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Maximum Vibrational Quantum Number Calculator

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Important formulae on Vibrational Spectroscopy Vibrational energy levels

✖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.ⓘ Maximum Vibrational Quantum Number [v_max]

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Maximum Vibrational Quantum Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Max Vibrational Number = (Vibrational Wavenumber/(2*Anharmonicity Constant*Vibrational Wavenumber))-1/2
v_max = (ω'/(2*x_e*ω'))-1/2
This formula uses 3 Variables

Variables Used

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.
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

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

Evaluating ... ...

v_max = 1.58333333333333

STEP 3: Convert Result to Output's Unit

1.58333333333333 --> No Conversion Required

FINAL ANSWER

1.58333333333333 ≈ 1.583333 <-- Max Vibrational Number

(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 Spectroscopy Calculators

Anharmonic Potential Constant

LaTeX Go Anharmonic Potential Constant = (Rotational Constant vib-Rotational Constant Equilibrium)/(Vibrational Quantum Number+1/2)

Anharmonicity Constant given Fundamental Frequency

LaTeX Go Anharmonicity Constant = (Vibration Frequency-Fundamental Frequency)/(2*Vibration Frequency)

Anharmonicity Constant given Second Overtone Frequency

LaTeX Go Anharmonicity Constant = 1/4*(1-(Second Overtone Frequency/(3*Vibrational Frequency)))

Anharmonicity Constant given First Overtone Frequency

LaTeX Go Anharmonicity Constant = 1/3*(1-(First Overtone Frequency/(2*Vibrational Frequency)))

< Important Calculators of Vibrational Spectroscopy Calculators

Rotational Constant Related to Equilibrium

LaTeX Go Rotational Constant Equilibrium = Rotational Constant vib-(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))

Rotational Constant for Vibrational State

LaTeX Go Rotational Constant vib = Rotational Constant Equilibrium+(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))

Vibrational Quantum Number using Vibrational Frequency

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

Vibrational Quantum Number using Vibrational Wavenumber

LaTeX Go Vibrational Quantum Number = (Vibrational Energy/[hP]*Vibrational Wavenumber)-1/2

Maximum Vibrational Quantum Number Formula

LaTeX Go

Max Vibrational Number = (Vibrational Wavenumber/(2*Anharmonicity Constant*Vibrational Wavenumber))-1/2
v_max = (ω'/(2*x_e*ω'))-1/2

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 Maximum Vibrational Quantum Number?

Maximum Vibrational Quantum Number calculator uses Max Vibrational Number = (Vibrational Wavenumber/(2*Anharmonicity Constant*Vibrational Wavenumber))-1/2 to calculate the Max Vibrational Number, The Maximum vibrational quantum number formula is defined as the maximum scalar quantum value that defines the energy state of a harmonic or approximately harmonic vibrating diatomic molecule. Max Vibrational Number is denoted by v_max symbol.

How to calculate Maximum Vibrational Quantum Number using this online calculator? To use this online calculator for Maximum Vibrational Quantum Number, enter Vibrational Wavenumber (ω') & Anharmonicity Constant (x_e) and hit the calculate button. Here is how the Maximum Vibrational Quantum Number calculation can be explained with given input values -> 1.583333 = (15/(2*0.24*15))-1/2.

FAQ

What is Maximum Vibrational Quantum Number?

The Maximum vibrational quantum number formula is defined as the maximum scalar quantum value that defines the energy state of a harmonic or approximately harmonic vibrating diatomic molecule and is represented as v_max = (ω'/(2*x_e*ω'))-1/2 or Max Vibrational Number = (Vibrational Wavenumber/(2*Anharmonicity Constant*Vibrational Wavenumber))-1/2. 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 Maximum Vibrational Quantum Number?

The Maximum vibrational quantum number formula is defined as the maximum scalar quantum value that defines the energy state of a harmonic or approximately harmonic vibrating diatomic molecule is calculated using Max Vibrational Number = (Vibrational Wavenumber/(2*Anharmonicity Constant*Vibrational Wavenumber))-1/2. To calculate Maximum Vibrational Quantum Number, 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 Max Vibrational Number?

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

Max Vibrational Number = ((Vibrational Wavenumber)^2)/(4*Vibrational Wavenumber*Vibrational Energy*Anharmonicity Constant)
Max Vibrational Number = ((Vibrational Wavenumber)^2)/(4*Vibrational Wavenumber*Vibrational Energy*Anharmonicity Constant)

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