Vibrational Energy Solution

STEP 0: Pre-Calculation Summary
Formula Used
Vibrational Energy in Transition = (Vibrational Quantum Number+1/2)*([hP]*Vibrational Frequency)
Et = (v+1/2)*([hP]*vvib)
This formula uses 1 Constants, 3 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.
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
Vibrational Frequency: 1.3 Hertz --> 1.3 Hertz No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Et = (v+1/2)*([hP]*vvib) --> (2+1/2)*([hP]*1.3)
Evaluating ... ...
Et = 2.153472763E-33
STEP 3: Convert Result to Output's Unit
2.153472763E-33 Joule --> No Conversion Required
FINAL ANSWER
2.153472763E-33 2.2E-33 Joule <-- Vibrational Energy in Transition
(Calculation completed in 00.004 seconds)

Credits

Created by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
Akshada Kulkarni has created this Calculator and 500+ more calculators!
Verified by Pragati Jaju
College Of Engineering (COEP), Pune
Pragati Jaju has verified this Calculator and 300+ 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

Vibrational Energy Formula

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

Vibrational Energy calculator uses Vibrational Energy in Transition = (Vibrational Quantum Number+1/2)*([hP]*Vibrational Frequency) to calculate the Vibrational Energy in Transition, The Vibrational energy formula is defined as the total energy of the respective rotation-vibration levels of a diatomic molecule. Vibrational Energy in Transition is denoted by Et symbol.

How to calculate Vibrational Energy using this online calculator? To use this online calculator for Vibrational Energy, enter Vibrational Quantum Number (v) & Vibrational Frequency (vvib) and hit the calculate button. Here is how the Vibrational Energy calculation can be explained with given input values -> 2.2E-33 = (2+1/2)*([hP]*1.3).

FAQ

What is Vibrational Energy?
The Vibrational energy formula is defined as the total energy of the respective rotation-vibration levels of a diatomic molecule and is represented as Et = (v+1/2)*([hP]*vvib) or Vibrational Energy in Transition = (Vibrational Quantum Number+1/2)*([hP]*Vibrational Frequency). Vibrational quantum number describes values of conserved quantities in the dynamics of a quantum system in a diatomic molecule & The Vibrational Frequency is the frequency of photons on the excited state.
How to calculate Vibrational Energy?
The Vibrational energy formula is defined as the total energy of the respective rotation-vibration levels of a diatomic molecule is calculated using Vibrational Energy in Transition = (Vibrational Quantum Number+1/2)*([hP]*Vibrational Frequency). To calculate Vibrational Energy, you need Vibrational Quantum Number (v) & Vibrational Frequency (vvib). With our tool, you need to enter the respective value for Vibrational Quantum Number & 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 & 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)-Anharmonicity Constant*((Vibrational Quantum Number+1/2)^2))*([hP]*Vibrational Frequency)
  • Vibrational Energy in Transition = ((Vibrational Quantum Number+1/2)-Anharmonicity Constant*((Vibrational Quantum Number+1/2)^2))*([hP]*Vibrational Frequency)
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