Energy Difference between Two Vibrational States Calculator

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Important formulae on Vibrational Spectroscopy

Vibrational energy levels

✖Equilibrium Vibrational Frequency is the vibrational frequency at equilibrium.ⓘ Equilibrium Vibrational Frequency [w_e]			+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%

✖Change in Energy is the energy difference between ground and excited state.ⓘ Energy Difference between Two Vibrational States [d_E]

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Formula

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Energy Difference between Two Vibrational States

Formula

`"d"_{"E"} = "w"_{"e"}*(1-(2*"x"_{"e"}))`

Example

`"41.6Hz"="80Hz"*(1-(2*"0.24"))`

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Energy Difference between Two Vibrational States Solution

STEP 0: Pre-Calculation Summary

Formula Used

Change in Energy = Equilibrium Vibrational Frequency*(1-(2*Anharmonicity Constant))
d_E = w_e*(1-(2*x_e))
This formula uses 3 Variables

Variables Used

Change in Energy - (Measured in Hertz) - Change in Energy is the energy difference between ground and excited state.
Equilibrium Vibrational Frequency - (Measured in Hertz) - Equilibrium Vibrational Frequency is the vibrational frequency at equilibrium.
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

Equilibrium Vibrational Frequency: 80 Hertz --> 80 Hertz No Conversion Required
Anharmonicity Constant: 0.24 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_E = w_e*(1-(2*x_e)) --> 80*(1-(2*0.24))

Evaluating ... ...

d_E = 41.6

STEP 3: Convert Result to Output's Unit

41.6 Hertz --> No Conversion Required

FINAL ANSWER

41.6 Hertz <-- Change in Energy

(Calculation completed in 00.004 seconds)

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Created by Torsha_Paul

University of Calcutta (CU), Kolkata

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National Institute Of Technology Warangal (NITW), Warangal

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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

Energy Difference between Two Vibrational States Formula

Change in Energy = Equilibrium Vibrational Frequency*(1-(2*Anharmonicity Constant))
d_E = w_e*(1-(2*x_e))

What is Vibrational State ?

The vibrational state – or VS, for short – is a condition that we can reach with our energy body. Both rotation and vibration are quantized, which leads to discrete energy levels. At room temperature, the lowest vibrational and rotational levels are the ones most commonly occupied. The different vibrational states are linked to the oscillatory motion of bonds.

How to Calculate Energy Difference between Two Vibrational States?

Energy Difference between Two Vibrational States calculator uses Change in Energy = Equilibrium Vibrational Frequency*(1-(2*Anharmonicity Constant)) to calculate the Change in Energy, Energy Difference between Two Vibrational States is defined as the energy difference between ground and excited state. Change in Energy is denoted by d_E symbol.

How to calculate Energy Difference between Two Vibrational States using this online calculator? To use this online calculator for Energy Difference between Two Vibrational States, enter Equilibrium Vibrational Frequency (w_e) & Anharmonicity Constant (x_e) and hit the calculate button. Here is how the Energy Difference between Two Vibrational States calculation can be explained with given input values -> 41.6 = 80*(1-(2*0.24)).

FAQ

What is Energy Difference between Two Vibrational States?

Energy Difference between Two Vibrational States is defined as the energy difference between ground and excited state and is represented as d_E = w_e*(1-(2*x_e)) or Change in Energy = Equilibrium Vibrational Frequency*(1-(2*Anharmonicity Constant)). Equilibrium Vibrational Frequency is the vibrational frequency at equilibrium & 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 Energy Difference between Two Vibrational States?

Energy Difference between Two Vibrational States is defined as the energy difference between ground and excited state is calculated using Change in Energy = Equilibrium Vibrational Frequency*(1-(2*Anharmonicity Constant)). To calculate Energy Difference between Two Vibrational States, you need Equilibrium Vibrational Frequency (w_e) & Anharmonicity Constant (x_e). With our tool, you need to enter the respective value for Equilibrium 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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