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Zero Point Energy of Particle in 3D Box Formula

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Zero Point Energy of Particle in 3D Box is defined as the lowest possible energy that the particle possess in the ground state. Check FAQs

Z.P.E = \frac{3 \cdot ({[hP]}^{2})}{8 \cdot m \cdot {(l)}^{2}}

Z.P.E - Zero Point Energy of Particle in 3D Box?m - Mass of Particle?l - Length of 3D Square Box?[hP] - Planck constant?

Zero Point Energy of Particle in 3D Box Example

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

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

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

1.1E+20 = \frac{3 \cdot ({6.6E-34}^{2})}{8 \cdot 9E-31 \cdot {(1E-9)}^{2}}

1.1E+20eV = \frac{3 \cdot ({6.6E-34}^{2})}{8 \cdot 9E-31kg \cdot {(1E-9A)}^{2}}

1.1E+20 = \frac{3 \cdot ({6.6E-34}^{2})}{8 \cdot 9E-31 \cdot {(1E-9)}^{2}}

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Zero Point Energy of Particle in 3D Box Solution

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

FIRST Step Consider the formula

Z.P.E = \frac{3 \cdot ({[hP]}^{2})}{8 \cdot m \cdot {(l)}^{2}}

Next Step Substitute values of Variables

∴

Z.P.E = \frac{3 \cdot ({[hP]}^{2})}{8 \cdot 9E-31kg \cdot {(1E-9A)}^{2}}

Next Step Substitute values of Constants

∴

Z.P.E = \frac{3 \cdot ({6.6E-34}^{2})}{8 \cdot 9E-31kg \cdot {(1E-9A)}^{2}}

Next Step Convert Units

∴

Z.P.E = \frac{3 \cdot ({6.6E-34}^{2})}{8 \cdot 9E-31kg \cdot {(1E-19m)}^{2}}

Next Step Prepare to Evaluate

∴

Z.P.E = \frac{3 \cdot ({6.6E-34}^{2})}{8 \cdot 9E-31 \cdot {(1E-19)}^{2}}

Next Step Evaluate

∴

Z.P.E = 18.293668406244J

Next Step Convert to Output's Unit

∴

Z.P.E = 1.14180047761904E+20eV

LAST Step Rounding Answer

∴

Z.P.E = 1.1E+20eV

Zero Point Energy of Particle in 3D Box Formula Elements

Variables

Constants

Zero Point Energy of Particle in 3D Box

Zero Point Energy of Particle in 3D Box is defined as the lowest possible energy that the particle possess in the ground state.

Symbol: Z.P.E

Measurement: EnergyUnit: eV

Note: Value can be positive or negative.

Formulas to find Zero Point Energy of Particle in 3D Box

Mass of Particle

Mass of Particle is defined as the energy of that system in a reference frame where it has zero momentum.

Symbol: m

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Mass of Particle

Length of 3D Square Box

Length of 3D Square Box is defined as the dimension of the box in which the particle stays.

Symbol: l

Measurement: LengthUnit: A

Note: Value can be positive or negative.

Formulas to find Length of 3D Square Box

Planck constant

Planck constant is a fundamental universal constant that defines the quantum nature of energy and relates the energy of a photon to its frequency.

Symbol: [hP]

Value: 6.626070040E-34

Other formulas in Particle in 3 Dimensional Box category

Go Energy of Particle in nx Level in 3D Box

E x = \frac{{(n x)}^{2} \cdot {([hP])}^{2}}{8 \cdot m \cdot {(l x)}^{2}}

Go Energy of Particle in ny Level in 3D Box

E y = \frac{{(n y)}^{2} \cdot {([hP])}^{2}}{8 \cdot m \cdot {(l y)}^{2}}

Go Energy of Particle in nz Level in 3D Box

E z = \frac{{(n z)}^{2} \cdot {([hP])}^{2}}{8 \cdot m \cdot {(l z)}^{2}}

Go Total Energy of Particle in 3D Box

E = \frac{{(n x)}^{2} \cdot {([hP])}^{2}}{8 \cdot m \cdot {(l x)}^{2}} + \frac{{(n y)}^{2} \cdot {([hP])}^{2}}{8 \cdot m \cdot {(l y)}^{2}} + \frac{{(n z)}^{2} \cdot {([hP])}^{2}}{8 \cdot m \cdot {(l z)}^{2}}

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

Zero Point Energy of Particle in 3D Box evaluator uses Zero Point Energy of Particle in 3D Box = (3*([hP]^2))/(8*Mass of Particle*(Length of 3D Square Box)^2) to evaluate the Zero Point Energy of Particle in 3D Box, The Zero Point Energy of Particle in 3D Box formula is defined as the lowest possible energy that a quantum mechanical system may have. Zero Point Energy of Particle in 3D Box is denoted by Z.P.E symbol.

How to evaluate Zero Point Energy of Particle in 3D Box using this online evaluator? To use this online evaluator for Zero Point Energy of Particle in 3D Box, enter Mass of Particle (m) & Length of 3D Square Box (l) and hit the calculate button.

FAQs on Zero Point Energy of Particle in 3D Box

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

The formula of Zero Point Energy of Particle in 3D Box is expressed as Zero Point Energy of Particle in 3D Box = (3*([hP]^2))/(8*Mass of Particle*(Length of 3D Square Box)^2). Here is an example- 7.1E+38 = (3*([hP]^2))/(8*9E-31*(1E-19)^2).

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

With Mass of Particle (m) & Length of 3D Square Box (l) we can find Zero Point Energy of Particle in 3D Box using the formula - Zero Point Energy of Particle in 3D Box = (3*([hP]^2))/(8*Mass of Particle*(Length of 3D Square Box)^2). This formula also uses Planck constant .

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

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

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

Zero Point Energy of Particle in 3D Box is usually measured using the Electron-Volt[eV] for Energy. Joule[eV], Kilojoule[eV], Gigajoule[eV] are the few other units in which Zero Point Energy of Particle in 3D Box can be measured.

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