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Rotational Constant for Vibrational State Formula

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

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

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

Rotational Constant for Vibrational State Example

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Here is how the Rotational Constant for Vibrational State equation looks like with Values.

Here is how the Rotational Constant for Vibrational State equation looks like with Units.

Here is how the Rotational Constant for Vibrational State equation looks like.

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

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

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

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Rotational Constant for Vibrational State Solution

Follow our step by step solution on how to calculate Rotational Constant for Vibrational State?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

B v = 20m⁻¹ + (6 \cdot (2 + \frac{1}{2}))

Next Step Prepare to Evaluate

∴

B v = 20 + (6 \cdot (2 + \frac{1}{2}))

Next Step Evaluate

∴

B v = 35Diopter

LAST Step Convert to Output's Unit

∴

B v = 351/m

Rotational Constant for Vibrational State Formula Elements

Variables

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

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

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 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}}

How to Evaluate Rotational Constant for Vibrational State?

Rotational Constant for Vibrational State evaluator uses Rotational Constant vib = Rotational Constant Equilibrium+(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2)) to evaluate the Rotational Constant vib, The Rotational constant for vibrational state formula is defined for relating in energy and vibrational energy levels in diatomic molecules. Rotational Constant vib is denoted by B_v symbol.

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

FAQs on Rotational Constant for Vibrational State

What is the formula to find Rotational Constant for Vibrational State?

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

How to calculate Rotational Constant for Vibrational State?

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

Can the Rotational Constant for Vibrational State be negative?

Yes, the Rotational Constant for Vibrational State, measured in Wave Number can be negative.

Which unit is used to measure Rotational Constant for Vibrational State?

Rotational Constant for Vibrational State is usually measured using the 1 per Meter[1/m] for Wave Number. Diopter[1/m], Kayser[1/m] are the few other units in which Rotational Constant for Vibrational State can be measured.

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Rotational Constant for Vibrational State Formula

Rotational Constant for Vibrational State Example

Rotational Constant for Vibrational State Solution

Rotational Constant for Vibrational State Formula Elements

Other formulas in Vibrational Spectroscopy category

How to Evaluate Rotational Constant for Vibrational State?

FAQs on Rotational Constant for Vibrational State

Variable Name