Zero Point Energy of Particle in 1D Box Calculator

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Particle in 1 Dimensional Box

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✖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 1D Box gives us the dimension of the box in which the particle is kept.ⓘ Length of 1D Box [a]			+10% -10%

✖Zero Point Energy of Particle in 1D Box is defined as the lowest possible energy that the particle possess in the ground state.ⓘ Zero Point Energy of Particle in 1D Box [Z.P.E]

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Formula

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Zero Point Energy of Particle in 1D Box

Formula

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

Example

`"26.43057eV"=("[hP]"^2)/(8*"9E^-31kg"*("1.2A")^2)`

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Zero Point Energy of Particle in 1D Box Solution

STEP 0: Pre-Calculation Summary

Formula Used

Zero Point Energy of Particle in 1D Box = ([hP]^2)/(8*Mass of Particle*(Length of 1D Box)^2)
Z.P.E = ([hP]^2)/(8*m*(a)^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 1D Box - (Measured in Joule) - Zero Point Energy of Particle in 1D 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 1D Box - (Measured in Meter) - Length of 1D Box gives us the dimension of the box in which the particle is kept.

STEP 1: Convert Input(s) to Base Unit

Mass of Particle: 9E-31 Kilogram --> 9E-31 Kilogram No Conversion Required
Length of 1D Box: 1.2 Angstrom --> 1.2E-10 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Z.P.E = ([hP]^2)/(8*m*(a)^2) --> ([hP]^2)/(8*9E-31*(1.2E-10)^2)

Evaluating ... ...

Z.P.E = 4.23464546440833E-18

STEP 3: Convert Result to Output's Unit

4.23464546440833E-18 Joule -->26.4305666115518 Electron-Volt (Check conversion here)

FINAL ANSWER

26.4305666115518 ≈ 26.43057 Electron-Volt <-- Zero Point Energy of Particle in 1D 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 1 Dimensional Box Calculators

Energy of Particle residing in nth Level in 1D Box

Go Energy of Particle in 1D Box = (Energy Levels in 1D Box^2*[hP]^2)/(8*Mass of Particle*Length of 1D Box^2)

Zero Point Energy of Particle in 1D Box

Go Zero Point Energy of Particle in 1D Box = ([hP]^2)/(8*Mass of Particle*(Length of 1D Box)^2)

Number of Nodes for particle in 1D Box

Go Number of Nodes in 1D Box = (Energy Levels in 1D Box-1)

Zero Point Energy of Particle in 1D Box Formula

Zero Point Energy of Particle in 1D Box = ([hP]^2)/(8*Mass of Particle*(Length of 1D Box)^2)
Z.P.E = ([hP]^2)/(8*m*(a)^2)

Is the zero point energy of 1D box in accordance with the uncertainty principle ?

The Z.P.E of particle in 1D box is finite which means that the particle inside the box is not at rest even at 0K. This means that the position of the particle cannot be precisely known. Since only the expectation value of kinetic energy is known the linear momentum of the particle is also not known. Thus Z.P.E is in accordance with the uncertainty principle.

How to Calculate Zero Point Energy of Particle in 1D Box?

Zero Point Energy of Particle in 1D Box calculator uses Zero Point Energy of Particle in 1D Box = ([hP]^2)/(8*Mass of Particle*(Length of 1D Box)^2) to calculate the Zero Point Energy of Particle in 1D Box, The Zero Point Energy of Particle in 1D Box formula is defined as the lowest possible energy of the particle in a 1D box of infinite height which is not zero. Zero Point Energy of Particle in 1D Box is denoted by Z.P.E symbol.

How to calculate Zero Point Energy of Particle in 1D Box using this online calculator? To use this online calculator for Zero Point Energy of Particle in 1D Box, enter Mass of Particle (m) & Length of 1D Box (a) and hit the calculate button. Here is how the Zero Point Energy of Particle in 1D Box calculation can be explained with given input values -> 1.6E+20 = ([hP]^2)/(8*9E-31*(1.2E-10)^2).

FAQ

What is Zero Point Energy of Particle in 1D Box?

The Zero Point Energy of Particle in 1D Box formula is defined as the lowest possible energy of the particle in a 1D box of infinite height which is not zero and is represented as Z.P.E = ([hP]^2)/(8*m*(a)^2) or Zero Point Energy of Particle in 1D Box = ([hP]^2)/(8*Mass of Particle*(Length of 1D Box)^2). Mass of Particle is defined as the energy of that system in a reference frame where it has zero momentum & Length of 1D Box gives us the dimension of the box in which the particle is kept.

How to calculate Zero Point Energy of Particle in 1D Box?

The Zero Point Energy of Particle in 1D Box formula is defined as the lowest possible energy of the particle in a 1D box of infinite height which is not zero is calculated using Zero Point Energy of Particle in 1D Box = ([hP]^2)/(8*Mass of Particle*(Length of 1D Box)^2). To calculate Zero Point Energy of Particle in 1D Box, you need Mass of Particle (m) & Length of 1D Box (a). With our tool, you need to enter the respective value for Mass of Particle & Length of 1D 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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