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Energy of Vibrational Transitions Calculator

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✖Vibrational quantum number describes values of conserved quantities in the dynamics of a quantum system in a diatomic molecule.ⓘ Vibrational Quantum Number [v]
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✖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 [xe]
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✖The Vibrational Frequency is the frequency of photons on the excited state.ⓘ Vibrational Frequency [vvib]
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✖Vibrational Energy in Transition is the total energy of the respective rotation-vibration levels of a diatomic molecule.ⓘ Energy of Vibrational Transitions [Et]
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Formula
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Energy of Vibrational Transitions

Formula
`"E"_{"t"} = (("v"+1/2)-"x"_{"e"}*(("v"+1/2)^2))*("[hP]"*"v"_{"vib"})`

Example
`"8.6E^-34J"=(("2"+1/2)-"0.24"*(("2"+1/2)^2))*("[hP]"*"1.3Hz")`

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Energy of Vibrational Transitions Solution

STEP 0: Pre-Calculation Summary
Formula Used
Vibrational Energy in Transition = ((Vibrational Quantum Number+1/2)-Anharmonicity Constant*((Vibrational Quantum Number+1/2)^2))*([hP]*Vibrational Frequency)
Et = ((v+1/2)-xe*((v+1/2)^2))*([hP]*vvib)
This formula uses 1 Constants, 4 Variables
Constants Used
[hP] - Planck constant Value Taken As 6.626070040E-34
Variables Used
Vibrational Energy in Transition - (Measured in Joule) - Vibrational Energy in Transition is the total energy of the respective rotation-vibration levels of a diatomic molecule.
Vibrational Quantum Number - Vibrational quantum number describes values of conserved quantities in the dynamics of a quantum system in a diatomic molecule.
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.
Vibrational Frequency - (Measured in Hertz) - The Vibrational Frequency is the frequency of photons on the excited state.
STEP 1: Convert Input(s) to Base Unit
Vibrational Quantum Number: 2 --> No Conversion Required
Anharmonicity Constant: 0.24 --> No Conversion Required
Vibrational Frequency: 1.3 Hertz --> 1.3 Hertz No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Et = ((v+1/2)-xe*((v+1/2)^2))*([hP]*vvib) --> ((2+1/2)-0.24*((2+1/2)^2))*([hP]*1.3)
Evaluating ... ...
Et = 8.613891052E-34
STEP 3: Convert Result to Output's Unit
8.613891052E-34 Joule --> No Conversion Required
FINAL ANSWER
8.613891052E-34 ≈ 8.6E-34 Joule <-- Vibrational Energy in Transition
(Calculation completed in 00.004 seconds)
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Home » Chemistry » Analytical chemistry » Molecular Spectroscopy » Vibrational spectroscopy » Vibrational Energy Levels » Energy of Vibrational Transitions

Credits

Created by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
Akshada Kulkarni has created this Calculator and 500+ more calculators!
Verified by Shivam Sinha
National Institute Of Technology (NIT), Surathkal
Shivam Sinha has verified this Calculator and 25+ more calculators!

15 Vibrational Energy Levels Calculators

Energy of Vibrational Transitions
Go Vibrational Energy in Transition = ((Vibrational Quantum Number+1/2)-Anharmonicity Constant*((Vibrational Quantum Number+1/2)^2))*([hP]*Vibrational Frequency)
Vibrational energy using Anharmonicity constant
Go Vibrational Energy given xe constant = ((Vibrational Wavenumber)^2)/(4*Anharmonicity Constant*Vibrational Wavenumber*Max Vibrational Number)
Anharmonicity Constant given Dissociation Energy
Go Anharmonicity Constant = ((Vibrational Wavenumber)^2)/(4*Dissociation Energy of Potential*Vibrational Wavenumber)
Dissociation Energy given Vibrational Wavenumber
Go Dissociation Energy of Potential = (Vibrational Wavenumber^2)/(4*Anharmonicity Constant*Vibrational Wavenumber)
Zero Point Energy
Go Zero Point Energy = (1/2*Vibrational Wavenumber)-(1/4*Anharmonicity Constant*Vibrational Wavenumber)
Vibrational Energy
Go Vibrational Energy in Transition = (Vibrational Quantum Number+1/2)*([hP]*Vibrational Frequency)
Vibrational Frequency given Vibrational Energy
Go Vibrational Frequency given VE = Vibrational Energy/(Vibrational Quantum Number+1/2)*[hP]
Vibrational Energy using Vibrational Wave Number
Go Vibrational Energy given wavenumber = (Vibrational Quantum Number+1/2)*Vibrational Wavenumber
Vibrational Wavenumber given Vibrational Energy
Go Vibrational Wavenumber given VE = Vibrational Energy/(Vibrational Quantum Number+1/2)
Vibrational Energy using Dissociation Energy
Go Vibrational Energy given DE = Dissociation Energy of Potential/Max Vibrational Number
Dissociation Energy of Potential using Zero Point Energy
Go Dissociation Energy of Potential = Zero Point Dissociation Energy+Zero Point Energy
Zero Point Energy given Dissociation Energy
Go Zero Point Energy = Dissociation Energy of Potential-Zero Point Dissociation Energy
Dissociation Energy of Potential
Go Actual Dissociation Energy of Potential = Vibrational Energy*Max Vibrational Number
Zero Point Dissociation Energy
Go Zero Point Dissociation Energy = Dissociation Energy of Potential-Zero Point Energy
Maximum Vibrational Quantum Number given Dissociation Energy
Go Maximum Vibrational Number = Dissociation Energy of Potential/Vibrational Energy

