## Potential Energy of Vibrating Atom Solution

STEP 0: Pre-Calculation Summary
Formula Used
Potential Energy of Vibrating Atom = 0.5*(Force Constant of Vibrating Molecule*(Displacement of Vibrating Atoms)^2)
V = 0.5*(k*(x)^2)
This formula uses 3 Variables
Variables Used
Potential Energy of Vibrating Atom - (Measured in Joule) - Potential Energy of Vibrating Atom is the energy stored in the bond when the bond is extended or compressed.
Force Constant of Vibrating Molecule - (Measured in Newton per Meter) - Force Constant of Vibrating Molecule reflects the stiffness or the rigidity of the bond between the vibrating atoms.
Displacement of Vibrating Atoms - (Measured in Meter) - Displacement of Vibrating Atoms is the distance covered by the atom during its vibration from its mean position to another extreme.
STEP 1: Convert Input(s) to Base Unit
Force Constant of Vibrating Molecule: 100 Newton per Meter --> 100 Newton per Meter No Conversion Required
Displacement of Vibrating Atoms: 0.1 Meter --> 0.1 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = 0.5*(k*(x)^2) --> 0.5*(100*(0.1)^2)
Evaluating ... ...
V = 0.5
STEP 3: Convert Result to Output's Unit
0.5 Joule --> No Conversion Required
0.5 Joule <-- Potential Energy of Vibrating Atom
(Calculation completed in 00.004 seconds)
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## Credits

Created by Ritacheta Sen
University of Calcutta (C.U), Kolkata
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National University of Judicial Science (NUJS), Kolkata
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## < 8 Simple Harmonic Oscillator Calculators

Energy Eigen Values for 3D SHO
Energy Eigen Values of 3D SHO = (Energy Levels of 3D Oscillator along X axis+Energy Levels of 3D Oscillator along Y axis+Energy Levels of 3D Oscillator along Z axis+1.5)*[h-]*Angular Frequency of Oscillator
Energy Eigen Values for 2D SHO
Energy Eigen Values of 2D SHO = (Energy Levels of 2D Oscillator along X axis+Energy Levels of 2D Oscillator along Y axis+1)*[h-]*Angular Frequency of Oscillator
Energy Eigen Values for 1D SHO
Energy Eigen Values of 1D SHO = (Energy Levels of 1D Oscillator+0.5)*([h-])*(Angular Frequency of Oscillator)
Restoring Force of Diatomic Vibrating Molecule
Restoring Force of Vibrating Diatomic Molecule = -(Force Constant of Vibrating Molecule*Displacement of Vibrating Atoms)
Potential Energy of Vibrating Atom
Potential Energy of Vibrating Atom = 0.5*(Force Constant of Vibrating Molecule*(Displacement of Vibrating Atoms)^2)
Zero Point Energy of Particle in 2D SHO
Zero Point Energy of Particle in 2D SHO = [h-]*Angular Frequency of Oscillator
Zero Point Energy of Particle in 1D SHO
Zero Point Energy of 1D SHO = 0.5*[h-]*Angular Frequency of Oscillator
Zero Point Energy of Particle in 3D SHO
Zero Point Energy of 3D SHO = 1.5*[h-]*Angular Frequency of Oscillator

## Potential Energy of Vibrating Atom Formula

Potential Energy of Vibrating Atom = 0.5*(Force Constant of Vibrating Molecule*(Displacement of Vibrating Atoms)^2)
V = 0.5*(k*(x)^2)

## What is the use of the negetive sign in the restoring force formula ?

The force constant k is a measure of the stiffness of the bond when it is compressed or relaxed. The variable x is chosen equal to zero at the equilibrium position, positive for stretching, negative for compression. The negative sign in the restoring force formula reflects the fact that F is a restoring force, always in the opposite sense to the displacement x.

## How to Calculate Potential Energy of Vibrating Atom?

Potential Energy of Vibrating Atom calculator uses Potential Energy of Vibrating Atom = 0.5*(Force Constant of Vibrating Molecule*(Displacement of Vibrating Atoms)^2) to calculate the Potential Energy of Vibrating Atom, The Potential Energy of Vibrating Atom formula is half the product of force constant with the square of the displacement of atoms vibrating. Potential Energy of Vibrating Atom is denoted by V symbol.

How to calculate Potential Energy of Vibrating Atom using this online calculator? To use this online calculator for Potential Energy of Vibrating Atom, enter Force Constant of Vibrating Molecule (k) & Displacement of Vibrating Atoms (x) and hit the calculate button. Here is how the Potential Energy of Vibrating Atom calculation can be explained with given input values -> 0.5 = 0.5*(100*(0.1)^2).

### FAQ

What is Potential Energy of Vibrating Atom?
The Potential Energy of Vibrating Atom formula is half the product of force constant with the square of the displacement of atoms vibrating and is represented as V = 0.5*(k*(x)^2) or Potential Energy of Vibrating Atom = 0.5*(Force Constant of Vibrating Molecule*(Displacement of Vibrating Atoms)^2). Force Constant of Vibrating Molecule reflects the stiffness or the rigidity of the bond between the vibrating atoms & Displacement of Vibrating Atoms is the distance covered by the atom during its vibration from its mean position to another extreme.
How to calculate Potential Energy of Vibrating Atom?
The Potential Energy of Vibrating Atom formula is half the product of force constant with the square of the displacement of atoms vibrating is calculated using Potential Energy of Vibrating Atom = 0.5*(Force Constant of Vibrating Molecule*(Displacement of Vibrating Atoms)^2). To calculate Potential Energy of Vibrating Atom, you need Force Constant of Vibrating Molecule (k) & Displacement of Vibrating Atoms (x). With our tool, you need to enter the respective value for Force Constant of Vibrating Molecule & Displacement of Vibrating 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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