Vibrational energy using Anharmonicity constant Calculator

✖Vibrational Wavenumber is simply the harmonic vibrational frequency or energy expressed in units of cm inverse.ⓘ Vibrational Wavenumber [ω']			+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%
✖Max Vibrational Number is the maximum scalar quantum value that defines the energy state of a harmonic or approximately harmonic vibrating diatomic molecule.ⓘ Max Vibrational Number [v_max]			+10% -10%

✖Vibrational Energy given xe constant is the total energy of the respective rotation-vibration levels of a diatomic molecule.ⓘ Vibrational energy using Anharmonicity constant [E_xe]

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Vibrational energy using Anharmonicity constant Solution

STEP 0: Pre-Calculation Summary

Formula Used

Vibrational Energy given xe constant = ((Vibrational Wavenumber)^2)/(4*Anharmonicity Constant*Vibrational Wavenumber*Max Vibrational Number)
E_xe = ((ω')^2)/(4*x_e*ω'*v_max)
This formula uses 4 Variables

Variables Used

Vibrational Energy given xe constant - (Measured in Joule) - Vibrational Energy given xe constant 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.
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.
Max Vibrational Number - Max Vibrational Number is the maximum scalar quantum value that defines the energy state of a harmonic or approximately harmonic vibrating diatomic molecule.

STEP 1: Convert Input(s) to Base Unit

Vibrational Wavenumber: 15 1 per Meter --> 15 Diopter (Check conversion here)
Anharmonicity Constant: 0.24 --> No Conversion Required
Max Vibrational Number: 5.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_xe = ((ω')^2)/(4*x_e*ω'*v_max) --> ((15)^2)/(4*0.24*15*5.5)

Evaluating ... ...

E_xe = 2.84090909090909

STEP 3: Convert Result to Output's Unit

2.84090909090909 Joule --> No Conversion Required

FINAL ANSWER

2.84090909090909 ≈ 2.840909 Joule <-- Vibrational Energy given xe constant

(Calculation completed in 00.004 seconds)

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Created by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

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< Vibrational Energy Levels Calculators

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

Vibrational energy using Anharmonicity constant Formula

LaTeX Go

Vibrational Energy given xe constant = ((Vibrational Wavenumber)^2)/(4*Anharmonicity Constant*Vibrational Wavenumber*Max Vibrational Number)
E_xe = ((ω')^2)/(4*x_e*ω'*v_max)

What is Dissociation energy?

The term dissociation energy may be appreciated by reference to potential energy internuclear distance curves. At about 0 K all molecules have no rotational energy but are merely vibrating with their zero-point energy. Thus, diatomic molecules are in the v = 0 vibrational level. The energy required to separate the stable molecule A - B initially in the v = 0 level into two unexcited atoms A and B, that is: A - B → A+B is known as the dissociation energy (D).

How to Calculate Vibrational energy using Anharmonicity constant?

Vibrational energy using Anharmonicity constant calculator uses Vibrational Energy given xe constant = ((Vibrational Wavenumber)^2)/(4*Anharmonicity Constant*Vibrational Wavenumber*Max Vibrational Number) to calculate the Vibrational Energy given xe constant, The Vibrational energy using Anharmonicity constant formula is defined as the total energy of the respective rotation-vibration levels of a diatomic molecule. Vibrational Energy given xe constant is denoted by E_xe symbol.

How to calculate Vibrational energy using Anharmonicity constant using this online calculator? To use this online calculator for Vibrational energy using Anharmonicity constant, enter Vibrational Wavenumber (ω'), Anharmonicity Constant (x_e) & Max Vibrational Number (v_max) and hit the calculate button. Here is how the Vibrational energy using Anharmonicity constant calculation can be explained with given input values -> 2.840909 = ((15)^2)/(4*0.24*15*5.5).

FAQ

What is Vibrational energy using Anharmonicity constant?

The Vibrational energy using Anharmonicity constant formula is defined as the total energy of the respective rotation-vibration levels of a diatomic molecule and is represented as E_xe = ((ω')^2)/(4*x_e*ω'*v_max) or Vibrational Energy given xe constant = ((Vibrational Wavenumber)^2)/(4*Anharmonicity Constant*Vibrational Wavenumber*Max Vibrational Number). Vibrational Wavenumber is simply the harmonic vibrational frequency or energy expressed in units of cm inverse, Anharmonicity Constant is the deviation of a system from being a harmonic oscillator which is related to the vibrational energy levels of diatomic molecule & Max Vibrational Number is the maximum scalar quantum value that defines the energy state of a harmonic or approximately harmonic vibrating diatomic molecule.

How to calculate Vibrational energy using Anharmonicity constant?

The Vibrational energy using Anharmonicity constant formula is defined as the total energy of the respective rotation-vibration levels of a diatomic molecule is calculated using Vibrational Energy given xe constant = ((Vibrational Wavenumber)^2)/(4*Anharmonicity Constant*Vibrational Wavenumber*Max Vibrational Number). To calculate Vibrational energy using Anharmonicity constant, you need Vibrational Wavenumber (ω'), Anharmonicity Constant (x_e) & Max Vibrational Number (v_max). With our tool, you need to enter the respective value for Vibrational Wavenumber, Anharmonicity Constant & Max Vibrational Number 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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