15 Vibrational energy levels Calculators

Energy of Vibrational Transitions
Go Vibrational Energy in Transition = ((Vibrational Quantum Number+1/2)-Anharmonicity Constant*((Vibrational Quantum Number+1/2)^2))*([hP]*Vibrational Frequency)
Vibrational energy using Anharmonicity constant
Go Vibrational Energy given xe constant = ((Vibrational Wavenumber)^2)/(4*Anharmonicity Constant*Vibrational Wavenumber*Max Vibrational Number)
Anharmonicity Constant given Dissociation Energy
Go Anharmonicity Constant = ((Vibrational Wavenumber)^2)/(4*Dissociation Energy of Potential*Vibrational Wavenumber)
Dissociation Energy given Vibrational Wavenumber
Go Dissociation Energy of Potential = (Vibrational Wavenumber^2)/(4*Anharmonicity Constant*Vibrational Wavenumber)
Zero Point Energy
Go Zero Point Energy = (1/2*Vibrational Wavenumber)-(1/4*Anharmonicity Constant*Vibrational Wavenumber)
Vibrational Energy
Go Vibrational Energy in Transition = (Vibrational Quantum Number+1/2)*([hP]*Vibrational Frequency)
Vibrational Frequency given Vibrational Energy
Go Vibrational Frequency given VE = Vibrational Energy/(Vibrational Quantum Number+1/2)*[hP]
Vibrational Energy using Vibrational Wave Number
Go Vibrational Energy given wavenumber = (Vibrational Quantum Number+1/2)*Vibrational Wavenumber
Vibrational Wavenumber given Vibrational Energy
Go Vibrational Wavenumber given VE = Vibrational Energy/(Vibrational Quantum Number+1/2)
Vibrational Energy using Dissociation Energy
Go Vibrational Energy given DE = Dissociation Energy of Potential/Max Vibrational Number
Dissociation Energy of Potential using Zero Point Energy
Go Dissociation Energy of Potential = Zero Point Dissociation Energy+Zero Point Energy
Zero Point Energy given Dissociation Energy
Go Zero Point Energy = Dissociation Energy of Potential-Zero Point Dissociation Energy
Dissociation Energy of Potential
Go Actual Dissociation Energy of Potential = Vibrational Energy*Max Vibrational Number
Zero Point Dissociation Energy
Go Zero Point Dissociation Energy = Dissociation Energy of Potential-Zero Point Energy
Maximum Vibrational Quantum Number given Dissociation Energy
Go Maximum Vibrational Number = Dissociation Energy of Potential/Vibrational Energy

Energy of Vibrational Transitions Formula

Vibrational Energy in Transition = ((Vibrational Quantum Number+1/2)-Anharmonicity Constant*((Vibrational Quantum Number+1/2)^2))*([hP]*Vibrational Frequency)
Et = ((v+1/2)-xe*((v+1/2)^2))*([hP]*vvib)

What is vibrational energy?

Vibrational spectroscopy looks at the differences in energy between the vibrational modes of a molecule. These are larger than the rotational energy states. This spectroscopy can provide a direct measure of bond strength. The vibration energy levels can be explained using diatomic molecules. To a first approximation, molecular vibrations can be approximated as simple harmonic oscillators, with an associated energy known as vibrational energy.

How to Calculate Energy of Vibrational Transitions?

Energy of Vibrational Transitions calculator uses Vibrational Energy in Transition = ((Vibrational Quantum Number+1/2)-Anharmonicity Constant*((Vibrational Quantum Number+1/2)^2))*([hP]*Vibrational Frequency) to calculate 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 Et symbol.

How to calculate Energy of Vibrational Transitions using this online calculator? To use this online calculator for Energy of Vibrational Transitions, enter Vibrational Quantum Number (v), Anharmonicity Constant (xe) & Vibrational Frequency (vvib) and hit the calculate button. Here is how the Energy of Vibrational Transitions calculation can be explained with given input values -> 8.6E-34 = ((2+1/2)-0.24*((2+1/2)^2))*([hP]*1.3).

FAQ

What is Energy of Vibrational Transitions?
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 and is represented as Et = ((v+1/2)-xe*((v+1/2)^2))*([hP]*vvib) or Vibrational Energy in Transition = ((Vibrational Quantum Number+1/2)-Anharmonicity Constant*((Vibrational Quantum Number+1/2)^2))*([hP]*Vibrational Frequency). Vibrational quantum number describes values of conserved quantities in the dynamics of a quantum system in a diatomic molecule, Anharmonicity Constant is the deviation of a system from being a harmonic oscillator which is related to the vibrational energy levels of diatomic molecule & The Vibrational Frequency is the frequency of photons on the excited state.
How to calculate Energy of Vibrational Transitions?
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 is calculated using Vibrational Energy in Transition = ((Vibrational Quantum Number+1/2)-Anharmonicity Constant*((Vibrational Quantum Number+1/2)^2))*([hP]*Vibrational Frequency). To calculate Energy of Vibrational Transitions, you need Vibrational Quantum Number (v), Anharmonicity Constant (xe) & Vibrational Frequency (vvib). With our tool, you need to enter the respective value for Vibrational Quantum Number, Anharmonicity Constant & Vibrational Frequency 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 Vibrational Energy in Transition?
In this formula, Vibrational Energy in Transition uses Vibrational Quantum Number, Anharmonicity Constant & Vibrational Frequency. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Vibrational Energy in Transition = (Vibrational Quantum Number+1/2)*([hP]*Vibrational Frequency)
  • Vibrational Energy in Transition = (Vibrational Quantum Number+1/2)*([hP]*Vibrational Frequency)
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