Zero Point Energy 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%

✖Zero Point Energy is the energy of vibration of energy levels of a diatomic molecule.ⓘ Zero Point Energy [E₀]

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Zero Point Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Zero Point Energy = (1/2*Vibrational Wavenumber)-(1/4*Anharmonicity Constant*Vibrational Wavenumber)
E₀ = (1/2*ω')-(1/4*x_e*ω')
This formula uses 3 Variables

Variables Used

Zero Point Energy - (Measured in Joule) - Zero Point Energy is the energy of vibration of energy 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.

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E₀ = (1/2*ω')-(1/4*x_e*ω') --> (1/2*15)-(1/4*0.24*15)

Evaluating ... ...

E₀ = 6.6

STEP 3: Convert Result to Output's Unit

6.6 Joule --> No Conversion Required

FINAL ANSWER

6.6 Joule <-- Zero Point Energy

(Calculation completed in 00.008 seconds)

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Credits

Created by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

Akshada Kulkarni has created this Calculator and 500+ more calculators!

Verified by Pragati Jaju

College Of Engineering (COEP), Pune

Pragati Jaju has verified this Calculator and 200+ more calculators!

< 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

Zero Point Energy Formula

LaTeX Go

Zero Point Energy = (1/2*Vibrational Wavenumber)-(1/4*Anharmonicity Constant*Vibrational Wavenumber)
E₀ = (1/2*ω')-(1/4*x_e*ω')

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 Zero Point Energy?

Zero Point Energy calculator uses Zero Point Energy = (1/2*Vibrational Wavenumber)-(1/4*Anharmonicity Constant*Vibrational Wavenumber) to calculate the Zero Point Energy, The Zero point energy formula is defined as the energy of a vibration of energy levels of a diatomic molecule. Zero Point Energy is denoted by E₀ symbol.

How to calculate Zero Point Energy using this online calculator? To use this online calculator for Zero Point Energy, enter Vibrational Wavenumber (ω') & Anharmonicity Constant (x_e) and hit the calculate button. Here is how the Zero Point Energy calculation can be explained with given input values -> 6.6 = (1/2*15)-(1/4*0.24*15).

FAQ

What is Zero Point Energy?

The Zero point energy formula is defined as the energy of a vibration of energy levels of a diatomic molecule and is represented as E₀ = (1/2*ω')-(1/4*x_e*ω') or Zero Point Energy = (1/2*Vibrational Wavenumber)-(1/4*Anharmonicity Constant*Vibrational Wavenumber). 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.

How to calculate Zero Point Energy?

The Zero point energy formula is defined as the energy of a vibration of energy levels of a diatomic molecule is calculated using Zero Point Energy = (1/2*Vibrational Wavenumber)-(1/4*Anharmonicity Constant*Vibrational Wavenumber). To calculate Zero Point Energy, you need Vibrational Wavenumber (ω') & Anharmonicity Constant (x_e). With our tool, you need to enter the respective value for Vibrational Wavenumber & Anharmonicity Constant 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 Zero Point Energy?

In this formula, Zero Point Energy uses Vibrational Wavenumber & Anharmonicity Constant. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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