmonicity Constant given Dissociation Energy

LaTeX Go Anharmonicity Constant = ((Vibrational Wavenumber)^2)/(4*Dissociation Energy of Potential*Vibrational Wavenumber)

Dissociation Energy given Vibrational Wavenumber

LaTeX Go Dissociation Energy of Potential = (Vibrational Wavenumber^2)/(4*Anharmonicity Constant*Vibrational Wavenumber)

Dissociation Energy of Potential using Zero Point Energy

LaTeX Go Dissociation Energy of Potential = Zero Point Dissociation Energy+Zero Point Energy

Dissociation Energy of Potential

LaTeX Go Actual Dissociation Energy of Potential = Vibrational Energy*Max Vibrational Number

Energy of Vibrational Transitions Formula

LaTeX Go

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 Energy of Vibrational Transitions?

Energy of Vibrational Transitions calculator uses Vibrational Energy in Transition = ((Vibrational Quantum Number+1/2)-Anharmonicity Constant*((Vibrational Quantum Number+1/2)^2))*([hP]*Vibrational Frequency) to calculate the Vibrational Energy in Transition, The Energy of Vibrational transitions formula is defined as the total energy of the respective rotation-vibration levels at different transitions of a diatomic molecule. Vibrational Energy in Transition is denoted by E_t symbol.

How to calculate Energy of Vibrational Transitions using this online calculator? To use this online calculator for Energy of Vibrational Transitions, enter Vibrational Quantum Number (v), Anharmonicity Constant (x_e) & Vibrational Frequency (v_vib) and hit the calculate button. Here is how the Energy of Vibrational Transitions calculation can be explained with given input values -> 8.6E-34 = ((2+1/2)-0.24*((2+1/2)^2))*([hP]*1.3).

FAQ

What is Energy of Vibrational Transitions?

The Energy of Vibrational transitions formula is defined as the total energy of the respective rotation-vibration levels at different transitions of a diatomic molecule and is represented as E_t = ((v+1/2)-x_e*((v+1/2)^2))*([hP]*v_vib) or Vibrational Energy in Transition = ((Vibrational Quantum Number+1/2)-Anharmonicity Constant*((Vibrational Quantum Number+1/2)^2))*([hP]*Vibrational Frequency). Vibrational quantum number describes values of conserved quantities in the dynamics of a quantum system in a diatomic molecule, Anharmonicity Constant is the deviation of a system from being a harmonic oscillator which is related to the vibrational energy levels of diatomic molecule & The Vibrational Frequency is the frequency of photons on the excited state.

How to calculate Energy of Vibrational Transitions?

The Energy of Vibrational transitions formula is defined as the total energy of the respective rotation-vibration levels at different transitions of a diatomic molecule is calculated using Vibrational Energy in Transition = ((Vibrational Quantum Number+1/2)-Anharmonicity Constant*((Vibrational Quantum Number+1/2)^2))*([hP]*Vibrational Frequency). To calculate Energy of Vibrational Transitions, you need Vibrational Quantum Number (v), Anharmonicity Constant (x_e) & Vibrational Frequency (v_vib). With our tool, you need to enter the respective value for Vibrational Quantum Number, Anharmonicity Constant & Vibrational 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 Vibrational Energy in Transition?

In this formula, Vibrational Energy in Transition uses Vibrational Quantum Number, Anharmonicity Constant & Vibrational Frequency. We can use 2 other way(s) to calculate the same, which is/are as follows -

Vibrational Energy in Transition = (Vibrational Quantum Number+1/2)*([hP]*Vibrational Frequency)
Vibrational Energy in Transition = (Vibrational Quantum Number+1/2)*([hP]*Vibrational Frequency)

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