Zero Point Energy of Particle in 3D Box Calculator

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Particle in Box

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Particle in 3 Dimensional Box

Particle in 1 Dimensional Box

Particle in 2 Dimensional Box

✖Mass of Particle is defined as the energy of that system in a reference frame where it has zero momentum.ⓘ Mass of Particle [m]			+10% -10%
✖Length of 3D Square Box is defined as the dimension of the box in which the particle stays.ⓘ Length of 3D Square Box [l]			+10% -10%

✖Zero Point Energy of Particle in 3D Box is defined as the lowest possible energy that the particle possess in the ground state.ⓘ Zero Point Energy of Particle in 3D Box [Z.P.E]

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Formula

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Zero Point Energy of Particle in 3D Box

Formula

`"Z.P.E" = (3*("[hP]"^2))/(8*"m"*("l")^2)`

Example

`"1.1E^20eV"=(3*("[hP]"^2))/(8*"9E^-31kg"*("10E^-10A")^2)`

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Zero Point Energy of Particle in 3D Box Solution

STEP 0: Pre-Calculation Summary

Formula Used

Zero Point Energy of Particle in 3D Box = (3*([hP]^2))/(8*Mass of Particle*(Length of 3D Square Box)^2)
Z.P.E = (3*([hP]^2))/(8*m*(l)^2)
This formula uses 1 Constants, 3 Variables

Constants Used

[hP] - Planck constant Value Taken As 6.626070040E-34

Variables Used

Zero Point Energy of Particle in 3D Box - (Measured in Joule) - Zero Point Energy of Particle in 3D Box is defined as the lowest possible energy that the particle possess in the ground state.
Mass of Particle - (Measured in Kilogram) - Mass of Particle is defined as the energy of that system in a reference frame where it has zero momentum.
Length of 3D Square Box - (Measured in Meter) - Length of 3D Square Box is defined as the dimension of the box in which the particle stays.

STEP 1: Convert Input(s) to Base Unit

Mass of Particle: 9E-31 Kilogram --> 9E-31 Kilogram No Conversion Required
Length of 3D Square Box: 1E-09 Angstrom --> 1E-19 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Z.P.E = (3*([hP]^2))/(8*m*(l)^2) --> (3*([hP]^2))/(8*9E-31*(1E-19)^2)

Evaluating ... ...

Z.P.E = 18.293668406244

STEP 3: Convert Result to Output's Unit

18.293668406244 Joule -->1.14180047761904E+20 Electron-Volt (Check conversion here)

FINAL ANSWER

1.14180047761904E+20 ≈ 1.1E+20 Electron-Volt <-- Zero Point Energy of Particle in 3D Box

(Calculation completed in 00.004 seconds)

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Created by Ritacheta Sen

University of Calcutta (C.U), Kolkata

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< 6 Particle in 3 Dimensional Box Calculators

Total Energy of Particle in 3D Box

Go 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)

Total Energy of Particle in Cubic Box

Go 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)

Energy of Particle in nx Level in 3D Box

Go Energy of Particle in Box along X axis = ((Energy Levels along X axis)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along X axis)^2)

Energy of Particle in ny Level in 3D Box

Go Energy of Particle in Box along Y axis = ((Energy Levels along Y axis)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along Y axis)^2)

Energy of Particle in nz Level in 3D Box

Go Energy of Particle in Box along Z axis = ((Energy Levels along Z axis)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along Z axis)^2)

Zero Point Energy of Particle in 3D Box

Go Zero Point Energy of Particle in 3D Box = (3*([hP]^2))/(8*Mass of Particle*(Length of 3D Square Box)^2)

Zero Point Energy of Particle in 3D Box Formula

Zero Point Energy of Particle in 3D Box = (3*([hP]^2))/(8*Mass of Particle*(Length of 3D Square Box)^2)
Z.P.E = (3*([hP]^2))/(8*m*(l)^2)

What is the combination of quantum numbers for the first excited state of a particle in a 3-D box ?

The ground state has only one wavefunction and no other state has this specific energy; the ground state and the energy level are said to be non-degenerate. However, in the 3-D cubical box potential the energy of a state depends upon the sum of the squares of the quantum numbers.
The particle having a particular value of energy in the excited state may has several different stationary states or wavefunctions. If so, these states and energy eigenvalues are said to be degenerate.
For the first excited state, three combinations of the quantum numbers (nx,ny,nz) are (2,1,1),(1,2,1),(1,1,2).

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

Zero Point Energy of Particle in 3D Box calculator uses Zero Point Energy of Particle in 3D Box = (3*([hP]^2))/(8*Mass of Particle*(Length of 3D Square Box)^2) to calculate 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 calculate Zero Point Energy of Particle in 3D Box using this online calculator? To use this online calculator 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. Here is how the Zero Point Energy of Particle in 3D Box calculation can be explained with given input values -> 7.1E+38 = (3*([hP]^2))/(8*9E-31*(1E-19)^2).

FAQ

What is 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 and is represented as Z.P.E = (3*([hP]^2))/(8*m*(l)^2) or Zero Point Energy of Particle in 3D Box = (3*([hP]^2))/(8*Mass of Particle*(Length of 3D Square Box)^2). Mass of Particle is defined as the energy of that system in a reference frame where it has zero momentum & Length of 3D Square Box is defined as the dimension of the box in which the particle stays.

How to calculate 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 is calculated using Zero Point Energy of Particle in 3D Box = (3*([hP]^2))/(8*Mass of Particle*(Length of 3D Square Box)^2). To calculate Zero Point Energy of Particle in 3D Box, you need Mass of Particle (m) & Length of 3D Square Box (l). With our tool, you need to enter the respective value for Mass of Particle & Length of 3D Square Box 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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