Vibrational Degree of Freedom for Nonlinear Molecules Solution

STEP 0: Pre-Calculation Summary
Formula Used
Vibrational Degree Nonlinear = (3*Number of Atoms)-6
vibdnl = (3*z)-6
This formula uses 2 Variables
Variables Used
Vibrational Degree Nonlinear - Vibrational Degree Nonlinear is the degree of freedom for non linear molecules in vibrational movement.
Number of Atoms - The Number of Atoms is the the total number of constituent atoms in the unit cell.
STEP 1: Convert Input(s) to Base Unit
Number of Atoms: 35 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
vibdnl = (3*z)-6 --> (3*35)-6
Evaluating ... ...
vibdnl = 99
STEP 3: Convert Result to Output's Unit
99 --> No Conversion Required
FINAL ANSWER
99 <-- Vibrational Degree Nonlinear
(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 Shivam Sinha
National Institute Of Technology (NIT), Surathkal
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22 Vibrational Spectroscopy Calculators

Maximum Vibrational Number using Anharmonicity Constant
Go Max Vibrational Number = ((Vibrational Wavenumber)^2)/(4*Vibrational Wavenumber*Vibrational Energy*Anharmonicity Constant)
Vibrational Quantum Number using Rotational Constant
Go Vibrational Quantum Number = ((Rotational Constant vib-Rotational Constant Equilibrium)/Anharmonic Potential Constant)-1/2
Rotational Constant Related to Equilibrium
Go Rotational Constant Equilibrium = Rotational Constant vib-(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))
Rotational Constant for Vibrational State
Go Rotational Constant vib = Rotational Constant Equilibrium+(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))
Anharmonic Potential Constant
Go Anharmonic Potential Constant = (Rotational Constant vib-Rotational Constant Equilibrium)/(Vibrational Quantum Number+1/2)
Maximum Vibrational Quantum Number
Go Max Vibrational Number = (Vibrational Wavenumber/(2*Anharmonicity Constant*Vibrational Wavenumber))-1/2
Anharmonicity Constant given Fundamental Frequency
Go Anharmonicity Constant = (Vibration Frequency-Fundamental Frequency)/(2*Vibration Frequency)
Vibrational Quantum Number using Vibrational Frequency
Go Vibrational Quantum Number = (Vibrational Energy/([hP]*Vibrational Frequency))-1/2
Vibrational Quantum Number using Vibrational Wavenumber
Go Vibrational Quantum Number = (Vibrational Energy/[hP]*Vibrational Wavenumber)-1/2
Anharmonicity Constant given Second Overtone Frequency
Go Anharmonicity Constant = 1/4*(1-(Second Overtone Frequency/(3*Vibrational Frequency)))
Anharmonicity Constant given First Overtone Frequency
Go Anharmonicity Constant = 1/3*(1-(First Overtone Frequency/(2*Vibrational Frequency)))
Energy Difference between Two Vibrational States
Go Change in Energy = Equilibrium Vibrational Frequency*(1-(2*Anharmonicity Constant))
Vibrational Frequency given Second Overtone Frequency
Go Vibrational Frequency = Second Overtone Frequency/3*(1-(4*Anharmonicity Constant))
Second Overtone Frequency
Go Second Overtone Frequency = (3*Vibrational Frequency)*(1-4*Anharmonicity Constant)
First Overtone Frequency
Go First Overtone Frequency = (2*Vibrational Frequency)*(1-3*Anharmonicity Constant)
Vibrational Frequency given First Overtone Frequency
Go Vibrational Frequency = First Overtone Frequency/2*(1-3*Anharmonicity Constant)
Vibrational Frequency given Fundamental Frequency
Go Vibrational Frequency = Fundamental Frequency/(1-2*Anharmonicity Constant)
Fundamental Frequency of Vibrational Transitions
Go Fundamental Frequency = Vibrational Frequency*(1-2*Anharmonicity Constant)
Vibrational Degree of Freedom for Nonlinear Molecules
Go Vibrational Degree Nonlinear = (3*Number of Atoms)-6
Vibrational Degree of Freedom for Linear Molecules
Go Vibrational Degree Linear = (3*Number of Atoms)-5
Total Degree of Freedom for Nonlinear Molecules
Go Degree of Freedom Non Linear = 3*Number of Atoms
Total Degree of Freedom for Linear Molecules
Go Degree of Freedom Linear = 3*Number of Atoms

