## Total Energy of Particle in Cubic Box Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
E = (([hP])^2*((nx)^2+(ny)^2+(nz)^2))/(8*m*(l)^2)
This formula uses 1 Constants, 6 Variables
Constants Used
[hP] - Planck constant Value Taken As 6.626070040E-34 Kilogram Meter² / Second
Variables Used
Energy of Particle in 3D Square Box - (Measured in Joule) - Energy of Particle in 3D Square Box is defined as the energy possessed by a particle residing in a three dimensional square box.
Energy Levels along x Direction - Energy Levels along x Direction are the quantised levels where the particle may be present.
Energy Levels along y Direction - Energy Levels along y Direction are the quantised levels where the particle may be present.
Energy Levels along z Direction - Energy Levels along z 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 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
Energy Levels along x Direction: 2 --> No Conversion Required
Energy Levels along y Direction: 2 --> No Conversion Required
Energy Levels along z Direction: 2 --> No Conversion Required
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
E = (([hP])^2*((nx)^2+(ny)^2+(nz)^2))/(8*m*(l)^2) --> (([hP])^2*((2)^2+(2)^2+(2)^2))/(8*9E-31*(1E-19)^2)
Evaluating ... ...
E = 73.174673624976
STEP 3: Convert Result to Output's Unit
73.174673624976 Joule -->4.56720191047614E+20 Electron-Volt (Check conversion here)
4.56720191047614E+20 4.6E+20 Electron-Volt <-- Energy of Particle in 3D Square Box
(Calculation completed in 00.004 seconds)
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## Credits

Created by Ritacheta Sen
University of Calcutta (C.U), Kolkata
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National University of Judicial Science (NUJS), 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 Cubic Box Formula

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)
E = (([hP])^2*((nx)^2+(ny)^2+(nz)^2))/(8*m*(l)^2)

## What do you mean by degeneracy in 3d cubic box ?

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 Total Energy of Particle in Cubic Box?

Total Energy of Particle in Cubic Box calculator uses 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) to calculate 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 calculate Total Energy of Particle in Cubic Box using this online calculator? To use this online calculator for Total Energy of Particle in Cubic Box, enter Energy Levels along x Direction (nx), Energy Levels along y Direction (ny), Energy Levels along z Direction (nz), Mass of Particle (m) & Length of 3D Square Box (l) and hit the calculate button. Here is how the Total Energy of Particle in Cubic Box calculation can be explained with given input values -> 2.9E+39 = (([hP])^2*((2)^2+(2)^2+(2)^2))/(8*9E-31*(1E-19)^2).

### FAQ

What is Total Energy of Particle in Cubic 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 and is represented as E = (([hP])^2*((nx)^2+(ny)^2+(nz)^2))/(8*m*(l)^2) or 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 Levels along x Direction are the quantised levels where the particle may be present, Energy Levels along y Direction are the quantised levels where the particle may be present, Energy Levels along z 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 3D Square Box is defined as the dimension of the box in which the particle stays.
How to calculate Total Energy of Particle in Cubic 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 is calculated using 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). To calculate Total Energy of Particle in Cubic Box, you need Energy Levels along x Direction (nx), Energy Levels along y Direction (ny), Energy Levels along z Direction (nz), Mass of Particle (m) & Length of 3D Square Box (l). With our tool, you need to enter the respective value for Energy Levels along x Direction, Energy Levels along y Direction, Energy Levels along z Direction, 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. Let Others Know