## Total Energy of Particle in 2D Box Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Energy of Particle in 2D 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))
E = ((nx)^2*([hP])^2/(8*m*(lx)^2))+((ny)^2*([hP])^2/(8*m*(ly)^2))
This formula uses 1 Constants, 6 Variables
Constants Used
[hP] - Planck constant Value Taken As 6.626070040E-34 Kilogram Meter² / Second
Variables Used
Total Energy of Particle in 2D Box - (Measured in Joule) - Total Energy of Particle in 2D Box is defined as the summation of the energy possessed by the particle in both x and y 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.
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)
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)) --> ((2)^2*([hP])^2/(8*9E-31*(1.01E-10)^2))+((2)^2*([hP])^2/(8*9E-31*(1.01E-10)^2))
Evaluating ... ...
E = 4.78218956474698E-17
STEP 3: Convert Result to Output's Unit
4.78218956474698E-17 Joule -->298.4806659789 Electron-Volt (Check conversion here)
298.4806659789 298.4807 Electron-Volt <-- Total Energy of Particle in 2D 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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## < 3 Particle in 2 Dimensional Box Calculators

Total Energy of Particle in 2D Box
Total Energy of Particle in 2D 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))
Total Energy of Particle in 2D Square Box
Energy of Particle in 2D Square Box = ([hP]^2*((Energy Levels along x Direction)^2+(Energy Levels along y Direction)^2))/(8*Mass of Particle*(Length of 2D Square Box)^2)
Zero Point Energy of Particle in 2D Box
Zero Point Energy of Particle in 2D Box = (2*[hP]^2)/(8*Mass of Particle*(Length of 2D Square Box)^2)

## Total Energy of Particle in 2D Box Formula

Total Energy of Particle in 2D 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))
E = ((nx)^2*([hP])^2/(8*m*(lx)^2))+((ny)^2*([hP])^2/(8*m*(ly)^2))

## When do we say that wavefunctions are degenerate ?

Two distinct wavefunctions are said to be degenerate if they correspond to the same energy. If the sides a, b of the rectangle are such that a/b is irrational (the general case), there will be no degeneracies. For the ground state of the particle in a 2D box, there is one wavefunction (and no other) with this specific energy; the ground state and the energy level are said to be non-degenerate. However, in the 2-D box potential, the energy of a state depends upon the sum of the squares of the two 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.

## How to Calculate Total Energy of Particle in 2D Box?

Total Energy of Particle in 2D Box calculator uses Total Energy of Particle in 2D 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)) to calculate the Total Energy of Particle in 2D Box, The Total Energy of Particle in 2D Box formula is defined as the total energy of particle in a 2 dimensional box which is now quantised by two numbers nx and ny. Total Energy of Particle in 2D Box is denoted by E symbol.

How to calculate Total Energy of Particle in 2D Box using this online calculator? To use this online calculator for Total Energy of Particle in 2D 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) and hit the calculate button. Here is how the Total Energy of Particle in 2D Box calculation can be explained with given input values -> 1.9E+21 = ((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 2D Box?
The Total Energy of Particle in 2D Box formula is defined as the total energy of particle in a 2 dimensional box which is now quantised by two numbers nx and ny and is represented as E = ((nx)^2*([hP])^2/(8*m*(lx)^2))+((ny)^2*([hP])^2/(8*m*(ly)^2)) or Total Energy of Particle in 2D 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 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.
How to calculate Total Energy of Particle in 2D Box?
The Total Energy of Particle in 2D Box formula is defined as the total energy of particle in a 2 dimensional box which is now quantised by two numbers nx and ny is calculated using Total Energy of Particle in 2D 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)). To calculate Total Energy of Particle in 2D 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). 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 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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