## Vibrational Mode of Linear Molecule Solution

STEP 0: Pre-Calculation Summary
Formula Used
Number of Normal modes = (3*Atomicity)-5
Nvib = (3*N)-5
This formula uses 2 Variables
Variables Used
Number of Normal modes - The Number of Normal modes is the fundamental modes responsible for the vibrational motion.
Atomicity - The Atomicity is defined as the total number of atoms present in a molecule or element.
STEP 1: Convert Input(s) to Base Unit
Atomicity: 3 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Nvib = (3*N)-5 --> (3*3)-5
Evaluating ... ...
Nvib = 4
STEP 3: Convert Result to Output's Unit
4 --> No Conversion Required
4 <-- Number of Normal modes
(Calculation completed in 00.004 seconds)
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## Credits

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University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA
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## <Equipartition Principle and Heat Capacity Calculators

Rotational Energy of Non-Linear Molecule
​ Go Rotational Energy = (0.5*Moment of Inertia along Y-axis*Angular Velocity along Y-axis^2)+(0.5*Moment of Inertia along Z-axis*Angular Velocity along Z-axis^2)+(0.5*Moment of Inertia along X-axis*Angular Velocity along X-axis^2)
Translational Energy
​ Go Translational Energy = ((Momentum along X-axis^2)/(2*Mass))+((Momentum along Y-axis^2)/(2*Mass))+((Momentum along Z-axis^2)/(2*Mass))
Rotational Energy of Linear Molecule
​ Go Rotational Energy = (0.5*Moment of Inertia along Y-axis*(Angular Velocity along Y-axis^2))+(0.5*Moment of Inertia along Z-axis*(Angular Velocity along Z-axis^2))
Vibrational Energy Modeled as Harmonic Oscillator
​ Go Vibrational Energy = ((Momentum of Harmonic Oscillator^2)/(2*Mass))+(0.5*Spring Constant*(Change in Position^2))

## <Important Formulae on Equipartition Principle and Heat Capacity Calculators

Average Thermal Energy of Non-linear polyatomic Gas Molecule given Atomicity
​ Go Thermal Energy given Atomicity = ((6*Atomicity)-6)*(0.5*[BoltZ]*Temperature)
Average Thermal Energy of Linear Polyatomic Gas Molecule given Atomicity
​ Go Thermal Energy given Atomicity = ((6*Atomicity)-5)*(0.5*[BoltZ]*Temperature)
Internal Molar Energy of Non-Linear Molecule given Atomicity
​ Go Molar Internal Energy = ((6*Atomicity)-6)*(0.5*[R]*Temperature)
Internal Molar Energy of Linear Molecule given Atomicity
​ Go Molar Internal Energy = ((6*Atomicity)-5)*(0.5*[R]*Temperature)

## Vibrational Mode of Linear Molecule Formula

Number of Normal modes = (3*Atomicity)-5
Nvib = (3*N)-5

## What is the statement of Equipartition Theorem?

The original concept of equipartition was that the total kinetic energy of a system is shared equally among all of its independent parts, on the average, once the system has reached thermal equilibrium. Equipartition also makes quantitative predictions for these energies. The key point is that the kinetic energy is quadratic in the velocity. The equipartition theorem shows that in thermal equilibrium, any degree of freedom (such as a component of the position or velocity of a particle) which appears only quadratically in the energy has an average energy of ​1⁄2kBT and therefore contributes ​1⁄2kB to the system's heat capacity.

## How to Calculate Vibrational Mode of Linear Molecule?

Vibrational Mode of Linear Molecule calculator uses Number of Normal modes = (3*Atomicity)-5 to calculate the Number of Normal modes, The Vibrational Mode of Linear Molecule is the fundamental modes responsible for the vibrational motion. Number of Normal modes is denoted by Nvib symbol.

How to calculate Vibrational Mode of Linear Molecule using this online calculator? To use this online calculator for Vibrational Mode of Linear Molecule, enter Atomicity (N) and hit the calculate button. Here is how the Vibrational Mode of Linear Molecule calculation can be explained with given input values -> 4 = (3*3)-5.

### FAQ

What is Vibrational Mode of Linear Molecule?
The Vibrational Mode of Linear Molecule is the fundamental modes responsible for the vibrational motion and is represented as Nvib = (3*N)-5 or Number of Normal modes = (3*Atomicity)-5. The Atomicity is defined as the total number of atoms present in a molecule or element.
How to calculate Vibrational Mode of Linear Molecule?
The Vibrational Mode of Linear Molecule is the fundamental modes responsible for the vibrational motion is calculated using Number of Normal modes = (3*Atomicity)-5. To calculate Vibrational Mode of Linear Molecule, you need Atomicity (N). With our tool, you need to enter the respective value for Atomicity 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 Number of Normal modes?
In this formula, Number of Normal modes uses Atomicity. We can use 1 other way(s) to calculate the same, which is/are as follows -
• Number of Normal modes = (3*Atomicity)-6
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