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Energy of Vibrational Transitions Formula

GoVibrational Energy Formula

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Vibrational Energy in Transition is the total energy of the respective rotation-vibration levels of a diatomic molecule. Check FAQs

E t = ((v + \frac{1}{2}) - x e \cdot ({(v + \frac{1}{2})}^{2})) \cdot ([hP] \cdot v vib)

E_t - Vibrational Energy in Transition?v - Vibrational Quantum Number?x_e - Anharmonicity Constant?v_vib - Vibrational Frequency?[hP] - Planck constant?

Energy of Vibrational Transitions Example

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Here is how the Energy of Vibrational Transitions equation looks like with Values.

Here is how the Energy of Vibrational Transitions equation looks like with Units.

Here is how the Energy of Vibrational Transitions equation looks like.

8.6E-34 = ((2 + \frac{1}{2}) - 0.24 \cdot ({(2 + \frac{1}{2})}^{2})) \cdot (6.6E-34 \cdot 1.3)

8.6E-34J = ((2 + \frac{1}{2}) - 0.24 \cdot ({(2 + \frac{1}{2})}^{2})) \cdot (6.6E-34 \cdot 1.3Hz)

8.6E-34 = ((2 + \frac{1}{2}) - 0.24 \cdot ({(2 + \frac{1}{2})}^{2})) \cdot (6.6E-34 \cdot 1.3)

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Energy of Vibrational Transitions Solution

Follow our step by step solution on how to calculate Energy of Vibrational Transitions?

FIRST Step Consider the formula

E t = ((v + \frac{1}{2}) - x e \cdot ({(v + \frac{1}{2})}^{2})) \cdot ([hP] \cdot v vib)

Next Step Substitute values of Variables

∴

E t = ((2 + \frac{1}{2}) - 0.24 \cdot ({(2 + \frac{1}{2})}^{2})) \cdot ([hP] \cdot 1.3Hz)

Next Step Substitute values of Constants

∴

E t = ((2 + \frac{1}{2}) - 0.24 \cdot ({(2 + \frac{1}{2})}^{2})) \cdot (6.6E-34 \cdot 1.3Hz)

Next Step Prepare to Evaluate

∴

E t = ((2 + \frac{1}{2}) - 0.24 \cdot ({(2 + \frac{1}{2})}^{2})) \cdot (6.6E-34 \cdot 1.3)

Next Step Evaluate

∴

E t = 8.613891052E-34J

LAST Step Rounding Answer

∴

E t = 8.6E-34J

Energy of Vibrational Transitions Formula Elements

Variables

Constants

Vibrational Energy in Transition

Vibrational Energy in Transition is the total energy of the respective rotation-vibration levels of a diatomic molecule.

Symbol: E_t

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Vibrational Energy in Transition

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

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

Vibrational Frequency

The Vibrational Frequency is the frequency of photons on the excited state.

Symbol: v_vib

Measurement: FrequencyUnit: Hz

Note: Value can be positive or negative.

Formulas to find Vibrational Frequency

Planck constant

Planck constant is a fundamental universal constant that defines the quantum nature of energy and relates the energy of a photon to its frequency.

Symbol: [hP]

Value: 6.626070040E-34

Other Formulas to find Vibrational Energy in Transition

Go Vibrational Energy

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

Other formulas in Vibrational Energy Levels category

Go Anharmonicity Constant given Dissociation Energy

x e = \frac{{(ω')}^{2}}{4 \cdot D e \cdot ω'}

Go Dissociation Energy given Vibrational Wavenumber

D e = \frac{{ω'}^{2}}{4 \cdot x e \cdot ω'}

Go Dissociation Energy of Potential

D ae = E vf \cdot v max

Go Dissociation Energy of Potential using Zero Point Energy

D e = D 0 + E 0

How to Evaluate Energy of Vibrational Transitions?

Energy of Vibrational Transitions evaluator uses Vibrational Energy in Transition = ((Vibrational Quantum Number+1/2)-Anharmonicity Constant*((Vibrational Quantum Number+1/2)^2))*([hP]*Vibrational Frequency) to evaluate the Vibrational Energy in Transition, The Energy of Vibrational transitions formula is defined as the total energy of the respective rotation-vibration levels at different transitions of a diatomic molecule. Vibrational Energy in Transition is denoted by E_t symbol.

How to evaluate Energy of Vibrational Transitions using this online evaluator? To use this online evaluator for Energy of Vibrational Transitions, enter Vibrational Quantum Number (v), Anharmonicity Constant (x_e) & Vibrational Frequency (v_vib) and hit the calculate button.

FAQs on Energy of Vibrational Transitions

What is the formula to find Energy of Vibrational Transitions?

The formula of Energy of Vibrational Transitions is expressed as Vibrational Energy in Transition = ((Vibrational Quantum Number+1/2)-Anharmonicity Constant*((Vibrational Quantum Number+1/2)^2))*([hP]*Vibrational Frequency). Here is an example- 8.6E-34 = ((2+1/2)-0.24*((2+1/2)^2))*([hP]*1.3).

How to calculate Energy of Vibrational Transitions?

With Vibrational Quantum Number (v), Anharmonicity Constant (x_e) & Vibrational Frequency (v_vib) we can find Energy of Vibrational Transitions using the formula - Vibrational Energy in Transition = ((Vibrational Quantum Number+1/2)-Anharmonicity Constant*((Vibrational Quantum Number+1/2)^2))*([hP]*Vibrational Frequency). This formula also uses Planck constant .

What are the other ways to Calculate Vibrational Energy in Transition?

Here are the different ways to Calculate Vibrational Energy in Transition-

Vibrational Energy in Transition=(Vibrational Quantum Number+1/2)*([hP]*Vibrational Frequency)

Can the Energy of Vibrational Transitions be negative?

Yes, the Energy of Vibrational Transitions, measured in Energy can be negative.

Which unit is used to measure Energy of Vibrational Transitions?

Energy of Vibrational Transitions is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Energy of Vibrational Transitions can be measured.

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Energy of Vibrational Transitions Formula

​GoVibrational Energy Formula

Energy of Vibrational Transitions Example

Energy of Vibrational Transitions Solution

Energy of Vibrational Transitions Formula Elements

Other Formulas to find Vibrational Energy in Transition

Other formulas in Vibrational Energy Levels category

How to Evaluate Energy of Vibrational Transitions?

FAQs on Energy of Vibrational Transitions

Variable Name

GoVibrational Energy Formula