Vibrational energy using Anharmonicity constant Calculator

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Molecular Spectroscopy

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Number of Theoretical Plates and Capacity Factor

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Important Formulae on Retention and Deviation

Method of Separation Technique

Relative and Adjusted Retention and Phase

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Vibrational spectroscopy

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Rotational Spectroscopy

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Vibrational Energy Levels

Important Calculators of Vibrational Spectroscopy

✖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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Formula

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Vibrational energy using Anharmonicity constant

Formula

`"E"_{"xe"} = (("ω'")^2)/(4*"x"_{"e"}*"ω'"*"v"_{"max"})`

Example

`"2.840909J"=(("15/m")^2)/(4*"0.24"*"15/m"*"5.5")`

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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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< 15 Vibrational Energy Levels Calculators

Energy of Vibrational Transitions

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

Vibrational energy using Anharmonicity constant

Go Vibrational Energy given xe constant = ((Vibrational Wavenumber)^2)/(4*Anharmonicity Constant*Vibrational Wavenumber*Max Vibrational Number)

Anharmonicity Constant given Dissociation Energy

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

Dissociation Energy given Vibrational Wavenumber

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

Zero Point Energy

Go Zero Point Energy = (1/2*Vibrational Wavenumber)-(1/4*Anharmonicity Constant*Vibrational Wavenumber)

Vibrational Energy

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

Vibrational Frequency given Vibrational Energy

Go Vibrational Frequency given VE = Vibrational Energy/(Vibrational Quantum Number+1/2)*[hP]

Vibrational Energy using Vibrational Wave Number

Go Vibrational Energy given wavenumber = (Vibrational Quantum Number+1/2)*Vibrational Wavenumber

Vibrational Wavenumber given Vibrational Energy

Go Vibrational Wavenumber given VE = Vibrational Energy/(Vibrational Quantum Number+1/2)

Vibrational Energy using Dissociation Energy

Go Vibrational Energy given DE = Dissociation Energy of Potential/Max Vibrational Number

Dissociation Energy of Potential using Zero Point Energy

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

Zero Point Energy given Dissociation Energy

Go Zero Point Energy = Dissociation Energy of Potential-Zero Point Dissociation Energy

Dissociation Energy of Potential

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

Zero Point Dissociation Energy

Go Zero Point Dissociation Energy = Dissociation Energy of Potential-Zero Point Energy

Maximum Vibrational Quantum Number given Dissociation Energy

Go Maximum Vibrational Number = Dissociation Energy of Potential/Vibrational Energy

< 15 Vibrational energy levels Calculators

Energy of Vibrational Transitions

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

Vibrational energy using Anharmonicity constant

Go Vibrational Energy given xe constant = ((Vibrational Wavenumber)^2)/(4*Anharmonicity Constant*Vibrational Wavenumber*Max Vibrational Number)

Anharmonicity Constant given Dissociation Energy

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

Dissociation Energy given Vibrational Wavenumber

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

Zero Point Energy

Go Zero Point Energy = (1/2*Vibrational Wavenumber)-(1/4*Anharmonicity Constant*Vibrational Wavenumber)

Vibrational Energy

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

Vibrational Frequency given Vibrational Energy

Go Vibrational Frequency given VE = Vibrational Energy/(Vibrational Quantum Number+1/2)*[hP]

Vibrational Energy using Vibrational Wave Number

Go Vibrational Energy given wavenumber = (Vibrational Quantum Number+1/2)*Vibrational Wavenumber

Vibrational Wavenumber given Vibrational Energy

Go Vibrational Wavenumber given VE = Vibrational Energy/(Vibrational Quantum Number+1/2)

Vibrational Energy using Dissociation Energy

Go Vibrational Energy given DE = Dissociation Energy of Potential/Max Vibrational Number

Dissociation Energy of Potential using Zero Point Energy

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

Zero Point Energy given Dissociation Energy

Go Zero Point Energy = Dissociation Energy of Potential-Zero Point Dissociation Energy

Dissociation Energy of Potential

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

Zero Point Dissociation Energy

Go Zero Point Dissociation Energy = Dissociation Energy of Potential-Zero Point Energy

Maximum Vibrational Quantum Number given Dissociation Energy

Go Maximum Vibrational Number = Dissociation Energy of Potential/Vibrational Energy

Vibrational energy using Anharmonicity constant Formula

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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