10+ Important formulae on Vibrational Spectroscopy Calculators

Vibrational Quantum Number using Rotational Constant
Go Vibrational Quantum Number = ((Rotational Constant vib-Rotational Constant Equilibrium)/Anharmonic Potential Constant)-1/2
Rotational Constant Related to Equilibrium
Go Rotational Constant Equilibrium = Rotational Constant vib-(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))
Rotational Constant for Vibrational State
Go Rotational Constant vib = Rotational Constant Equilibrium+(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))
Anharmonicity Constant given First Overtone Frequency
Go Anharmonicity Constant = 1/3*(1-(First Overtone Frequency/(2*Vibrational Frequency)))
First Overtone Frequency
Go First Overtone Frequency = (2*Vibrational Frequency)*(1-3*Anharmonicity Constant)
Fundamental Frequency of Vibrational Transitions
Go Fundamental Frequency = Vibrational Frequency*(1-2*Anharmonicity Constant)
Vibrational Degree of Freedom for Nonlinear Molecules
Go Vibrational Degree Nonlinear = (3*Number of Atoms)-6
Vibrational Degree of Freedom for Linear Molecules
Go Vibrational Degree Linear = (3*Number of Atoms)-5
Total Degree of Freedom for Nonlinear Molecules
Go Degree of Freedom Non Linear = 3*Number of Atoms
Total Degree of Freedom for Linear Molecules
Go Degree of Freedom Linear = 3*Number of Atoms

21 Important Calculators of Vibrational Spectroscopy Calculators

Maximum Vibrational Number using Anharmonicity Constant
Go Max Vibrational Number = ((Vibrational Wavenumber)^2)/(4*Vibrational Wavenumber*Vibrational Energy*Anharmonicity Constant)
Vibrational Quantum Number using Rotational Constant
Go Vibrational Quantum Number = ((Rotational Constant vib-Rotational Constant Equilibrium)/Anharmonic Potential Constant)-1/2
Rotational Constant Related to Equilibrium
Go Rotational Constant Equilibrium = Rotational Constant vib-(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))
Rotational Constant for Vibrational State
Go Rotational Constant vib = Rotational Constant Equilibrium+(Anharmonic Potential Constant*(Vibrational Quantum Number+1/2))
Anharmonic Potential Constant
Go Anharmonic Potential Constant = (Rotational Constant vib-Rotational Constant Equilibrium)/(Vibrational Quantum Number+1/2)
Maximum Vibrational Quantum Number
Go Max Vibrational Number = (Vibrational Wavenumber/(2*Anharmonicity Constant*Vibrational Wavenumber))-1/2
Anharmonicity Constant given Fundamental Frequency
Go Anharmonicity Constant = (Vibration Frequency-Fundamental Frequency)/(2*Vibration Frequency)
Vibrational Quantum Number using Vibrational Frequency
Go Vibrational Quantum Number = (Vibrational Energy/([hP]*Vibrational Frequency))-1/2
Vibrational Quantum Number using Vibrational Wavenumber
Go Vibrational Quantum Number = (Vibrational Energy/[hP]*Vibrational Wavenumber)-1/2
Anharmonicity Constant given Second Overtone Frequency
Go Anharmonicity Constant = 1/4*(1-(Second Overtone Frequency/(3*Vibrational Frequency)))
Anharmonicity Constant given First Overtone Frequency
Go Anharmonicity Constant = 1/3*(1-(First Overtone Frequency/(2*Vibrational Frequency)))
Vibrational Frequency given Second Overtone Frequency
Go Vibrational Frequency = Second Overtone Frequency/3*(1-(4*Anharmonicity Constant))
Second Overtone Frequency
Go Second Overtone Frequency = (3*Vibrational Frequency)*(1-4*Anharmonicity Constant)
First Overtone Frequency
Go First Overtone Frequency = (2*Vibrational Frequency)*(1-3*Anharmonicity Constant)
Vibrational Frequency given First Overtone Frequency
Go Vibrational Frequency = First Overtone Frequency/2*(1-3*Anharmonicity Constant)
Vibrational Frequency given Fundamental Frequency
Go Vibrational Frequency = Fundamental Frequency/(1-2*Anharmonicity Constant)
Fundamental Frequency of Vibrational Transitions
Go Fundamental Frequency = Vibrational Frequency*(1-2*Anharmonicity Constant)
Vibrational Degree of Freedom for Nonlinear Molecules
Go Vibrational Degree Nonlinear = (3*Number of Atoms)-6
Vibrational Degree of Freedom for Linear Molecules
Go Vibrational Degree Linear = (3*Number of Atoms)-5
Total Degree of Freedom for Nonlinear Molecules
Go Degree of Freedom Non Linear = 3*Number of Atoms
Total Degree of Freedom for Linear Molecules
Go Degree of Freedom Linear = 3*Number of Atoms

