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Zero Point Energy of Particle in 3D SHO Formula

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Zero Point Energy of 3D SHO is the lowest possible energy possessed by the particle. Check FAQs

Z.P.E = 1.5 \cdot [h-] \cdot ω

Z.P.E - Zero Point Energy of 3D SHO?ω - Angular Frequency of Oscillator?[h-] - Reduced Planck constant?

Zero Point Energy of Particle in 3D SHO Example

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Here is how the Zero Point Energy of Particle in 3D SHO equation looks like with Values.

Here is how the Zero Point Energy of Particle in 3D SHO equation looks like with Units.

Here is how the Zero Point Energy of Particle in 3D SHO equation looks like.

2.6E-34 = 1.5 \cdot 1.1E-34 \cdot 1.666

2.6E-34J = 1.5 \cdot 1.1E-34 \cdot 1.666rad/s

2.6E-34 = 1.5 \cdot 1.1E-34 \cdot 1.666

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Zero Point Energy of Particle in 3D SHO Solution

Follow our step by step solution on how to calculate Zero Point Energy of Particle in 3D SHO?

FIRST Step Consider the formula

Z.P.E = 1.5 \cdot [h-] \cdot ω

Next Step Substitute values of Variables

∴

Z.P.E = 1.5 \cdot [h-] \cdot 1.666rad/s

Next Step Substitute values of Constants

∴

Z.P.E = 1.5 \cdot 1.1E-34 \cdot 1.666rad/s

Next Step Prepare to Evaluate

∴

Z.P.E = 1.5 \cdot 1.1E-34 \cdot 1.666

Next Step Evaluate

∴

Z.P.E = 2.63537492854764E-34J

LAST Step Rounding Answer

∴

Z.P.E = 2.6E-34J

Zero Point Energy of Particle in 3D SHO Formula Elements

Variables

Constants

Zero Point Energy of 3D SHO

Zero Point Energy of 3D SHO is the lowest possible energy possessed by the particle.

Symbol: Z.P.E

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Zero Point Energy of 3D SHO

Angular Frequency of Oscillator

Angular Frequency of Oscillator is the angular displacement of any element of the wave per unit of time or the rate of change of the phase of the waveform.

Symbol: ω

Measurement: Angular FrequencyUnit: rad/s

Note: Value can be positive or negative.

Formulas to find Angular Frequency of Oscillator

Reduced Planck constant

Reduced Planck constant is a fundamental physical constant that relates the energy of a quantum system to the frequency of its associated wave function.

Symbol: [h-]

Value: 1.054571817E-34

Other formulas in Simple Harmonic Oscillator category

Go Restoring Force of Diatomic Vibrating Molecule

F = - (k \cdot x)

Go Potential Energy of Vibrating Atom

V = 0.5 \cdot (k \cdot {(x)}^{2})

Go Energy Eigen Values for 1D SHO

E n = (n + 0.5) \cdot ([h-]) \cdot (ω)

Go Zero Point Energy of Particle in 1D SHO

Z.P.E = 0.5 \cdot [h-] \cdot ω

How to Evaluate Zero Point Energy of Particle in 3D SHO?

Zero Point Energy of Particle in 3D SHO evaluator uses Zero Point Energy of 3D SHO = 1.5*[h-]*Angular Frequency of Oscillator to evaluate the Zero Point Energy of 3D SHO, The Zero Point Energy of Particle in 3D SHO formula is defined as the lowest possible energy that a quantum mechanical system may have. Zero Point Energy of 3D SHO is denoted by Z.P.E symbol.

How to evaluate Zero Point Energy of Particle in 3D SHO using this online evaluator? To use this online evaluator for Zero Point Energy of Particle in 3D SHO, enter Angular Frequency of Oscillator (ω) and hit the calculate button.

FAQs on Zero Point Energy of Particle in 3D SHO

What is the formula to find Zero Point Energy of Particle in 3D SHO?

The formula of Zero Point Energy of Particle in 3D SHO is expressed as Zero Point Energy of 3D SHO = 1.5*[h-]*Angular Frequency of Oscillator. Here is an example- 2.6E-34 = 1.5*[h-]*1.666.

How to calculate Zero Point Energy of Particle in 3D SHO?

With Angular Frequency of Oscillator (ω) we can find Zero Point Energy of Particle in 3D SHO using the formula - Zero Point Energy of 3D SHO = 1.5*[h-]*Angular Frequency of Oscillator. This formula also uses Reduced Planck constant .

Can the Zero Point Energy of Particle in 3D SHO be negative?

Yes, the Zero Point Energy of Particle in 3D SHO, measured in Energy can be negative.

Which unit is used to measure Zero Point Energy of Particle in 3D SHO?

Zero Point Energy of Particle in 3D SHO is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Zero Point Energy of Particle in 3D SHO can be measured.

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