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Total Energy of Particle in 3D Box Formula

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Total Energy of Particle in 3D Box is defined as the summation of the energy possessed by the particle in both x , y and z directions. Check FAQs

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}}

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

Total Energy of Particle in 3D Box Example

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

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

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

447.721 = \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31 \cdot {(1.01)}^{2}} + \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31 \cdot {(1.01)}^{2}} + \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31 \cdot {(1.01)}^{2}}

447.721eV = \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31kg \cdot {(1.01A)}^{2}} + \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31kg \cdot {(1.01A)}^{2}} + \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31kg \cdot {(1.01A)}^{2}}

447.721 = \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31 \cdot {(1.01)}^{2}} + \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31 \cdot {(1.01)}^{2}} + \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31 \cdot {(1.01)}^{2}}

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Total Energy of Particle in 3D Box Solution

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

FIRST Step Consider the formula

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}}

Next Step Substitute values of Variables

∴

E = \frac{{(2)}^{2} \cdot {([hP])}^{2}}{8 \cdot 9E-31kg \cdot {(1.01A)}^{2}} + \frac{{(2)}^{2} \cdot {([hP])}^{2}}{8 \cdot 9E-31kg \cdot {(1.01A)}^{2}} + \frac{{(2)}^{2} \cdot {([hP])}^{2}}{8 \cdot 9E-31kg \cdot {(1.01A)}^{2}}

Next Step Substitute values of Constants

∴

E = \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31kg \cdot {(1.01A)}^{2}} + \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31kg \cdot {(1.01A)}^{2}} + \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31kg \cdot {(1.01A)}^{2}}

Next Step Convert Units

∴

E = \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31kg \cdot {(1E-10m)}^{2}} + \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31kg \cdot {(1E-10m)}^{2}} + \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31kg \cdot {(1E-10m)}^{2}}

Next Step Prepare to Evaluate

∴

E = \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31 \cdot {(1E-10)}^{2}} + \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31 \cdot {(1E-10)}^{2}} + \frac{{(2)}^{2} \cdot {(6.6E-34)}^{2}}{8 \cdot 9E-31 \cdot {(1E-10)}^{2}}

Next Step Evaluate

∴

E = 7.17328434712048E-17J

Next Step Convert to Output's Unit

∴

E = 447.72099896835eV

LAST Step Rounding Answer

∴

E = 447.721eV

Total Energy of Particle in 3D Box Formula Elements

Variables

Constants

Total Energy of Particle in 3D Box

Total Energy of Particle in 3D Box is defined as the summation of the energy possessed by the particle in both x , y and z directions.

Symbol: E

Measurement: EnergyUnit: eV

Note: Value can be positive or negative.

Formulas to find Total Energy of Particle in 3D 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

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 Box along X axis

Length of Box along X axis gives us the dimension of the box in which the particle is kept.

Symbol: l_x

Measurement: LengthUnit: A

Note: Value can be positive or negative.

Formulas to find Length of Box 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

Length of Box along Y axis

Length of Box along Y axis gives us the dimension of the box in which the particle is kept.

Symbol: l_y

Measurement: LengthUnit: A

Note: Value should be greater than 0.

Formulas to find Length of Box 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

Length of Box along Z axis

Length of Box along Z axis gives us the dimension of the box in which the particle is kept.

Symbol: l_z

Measurement: LengthUnit: A

Note: Value should be greater than 0.

Formulas to find Length of Box along Z axis

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

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

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}}

How to Evaluate Total Energy of Particle in 3D Box?

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

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

FAQs on Total Energy of Particle in 3D Box

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

The formula of Total Energy of Particle in 3D Box is expressed as Total Energy of Particle in 3D Box = ((Energy Levels along X axis)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along X axis)^2)+((Energy Levels along Y axis)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along Y axis)^2)+((Energy Levels along Z axis)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along Z axis)^2). Here is an example- 2.8E+21 = ((2)^2*([hP])^2)/(8*9E-31*(1.01E-10)^2)+((2)^2*([hP])^2)/(8*9E-31*(1.01E-10)^2)+((2)^2*([hP])^2)/(8*9E-31*(1.01E-10)^2).

How to calculate Total Energy of Particle in 3D Box?

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

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

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

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

Total 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 Total Energy of Particle in 3D Box can be measured.

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Total Energy of Particle in 3D Box Formula

Total Energy of Particle in 3D Box Example

Total Energy of Particle in 3D Box Solution

Total Energy of Particle in 3D Box Formula Elements

Other formulas in Particle in 3 Dimensional Box category

How to Evaluate Total Energy of Particle in 3D Box?

FAQs on Total Energy of Particle in 3D Box

Variable Name