Vibrational Degree of Freedom for Nonlinear Molecules Formula

Vibrational Degree Nonlinear = (3*Number of Atoms)-6
vibdnl = (3*z)-6

What is Vibrational degree of freedom?

Vibrational degree of freedom are any other types of movement not assigned to rotational or translational movement and thus there are 3N – 6 degrees of vibrational freedom for a nonlinear molecule and 3N – 5 for a linear molecule. These vibrations include bending, stretching, wagging and many other aptly named internal movements of a molecule. These various vibrations arise due to the numerous combinations of different stretches, contractions, and bends that can occur between the bonds of atoms in the molecule.

How is Vibrational degrees of freedom related to energy of molecule?

Each of these vibrational degrees of freedom is able to store energy. However, In the case of rotational and vibrational degrees of freedom, energy can only be stored in discrete amounts. This is due to the quantized break down of energy levels in a molecule described by quantum mechanics. In the case of rotations the energy stored is dependent on the rotational inertia of the gas along with the corresponding quantum number describing the energy level.

How to Calculate Vibrational Degree of Freedom for Nonlinear Molecules?

Vibrational Degree of Freedom for Nonlinear Molecules calculator uses Vibrational Degree Nonlinear = (3*Number of Atoms)-6 to calculate the Vibrational Degree Nonlinear, The Vibrational degree of freedom for nonlinear molecules formula is defined as the maximum number of logically independent values, which are values that have the freedom to vary in vibrational movement for non linear molecules. Vibrational Degree Nonlinear is denoted by vibdnl symbol.

How to calculate Vibrational Degree of Freedom for Nonlinear Molecules using this online calculator? To use this online calculator for Vibrational Degree of Freedom for Nonlinear Molecules, enter Number of Atoms (z) and hit the calculate button. Here is how the Vibrational Degree of Freedom for Nonlinear Molecules calculation can be explained with given input values -> 99 = (3*35)-6.

FAQ

What is Vibrational Degree of Freedom for Nonlinear Molecules?
The Vibrational degree of freedom for nonlinear molecules formula is defined as the maximum number of logically independent values, which are values that have the freedom to vary in vibrational movement for non linear molecules and is represented as vibdnl = (3*z)-6 or Vibrational Degree Nonlinear = (3*Number of Atoms)-6. The Number of Atoms is the the total number of constituent atoms in the unit cell.
How to calculate Vibrational Degree of Freedom for Nonlinear Molecules?
The Vibrational degree of freedom for nonlinear molecules formula is defined as the maximum number of logically independent values, which are values that have the freedom to vary in vibrational movement for non linear molecules is calculated using Vibrational Degree Nonlinear = (3*Number of Atoms)-6. To calculate Vibrational Degree of Freedom for Nonlinear Molecules, you need Number of Atoms (z). With our tool, you need to enter the respective value for Number of Atoms and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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