## Total Energy of Particle in 3D Box Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Energy of Particle in 3D Box = ((Energy Levels along x Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along x Direction)^2)+((Energy Levels along y Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along y Direction)^2)+((Energy Levels along z Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along z Direction)^2)
E = ((nx)^2*([hP])^2)/(8*m*(lx)^2)+((ny)^2*([hP])^2)/(8*m*(ly)^2)+((nz)^2*([hP])^2)/(8*m*(lz)^2)
This formula uses 1 Constants, 8 Variables
Constants Used
[hP] - Planck constant Value Taken As 6.626070040E-34 Kilogram Meter² / Second
Variables Used
Total Energy of Particle in 3D Box - (Measured in Joule) - 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.
Energy Levels along x Direction - Energy Levels along x Direction are the quantised levels where the particle may be present.
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 Box along x Direction - (Measured in Meter) - Length of Box along x Direction gives us the dimension of the box in which the particle is kept.
Energy Levels along y Direction - Energy Levels along y Direction are the quantised levels where the particle may be present.
Length of Box along y Direction - (Measured in Meter) - Length of Box along y Direction gives us the dimension of the box in which the particle is kept.
Energy Levels along z Direction - Energy Levels along z Direction are the quantised levels where the particle may be present.
Length of Box along z Direction - (Measured in Meter) - Length of Box along z Direction gives us the dimension of the box in which the particle is kept.
STEP 1: Convert Input(s) to Base Unit
Energy Levels along x Direction: 2 --> No Conversion Required
Mass of Particle: 9E-31 Kilogram --> 9E-31 Kilogram No Conversion Required
Length of Box along x Direction: 1.01 Angstrom --> 1.01E-10 Meter (Check conversion here)
Energy Levels along y Direction: 2 --> No Conversion Required
Length of Box along y Direction: 1.01 Angstrom --> 1.01E-10 Meter (Check conversion here)
Energy Levels along z Direction: 2 --> No Conversion Required
Length of Box along z Direction: 1.01 Angstrom --> 1.01E-10 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
E = ((nx)^2*([hP])^2)/(8*m*(lx)^2)+((ny)^2*([hP])^2)/(8*m*(ly)^2)+((nz)^2*([hP])^2)/(8*m*(lz)^2) --> ((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)
Evaluating ... ...
E = 7.17328434712048E-17
STEP 3: Convert Result to Output's Unit
7.17328434712048E-17 Joule -->447.72099896835 Electron-Volt (Check conversion here)
447.72099896835 447.721 Electron-Volt <-- Total 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
Total Energy of Particle in 3D Box = ((Energy Levels along x Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along x Direction)^2)+((Energy Levels along y Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along y Direction)^2)+((Energy Levels along z Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along z Direction)^2)
Total Energy of Particle in Cubic Box
Energy of Particle in 3D Square Box = (([hP])^2*((Energy Levels along x Direction)^2+(Energy Levels along y Direction)^2+(Energy Levels along z Direction)^2))/(8*Mass of Particle*(Length of 3D Square Box)^2)
Energy of Particle in nx Level in 3D Box
Energy of Particle in Box along x Direction = ((Energy Levels along x Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along x Direction)^2)
Energy of Particle in ny Level in 3D Box
Energy of Particle in Box along y Direction = ((Energy Levels along y Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along y Direction)^2)
Energy of Particle in nz Level in 3D Box
Energy of Particle in Box along z Direction = ((Energy Levels along z Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along z Direction)^2)
Zero Point Energy of Particle in 3D Box
Zero Point Energy of Particle in 3D Box = (3*([hP]^2))/(8*Mass of Particle*(Length of 3D Square Box)^2)

## Total Energy of Particle in 3D Box Formula

Total Energy of Particle in 3D Box = ((Energy Levels along x Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along x Direction)^2)+((Energy Levels along y Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along y Direction)^2)+((Energy Levels along z Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along z Direction)^2)
E = ((nx)^2*([hP])^2)/(8*m*(lx)^2)+((ny)^2*([hP])^2)/(8*m*(ly)^2)+((nz)^2*([hP])^2)/(8*m*(lz)^2)

## What do you mean by accidental degeneracy in quantum mechanics?

In quantum mechanics, accidental degeneracy refers to energy degeneracy that occurs coincidentally, without any protection by symmetry. Generally, an accidental degeneracy occurs due to accidental symmetries that can lead to additional degeneracies in the discrete energy spectrum. As an example of accidental degeneracy, we can consider a particle in a constant magnetic field.

## How to Calculate Total Energy of Particle in 3D Box?

Total Energy of Particle in 3D Box calculator uses Total Energy of Particle in 3D Box = ((Energy Levels along x Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along x Direction)^2)+((Energy Levels along y Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along y Direction)^2)+((Energy Levels along z Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along z Direction)^2) to calculate 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 calculate Total Energy of Particle in 3D Box using this online calculator? To use this online calculator for Total Energy of Particle in 3D Box, enter Energy Levels along x Direction (nx), Mass of Particle (m), Length of Box along x Direction (lx), Energy Levels along y Direction (ny), Length of Box along y Direction (ly), Energy Levels along z Direction (nz) & Length of Box along z Direction (lz) and hit the calculate button. Here is how the Total Energy of Particle in 3D Box calculation can be explained with given input values -> 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).

### FAQ

What is 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 and is represented as E = ((nx)^2*([hP])^2)/(8*m*(lx)^2)+((ny)^2*([hP])^2)/(8*m*(ly)^2)+((nz)^2*([hP])^2)/(8*m*(lz)^2) or Total Energy of Particle in 3D Box = ((Energy Levels along x Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along x Direction)^2)+((Energy Levels along y Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along y Direction)^2)+((Energy Levels along z Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along z Direction)^2). Energy Levels along x Direction are the quantised levels where the particle may be present, Mass of Particle is defined as the energy of that system in a reference frame where it has zero momentum, Length of Box along x Direction gives us the dimension of the box in which the particle is kept, Energy Levels along y Direction are the quantised levels where the particle may be present, Length of Box along y Direction gives us the dimension of the box in which the particle is kept, Energy Levels along z Direction are the quantised levels where the particle may be present & Length of Box along z Direction gives us the dimension of the box in which the particle is kept.
How to calculate 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 is calculated using Total Energy of Particle in 3D Box = ((Energy Levels along x Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along x Direction)^2)+((Energy Levels along y Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along y Direction)^2)+((Energy Levels along z Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along z Direction)^2). To calculate Total Energy of Particle in 3D Box, you need Energy Levels along x Direction (nx), Mass of Particle (m), Length of Box along x Direction (lx), Energy Levels along y Direction (ny), Length of Box along y Direction (ly), Energy Levels along z Direction (nz) & Length of Box along z Direction (lz). With our tool, you need to enter the respective value for Energy Levels along x Direction, Mass of Particle, Length of Box along x Direction, Energy Levels along y Direction, Length of Box along y Direction, Energy Levels along z Direction & Length of Box along z Direction and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well. Let Others Know