Zero Point Energy of Particle in 2D 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

✖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%

✖Zero Point Energy of Particle in 2D Box is defined as the lowest possible energy that the particle possess in the ground state.ⓘ Zero Point Energy of Particle in 2D Box [Z.P.E]

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Formula

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Zero Point Energy of Particle in 2D Box

Formula

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

Example

`"7.6E^21eV"=(2*"[hP]"^2)/(8*"9E^-31kg"*("1E^-10A")^2)`

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Zero Point Energy of Particle in 2D Box Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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

Z.P.E = (2*[hP]^2)/(8*m*(l)^2) --> (2*[hP]^2)/(8*9E-31*(1E-20)^2)

Evaluating ... ...

Z.P.E = 1219.5778937496

STEP 3: Convert Result to Output's Unit

1219.5778937496 Joule -->7.61200318412691E+21 Electron-Volt (Check conversion here)

FINAL ANSWER

7.61200318412691E+21 ≈ 7.6E+21 Electron-Volt <-- Zero Point Energy of Particle in 2D 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)

Zero Point Energy of Particle in 2D Box Formula

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

Which has greater ZPE - particle in 1D box or particle in 2D box ?

The degeneracy of a state is the number of ways that state can be realized. In the case of a 2D-box, the degeneracy is given by the number of combinations of nx and ny that give the same energy. These two combinations give the same energy, so the degeneracy of the state is 2. Hence the zero point energy becomes greater than that of 1D box.

How to Calculate Zero Point Energy of Particle in 2D Box?

Zero Point Energy of Particle in 2D Box calculator uses Zero Point Energy of Particle in 2D Box = (2*[hP]^2)/(8*Mass of Particle*(Length of 2D Square Box)^2) to calculate the Zero Point Energy of Particle in 2D Box, The Zero Point Energy of Particle in 2D Box formula is defined as the lowest possible energy that a quantum mechanical system may have. Zero Point Energy of Particle in 2D Box is denoted by Z.P.E symbol.

How to calculate Zero Point Energy of Particle in 2D Box using this online calculator? To use this online calculator for Zero Point Energy of Particle in 2D Box, enter Mass of Particle (m) & Length of 2D Square Box (l) and hit the calculate button. Here is how the Zero Point Energy of Particle in 2D Box calculation can be explained with given input values -> 4.8E+40 = (2*[hP]^2)/(8*9E-31*(1E-20)^2).

FAQ

What is Zero Point Energy of Particle in 2D Box?

The Zero Point Energy of Particle in 2D Box formula is defined as the lowest possible energy that a quantum mechanical system may have and is represented as Z.P.E = (2*[hP]^2)/(8*m*(l)^2) or Zero Point Energy of Particle in 2D Box = (2*[hP]^2)/(8*Mass of Particle*(Length of 2D 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 2D Square Box is defined as the dimension of the box in which the particle stays.

How to calculate Zero Point Energy of Particle in 2D Box?

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