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Maximum Vibrational Quantum Number Formula

GoMaximum Vibrational Number using Anharmonicity Constant Formula

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Max Vibrational Number is the maximum scalar quantum value that defines the energy state of a harmonic or approximately harmonic vibrating diatomic molecule. Check FAQs

v max = (\frac{ω'}{2 \cdot x e \cdot ω'}) - \frac{1}{2}

v_max - Max Vibrational Number?ω' - Vibrational Wavenumber?x_e - Anharmonicity Constant?

Maximum Vibrational Quantum Number Example

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Here is how the Maximum Vibrational Quantum Number equation looks like with Values.

Here is how the Maximum Vibrational Quantum Number equation looks like with Units.

Here is how the Maximum Vibrational Quantum Number equation looks like.

1.5833 = (\frac{15}{2 \cdot 0.24 \cdot 15}) - \frac{1}{2}

1.5833 = (\frac{151/m}{2 \cdot 0.24 \cdot 151/m}) - \frac{1}{2}

1.5833 = (\frac{15}{2 \cdot 0.24 \cdot 15}) - \frac{1}{2}

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Maximum Vibrational Quantum Number Solution

Follow our step by step solution on how to calculate Maximum Vibrational Quantum Number?

FIRST Step Consider the formula

v max = (\frac{ω'}{2 \cdot x e \cdot ω'}) - \frac{1}{2}

Next Step Substitute values of Variables

∴

v max = (\frac{151/m}{2 \cdot 0.24 \cdot 151/m}) - \frac{1}{2}

Next Step Convert Units

∴

v max = (\frac{15Diopter}{2 \cdot 0.24 \cdot 15Diopter}) - \frac{1}{2}

Next Step Prepare to Evaluate

∴

v max = (\frac{15}{2 \cdot 0.24 \cdot 15}) - \frac{1}{2}

Next Step Evaluate

∴

v max = 1.58333333333333

LAST Step Rounding Answer

∴

v max = 1.5833

Maximum Vibrational Quantum Number Formula Elements

Variables

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.

Symbol: v_max

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Max Vibrational Number

Vibrational Wavenumber

Vibrational Wavenumber is simply the harmonic vibrational frequency or energy expressed in units of cm inverse.

Symbol: ω'

Measurement: Wave NumberUnit: 1/m

Note: Value can be positive or negative.

Formulas to find Vibrational Wavenumber

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.

Symbol: x_e

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Anharmonicity Constant

Other Formulas to find Max Vibrational Number

Go Maximum Vibrational Number using Anharmonicity Constant

v max = \frac{{(ω')}^{2}}{4 \cdot ω' \cdot E vf \cdot x e}

Other formulas in Vibrational Spectroscopy category

Go Vibrational Quantum Number using Vibrational Frequency

v = (\frac{E vf}{[hP] \cdot v vib}) - \frac{1}{2}

Go Vibrational Quantum Number using Vibrational Wavenumber

v = (\frac{E vf}{[hP]} \cdot ω') - \frac{1}{2}

Go Rotational Constant for Vibrational State

B v = B e + (α e \cdot (v + \frac{1}{2}))

Go Rotational Constant Related to Equilibrium

B e = B v - (α e \cdot (v + \frac{1}{2}))

How to Evaluate Maximum Vibrational Quantum Number?

Maximum Vibrational Quantum Number evaluator uses Max Vibrational Number = (Vibrational Wavenumber/(2*Anharmonicity Constant*Vibrational Wavenumber))-1/2 to evaluate 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 evaluate Maximum Vibrational Quantum Number using this online evaluator? To use this online evaluator for Maximum Vibrational Quantum Number, enter Vibrational Wavenumber (ω') & Anharmonicity Constant (x_e) and hit the calculate button.

FAQs on Maximum Vibrational Quantum Number

What is the formula to find Maximum Vibrational Quantum Number?

The formula of Maximum Vibrational Quantum Number is expressed as Max Vibrational Number = (Vibrational Wavenumber/(2*Anharmonicity Constant*Vibrational Wavenumber))-1/2. Here is an example- 1.583333 = (15/(2*0.24*15))-1/2.

How to calculate Maximum Vibrational Quantum Number?

With Vibrational Wavenumber (ω') & Anharmonicity Constant (x_e) we can find Maximum Vibrational Quantum Number using the formula - Max Vibrational Number = (Vibrational Wavenumber/(2*Anharmonicity Constant*Vibrational Wavenumber))-1/2.

What are the other ways to Calculate Max Vibrational Number?

Here are the different ways to Calculate Max Vibrational Number-

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

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Maximum Vibrational Quantum Number Formula

​GoMaximum Vibrational Number using Anharmonicity Constant Formula

Maximum Vibrational Quantum Number Example

Maximum Vibrational Quantum Number Solution

Maximum Vibrational Quantum Number Formula Elements

Other Formulas to find Max Vibrational Number

Other formulas in Vibrational Spectroscopy category

How to Evaluate Maximum Vibrational Quantum Number?

FAQs on Maximum Vibrational Quantum Number

Variable Name

GoMaximum Vibrational Number using Anharmonicity Constant Formula