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Total Energy of Particle in Cubic Box Formula

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Energy of Particle in 3D Square Box is defined as the energy possessed by a particle residing in a three dimensional square box. Check FAQs

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

E - Energy of Particle in 3D Square Box?n_x - Energy Levels along X axis?n_y - Energy Levels along Y axis?n_z - Energy Levels along Z axis?m - Mass of Particle?l - Length of 3D Square Box?[hP] - Planck constant?

Total Energy of Particle in Cubic Box Example

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Here is how the Total Energy of Particle in Cubic Box equation looks like with Values.

Here is how the Total Energy of Particle in Cubic Box equation looks like with Units.

Here is how the Total Energy of Particle in Cubic Box equation looks like.

4.6E+20 = \frac{{(6.6E-34)}^{2} \cdot ({(2)}^{2} + {(2)}^{2} + {(2)}^{2})}{8 \cdot 9E-31 \cdot {(1E-9)}^{2}}

4.6E+20eV = \frac{{(6.6E-34)}^{2} \cdot ({(2)}^{2} + {(2)}^{2} + {(2)}^{2})}{8 \cdot 9E-31kg \cdot {(1E-9A)}^{2}}

4.6E+20 = \frac{{(6.6E-34)}^{2} \cdot ({(2)}^{2} + {(2)}^{2} + {(2)}^{2})}{8 \cdot 9E-31 \cdot {(1E-9)}^{2}}

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Total Energy of Particle in Cubic Box Solution

Follow our step by step solution on how to calculate Total Energy of Particle in Cubic Box?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

E = \frac{{(6.6E-34)}^{2} \cdot ({(2)}^{2} + {(2)}^{2} + {(2)}^{2})}{8 \cdot 9E-31 \cdot {(1E-19)}^{2}}

Next Step Evaluate

∴

E = 73.174673624976J

Next Step Convert to Output's Unit

∴

E = 4.56720191047614E+20eV

LAST Step Rounding Answer

∴

E = 4.6E+20eV

Total Energy of Particle in Cubic Box Formula Elements

Variables

Constants

Energy of Particle in 3D Square Box

Energy of Particle in 3D Square Box is defined as the energy possessed by a particle residing in a three dimensional square box.

Symbol: E

Measurement: EnergyUnit: eV

Note: Value can be positive or negative.

Formulas to find Energy of Particle in 3D Square Box

Energy Levels along X axis

Energy Levels along X axis are the quantised levels where the particle may be present.

Symbol: n_x

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Energy Levels along X axis

Energy Levels along Y axis

Energy Levels along Y axis are the quantised levels where the particle may be present.

Symbol: n_y

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Energy Levels along Y axis

Energy Levels along Z axis

Energy Levels along Z axis are the quantised levels where the particle may be present.

Symbol: n_z

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Energy Levels along Z axis

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 Total Energy of Particle in Cubic Box?

Total Energy of Particle in Cubic Box evaluator uses Energy of Particle in 3D Square Box = (([hP])^2*((Energy Levels along X axis)^2+(Energy Levels along Y axis)^2+(Energy Levels along Z axis)^2))/(8*Mass of Particle*(Length of 3D Square Box)^2) to evaluate the Energy of Particle in 3D Square Box, The Total Energy of Particle in Cubic Box formula is defined as as the total energy of particle in a 3 dimensional box which is now quantised by two numbers nx, ny and nz. Energy of Particle in 3D Square Box is denoted by E symbol.

How to evaluate Total Energy of Particle in Cubic Box using this online evaluator? To use this online evaluator for Total Energy of Particle in Cubic Box, enter Energy Levels along X axis (n_x), Energy Levels along Y axis (n_y), Energy Levels along Z axis (n_z), Mass of Particle (m) & Length of 3D Square Box (l) and hit the calculate button.

FAQs on Total Energy of Particle in Cubic Box

What is the formula to find Total Energy of Particle in Cubic Box?

The formula of Total Energy of Particle in Cubic Box is expressed as Energy of Particle in 3D Square Box = (([hP])^2*((Energy Levels along X axis)^2+(Energy Levels along Y axis)^2+(Energy Levels along Z axis)^2))/(8*Mass of Particle*(Length of 3D Square Box)^2). Here is an example- 2.9E+39 = (([hP])^2*((2)^2+(2)^2+(2)^2))/(8*9E-31*(1E-19)^2).

How to calculate Total Energy of Particle in Cubic Box?

With Energy Levels along X axis (n_x), Energy Levels along Y axis (n_y), Energy Levels along Z axis (n_z), Mass of Particle (m) & Length of 3D Square Box (l) we can find Total Energy of Particle in Cubic Box using the formula - Energy of Particle in 3D Square Box = (([hP])^2*((Energy Levels along X axis)^2+(Energy Levels along Y axis)^2+(Energy Levels along Z axis)^2))/(8*Mass of Particle*(Length of 3D Square Box)^2). This formula also uses Planck constant .

Can the Total Energy of Particle in Cubic Box be negative?

Yes, the Total Energy of Particle in Cubic Box, measured in Energy can be negative.

Which unit is used to measure Total Energy of Particle in Cubic Box?

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

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Total Energy of Particle in Cubic Box Formula

Total Energy of Particle in Cubic Box Example

Total Energy of Particle in Cubic Box Solution

Total Energy of Particle in Cubic Box Formula Elements

Other formulas in Particle in 3 Dimensional Box category

How to Evaluate Total Energy of Particle in Cubic Box?

FAQs on Total Energy of Particle in Cubic Box

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