## Energy of Particle in nz Level in 3D Box Solution

STEP 0: Pre-Calculation Summary
Formula Used
Energy of Particle in Box along z Direction = ((Energy Levels along z Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along z Direction)^2)
Ez = ((nz)^2*([hP])^2)/(8*m*(lz)^2)
This formula uses 1 Constants, 4 Variables
Constants Used
[hP] - Planck constant Value Taken As 6.626070040E-34 Kilogram Meter² / Second
Variables Used
Energy of Particle in Box along z Direction - (Measured in Joule) - Energy of Particle in Box along z Direction is defined as the energy values that a particle can have residing in one particular level.
Energy Levels along z Direction - Energy Levels along z 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 z Direction - (Measured in Meter) - Length of Box along z 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 z Direction: 2 --> No Conversion Required
Mass of Particle: 9E-31 Kilogram --> 9E-31 Kilogram No Conversion Required
Length of Box along z Direction: 1.01 Angstrom --> 1.01E-10 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Ez = ((nz)^2*([hP])^2)/(8*m*(lz)^2) --> ((2)^2*([hP])^2)/(8*9E-31*(1.01E-10)^2)
Evaluating ... ...
Ez = 2.39109478237349E-17
STEP 3: Convert Result to Output's Unit
2.39109478237349E-17 Joule -->149.24033298945 Electron-Volt (Check conversion here)
149.24033298945 149.2403 Electron-Volt <-- Energy of Particle in Box along z Direction
(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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## < 6 Particle in 3 Dimensional Box Calculators

Total Energy of Particle in 3D Box
Total Energy of Particle in 3D 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 z Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along z Direction)^2)
Total Energy of Particle in Cubic Box
Energy of Particle in 3D Square Box = (([hP])^2*((Energy Levels along x Direction)^2+(Energy Levels along y Direction)^2+(Energy Levels along z Direction)^2))/(8*Mass of Particle*(Length of 3D Square Box)^2)
Energy of Particle in nx Level in 3D Box
Energy of Particle in Box along x Direction = ((Energy Levels along x Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along x Direction)^2)
Energy of Particle in ny Level in 3D Box
Energy of Particle in Box along y Direction = ((Energy Levels along y Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along y Direction)^2)
Energy of Particle in nz Level in 3D Box
Energy of Particle in Box along z Direction = ((Energy Levels along z Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along z Direction)^2)
Zero Point Energy of Particle in 3D Box
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 Direction = ((Energy Levels along z Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along z Direction)^2)
Ez = ((nz)^2*([hP])^2)/(8*m*(lz)^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 Direction = ((Energy Levels along z Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along z Direction)^2) to calculate the Energy of Particle in Box along z Direction, 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 Direction is denoted by Ez 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 Direction (nz), Mass of Particle (m) & Length of Box along z Direction (lz) 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 Ez = ((nz)^2*([hP])^2)/(8*m*(lz)^2) or Energy of Particle in Box along z Direction = ((Energy Levels along z Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along z Direction)^2). Energy Levels along z 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 z Direction 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 Direction = ((Energy Levels along z Direction)^2*([hP])^2)/(8*Mass of Particle*(Length of Box along z Direction)^2). To calculate Energy of Particle in nz Level in 3D Box, you need Energy Levels along z Direction (nz), Mass of Particle (m) & Length of Box along z Direction (lz). With our tool, you need to enter the respective value for Energy Levels along z Direction, Mass of Particle & Length of Box along z Direction and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well. Let Others Know