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Vibrational Quantum Number using Rotational Constant Formula

GoVibrational Quantum Number using Vibrational Frequency Formula

GoVibrational Quantum Number using Vibrational Wavenumber Formula

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Vibrational quantum number describes values of conserved quantities in the dynamics of a quantum system in a diatomic molecule. Check FAQs

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

v - Vibrational Quantum Number?B_v - Rotational Constant vib?B_e - Rotational Constant Equilibrium?α_e - Anharmonic Potential Constant?

Vibrational Quantum Number using Rotational Constant Example

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Here is how the Vibrational Quantum Number using Rotational Constant equation looks like with Values.

Here is how the Vibrational Quantum Number using Rotational Constant equation looks like with Units.

Here is how the Vibrational Quantum Number using Rotational Constant equation looks like.

2 = (\frac{35 - 20}{6}) - \frac{1}{2}

2 = (\frac{351/m - 20m⁻¹}{6}) - \frac{1}{2}

2 = (\frac{35 - 20}{6}) - \frac{1}{2}

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Vibrational Quantum Number using Rotational Constant Solution

Follow our step by step solution on how to calculate Vibrational Quantum Number using Rotational Constant?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

v = (\frac{351/m - 20m⁻¹}{6}) - \frac{1}{2}

Next Step Convert Units

∴

v = (\frac{35Diopter - 20m⁻¹}{6}) - \frac{1}{2}

Next Step Prepare to Evaluate

∴

v = (\frac{35 - 20}{6}) - \frac{1}{2}

LAST Step Evaluate

∴

v = 2

Vibrational Quantum Number using Rotational Constant Formula Elements

Variables

Vibrational Quantum Number

Vibrational quantum number describes values of conserved quantities in the dynamics of a quantum system in a diatomic molecule.

Symbol: v

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Vibrational Quantum Number

Rotational Constant vib

Rotational Constant vib is the rotational constant for a given vibrational state of a diatomic molecule.

Symbol: B_v

Measurement: Wave NumberUnit: 1/m

Note: Value can be positive or negative.

Formulas to find Rotational Constant vib

Rotational Constant Equilibrium

Rotational Constant Equilibrium is the rotational constant corresponding to the equilibrium geometry of the molecule.

Symbol: B_e

Measurement: Linear Atomic DensityUnit: m⁻¹

Note: Value can be positive or negative.

Formulas to find Rotational Constant Equilibrium

Anharmonic Potential Constant

Anharmonic Potential Constant is a constant determined by the shape of the Anharmonic potential of a molecule in vibrational state.

Symbol: α_e

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Anharmonic Potential Constant

Credits

Created by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

Akshada Kulkarni has created this Formula and 500+ more formulas!

Verified by Pragati Jaju

College Of Engineering (COEP), Pune

Pragati Jaju has verified this Formula and 300+ more formulas!

Other Formulas to find Vibrational Quantum Number

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}

Other formulas in Vibrational Spectroscopy category

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}))

Go Anharmonic Potential Constant

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

Go Maximum Vibrational Quantum Number

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

How to Evaluate Vibrational Quantum Number using Rotational Constant?

Vibrational Quantum Number using Rotational Constant evaluator uses Vibrational Quantum Number = ((Rotational Constant vib-Rotational Constant Equilibrium)/Anharmonic Potential Constant)-1/2 to evaluate the Vibrational Quantum Number, The Vibrational quantum number using rotational constant formula is defined as a scalar quantum number that defines the energy state of a harmonic or approximately harmonic vibrating diatomic molecule. Vibrational Quantum Number is denoted by v symbol.

How to evaluate Vibrational Quantum Number using Rotational Constant using this online evaluator? To use this online evaluator for Vibrational Quantum Number using Rotational Constant, enter Rotational Constant vib (B_v), Rotational Constant Equilibrium (B_e) & Anharmonic Potential Constant (α_e) and hit the calculate button.

FAQs on Vibrational Quantum Number using Rotational Constant

What is the formula to find Vibrational Quantum Number using Rotational Constant?

The formula of Vibrational Quantum Number using Rotational Constant is expressed as Vibrational Quantum Number = ((Rotational Constant vib-Rotational Constant Equilibrium)/Anharmonic Potential Constant)-1/2. Here is an example- 2 = ((35-20)/6)-1/2.

How to calculate Vibrational Quantum Number using Rotational Constant?

With Rotational Constant vib (B_v), Rotational Constant Equilibrium (B_e) & Anharmonic Potential Constant (α_e) we can find Vibrational Quantum Number using Rotational Constant using the formula - Vibrational Quantum Number = ((Rotational Constant vib-Rotational Constant Equilibrium)/Anharmonic Potential Constant)-1/2.

What are the other ways to Calculate Vibrational Quantum Number?

Here are the different ways to Calculate Vibrational Quantum Number-

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

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Vibrational Quantum Number using Rotational Constant Formula

​GoVibrational Quantum Number using Vibrational Frequency Formula

​GoVibrational Quantum Number using Vibrational Wavenumber Formula

Vibrational Quantum Number using Rotational Constant Example

Vibrational Quantum Number using Rotational Constant Solution

Vibrational Quantum Number using Rotational Constant Formula Elements

Credits

Other Formulas to find Vibrational Quantum Number

Other formulas in Vibrational Spectroscopy category

How to Evaluate Vibrational Quantum Number using Rotational Constant?

FAQs on Vibrational Quantum Number using Rotational Constant

Variable Name

GoVibrational Quantum Number using Vibrational Frequency Formula

GoVibrational Quantum Number using Vibrational Wavenumber Formula