Energy of Particle in nz Level in 3D Box Calculator

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Particle in Box

Hamiltonian System

Molecular Reaction Dynamics

Quantum Dots

Simple Harmonic Oscillator

Wien's Displacement Law

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Particle in 3 Dimensional Box

Particle in 1 Dimensional Box

Particle in 2 Dimensional Box

✖Energy Levels along Z axis are the quantised levels where the particle may be present.ⓘ Energy Levels along Z axis [n_z]			+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 Box along Z axis gives us the dimension of the box in which the particle is kept.ⓘ Length of Box along Z axis [l_z]			+10% -10%

✖Energy of Particle in Box along Z axis is defined as the energy values that a particle can have residing in one particular level.ⓘ Energy of Particle in nz Level in 3D Box [E_z]

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Formula

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Energy of Particle in nz Level in 3D Box

Formula

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

Example

`"149.2403eV"=(("2")^2*("[hP]")^2)/(8*"9E^-31kg"*("1.01A")^2)`

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Energy of Particle in nz Level in 3D Box Solution

STEP 0: Pre-Calculation Summary

Formula Used

Energy of Particle in Box along Z axis = ((Energy Levels along Z axis)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along Z axis)^2)
E_z = ((n_z)^2*([hP])^2)/(8*m*(l_z)^2)
This formula uses 1 Constants, 4 Variables

Constants Used

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

Variables Used

Energy of Particle in Box along Z axis - (Measured in Joule) - Energy of Particle in Box along Z axis is defined as the energy values that a particle can have residing in one particular level.
Energy Levels along Z axis - Energy Levels along Z 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 Box along Z axis - (Measured in Meter) - Length of Box along Z axis gives us the dimension of the box in which the particle is kept.

STEP 1: Convert Input(s) to Base Unit

Energy Levels along Z axis: 2 --> No Conversion Required
Mass of Particle: 9E-31 Kilogram --> 9E-31 Kilogram No Conversion Required
Length of Box along Z axis: 1.01 Angstrom --> 1.01E-10 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_z = ((n_z)^2*([hP])^2)/(8*m*(l_z)^2) --> ((2)^2*([hP])^2)/(8*9E-31*(1.01E-10)^2)

Evaluating ... ...

E_z = 2.39109478237349E-17

STEP 3: Convert Result to Output's Unit

2.39109478237349E-17 Joule -->149.24033298945 Electron-Volt (Check conversion here)

FINAL ANSWER

149.24033298945 ≈ 149.2403 Electron-Volt <-- Energy of Particle in Box along Z axis

(Calculation completed in 00.004 seconds)

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Created by Ritacheta Sen

University of Calcutta (C.U), Kolkata

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< 6 Particle in 3 Dimensional Box Calculators

Total Energy of Particle in 3D Box

Go Total Energy of Particle in 3D 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)+((Energy Levels along Z axis)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along Z axis)^2)

Total Energy of Particle in Cubic Box

Go Energy of Particle in 3D Square Box = (([hP])^2*((Energy Levels along X axis)^2+(Energy Levels along Y axis)^2+(Energy Levels along Z axis)^2))/(8*Mass of Particle*(Length of 3D Square Box)^2)

Energy of Particle in nx Level in 3D Box

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

Energy of Particle in ny Level in 3D Box

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

Energy of Particle in nz Level in 3D Box

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

Zero Point Energy of Particle in 3D Box

Go Zero Point Energy of Particle in 3D Box = (3*([hP]^2))/(8*Mass of Particle*(Length of 3D Square Box)^2)

Energy of Particle in nz Level in 3D Box Formula

Energy of Particle in Box along Z axis = ((Energy Levels along Z axis)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along Z axis)^2)
E_z = ((n_z)^2*([hP])^2)/(8*m*(l_z)^2)

What does the solution of the particle in a box interpret ?

Solutions ψ(x)
to this equation have a probabilistic interpretation. In particular, the square |ψ(x)|2
represents the probability density of finding the particle at a particular location x. This function must be integrated to determine the probability of finding the particle in some interval of space.

How to Calculate Energy of Particle in nz Level in 3D Box?

Energy of Particle in nz Level in 3D Box calculator uses Energy of Particle in Box along Z axis = ((Energy Levels along Z axis)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along Z axis)^2) to calculate the Energy of Particle in Box along Z axis, The Energy of Particle in nz Level in 3D Box formula is defined as the energy values that a particle can have residing in that level. Energy of Particle in Box along Z axis is denoted by E_z symbol.

How to calculate Energy of Particle in nz Level in 3D Box using this online calculator? To use this online calculator for Energy of Particle in nz Level in 3D Box, enter Energy Levels along Z axis (n_z), Mass of Particle (m) & Length of Box along Z axis (l_z) and hit the calculate button. Here is how the Energy of Particle in nz Level in 3D Box calculation can be explained with given input values -> 9.3E+20 = ((2)^2*([hP])^2)/(8*9E-31*(1.01E-10)^2).

FAQ

What is Energy of Particle in nz Level in 3D Box?

The Energy of Particle in nz Level in 3D Box formula is defined as the energy values that a particle can have residing in that level and is represented as E_z = ((n_z)^2*([hP])^2)/(8*m*(l_z)^2) or Energy of Particle in Box along Z axis = ((Energy Levels along Z axis)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along Z axis)^2). Energy Levels along Z 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 Box along Z axis gives us the dimension of the box in which the particle is kept.

How to calculate Energy of Particle in nz Level in 3D Box?

The Energy of Particle in nz Level in 3D Box formula is defined as the energy values that a particle can have residing in that level is calculated using Energy of Particle in Box along Z axis = ((Energy Levels along Z axis)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along Z axis)^2). To calculate Energy of Particle in nz Level in 3D Box, you need Energy Levels along Z axis (n_z), Mass of Particle (m) & Length of Box along Z axis (l_z). With our tool, you need to enter the respective value for Energy Levels along Z axis, Mass of Particle & Length of Box along Z axis 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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