Total Energy of Particle in 2D Square Box Calculator

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Particle in Box

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Particle in 2 Dimensional Box

Particle in 1 Dimensional Box

Particle in 3 Dimensional Box

✖Energy Levels along X axis are the quantised levels where the particle may be present.ⓘ Energy Levels along X axis [n_x]			+10% -10%
✖Energy Levels along Y axis are the quantised levels where the particle may be present.ⓘ Energy Levels along Y axis [n_y]			+10% -10%
✖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 2D Square Box is defined as the dimension of the box in which the particle stays.ⓘ Length of 2D Square Box [l]			+10% -10%

✖Energy of Particle in 2D Square Box is defined as the energy possessed by a particle residing in two dimensional square box.ⓘ Total Energy of Particle in 2D Square Box [E]

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Formula

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Total Energy of Particle in 2D Square Box

Formula

`"E" = ("[hP]"^2*(("n"_{"x"})^2+("n"_{"y"})^2))/(8*"m"*("l")^2)`

Example

`"3E^22eV"=("[hP]"^2*(("2")^2+("2")^2))/(8*"9E^-31kg"*("1E^-10A")^2)`

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Total Energy of Particle in 2D Square Box Solution

STEP 0: Pre-Calculation Summary

Formula Used

Energy of Particle in 2D Square Box = ([hP]^2*((Energy Levels along X axis)^2+(Energy Levels along Y axis)^2))/(8*Mass of Particle*(Length of 2D Square Box)^2)
E = ([hP]^2*((n_x)^2+(n_y)^2))/(8*m*(l)^2)
This formula uses 1 Constants, 5 Variables

Constants Used

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

Variables Used

Energy of Particle in 2D Square Box - (Measured in Joule) - Energy of Particle in 2D Square Box is defined as the energy possessed by a particle residing in two dimensional square box.
Energy Levels along X axis - Energy Levels along X axis are the quantised levels where the particle may be present.
Energy Levels along Y axis - Energy Levels along Y axis 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 2D Square Box - (Measured in Meter) - Length of 2D 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 axis: 2 --> No Conversion Required
Energy Levels along Y axis: 2 --> No Conversion Required
Mass of Particle: 9E-31 Kilogram --> 9E-31 Kilogram No Conversion Required
Length of 2D Square Box: 1E-10 Angstrom --> 1E-20 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E = ([hP]^2*((n_x)^2+(n_y)^2))/(8*m*(l)^2) --> ([hP]^2*((2)^2+(2)^2))/(8*9E-31*(1E-20)^2)

Evaluating ... ...

E = 4878.3115749984

STEP 3: Convert Result to Output's Unit

4878.3115749984 Joule -->3.04480127365076E+22 Electron-Volt (Check conversion here)

FINAL ANSWER

3.04480127365076E+22 ≈ 3E+22 Electron-Volt <-- Energy of Particle in 2D Square 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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< 3 Particle in 2 Dimensional Box Calculators

Total Energy of Particle in 2D Box

Go Total Energy of Particle in 2D 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))

Total Energy of Particle in 2D Square Box

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

Zero Point Energy of Particle in 2D Box

Go 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 Square Box Formula

Which is the most degenerate case when a particle is in a two dimensional box ?

The most degenerate case is the square, Lx=Ly for which clearly Em,n=En,m. Degeneracies in quantum physics are most often associated with symmetries in this way. 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. For the first excited state, three combinations of the quantum numbers (nx,ny) are (2,1) and (1,2).

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

Total Energy of Particle in 2D Square Box calculator uses Energy of Particle in 2D Square Box = ([hP]^2*((Energy Levels along X axis)^2+(Energy Levels along Y axis)^2))/(8*Mass of Particle*(Length of 2D Square Box)^2) to calculate the Energy of Particle in 2D Square Box, The Total Energy of Particle in 2D Square 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. Energy of Particle in 2D Square Box is denoted by E symbol.

How to calculate Total Energy of Particle in 2D Square Box using this online calculator? To use this online calculator for Total Energy of Particle in 2D Square Box, enter Energy Levels along X axis (n_x), Energy Levels along Y axis (n_y), Mass of Particle (m) & Length of 2D Square Box (l) and hit the calculate button. Here is how the Total Energy of Particle in 2D Square Box calculation can be explained with given input values -> 1.9E+41 = ([hP]^2*((2)^2+(2)^2))/(8*9E-31*(1E-20)^2).

FAQ

What is Total Energy of Particle in 2D Square Box?

The Total Energy of Particle in 2D Square 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 = ([hP]^2*((n_x)^2+(n_y)^2))/(8*m*(l)^2) or Energy of Particle in 2D Square Box = ([hP]^2*((Energy Levels along X axis)^2+(Energy Levels along Y axis)^2))/(8*Mass of Particle*(Length of 2D Square Box)^2). Energy Levels along X axis are the quantised levels where the particle may be present, Energy Levels along Y axis 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 2D Square Box is defined as the dimension of the box in which the particle stays.

How to calculate Total Energy of Particle in 2D Square Box?

The Total Energy of Particle in 2D Square 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 Energy of Particle in 2D Square Box = ([hP]^2*((Energy Levels along X axis)^2+(Energy Levels along Y axis)^2))/(8*Mass of Particle*(Length of 2D Square Box)^2). To calculate Total Energy of Particle in 2D Square Box, you need Energy Levels along X axis (n_x), Energy Levels along Y axis (n_y), Mass of Particle (m) & Length of 2D Square Box (l). With our tool, you need to enter the respective value for Energy Levels along X axis, Energy Levels along Y axis, Mass of Particle & Length of 2D 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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