Energy of Particle residing in nth Level in 1D 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 1 Dimensional Box

Particle in 2 Dimensional Box

Particle in 3 Dimensional Box

✖Energy Levels in 1D Box are the quantised levels where the particle may be present.ⓘ Energy Levels in 1D Box [n]			+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 1D Box gives us the dimension of the box in which the particle is kept.ⓘ Length of 1D Box [a]			+10% -10%

✖Energy of Particle in 1D Box is defined as the discrete energy values that a particle can have residing in a level.ⓘ Energy of Particle residing in nth Level in 1D Box [E_n]

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Formula

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Energy of Particle residing in nth Level in 1D Box

Formula

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

Example

`"660.7642eV"=(("5")^2*"[hP]"^2)/(8*"9E^-31kg"*("1.2A")^2)`

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Energy of Particle residing in nth Level in 1D Box Solution

STEP 0: Pre-Calculation Summary

Formula Used

Energy of Particle in 1D Box = (Energy Levels in 1D Box^2*[hP]^2)/(8*Mass of Particle*Length of 1D Box^2)
E_n = (n^2*[hP]^2)/(8*m*a^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 1D Box - (Measured in Joule) - Energy of Particle in 1D Box is defined as the discrete energy values that a particle can have residing in a level.
Energy Levels in 1D Box - Energy Levels in 1D Box 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 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

Energy Levels in 1D Box: 5 --> No Conversion Required
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

E_n = (n^2*[hP]^2)/(8*m*a^2) --> (5^2*[hP]^2)/(8*9E-31*1.2E-10^2)

Evaluating ... ...

E_n = 1.05866136610208E-16

STEP 3: Convert Result to Output's Unit

1.05866136610208E-16 Joule -->660.764165288794 Electron-Volt (Check conversion here)

FINAL ANSWER

660.764165288794 ≈ 660.7642 Electron-Volt <-- 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)

Energy of Particle residing in nth Level in 1D Box Formula

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

What does particle in 1D Box actually represent?

This is the simplest quantum mechanical problem that represents translational motion. Here, a particle of mass m is confined to move in a one-dimensional box having infinite high walls. It is assumed that the potential energy of the particle inside the box is zero while its potential energy outside the box is infinite.

How to Calculate Energy of Particle residing in nth Level in 1D Box?

Energy of Particle residing in nth Level in 1D Box calculator uses Energy of Particle in 1D Box = (Energy Levels in 1D Box^2*[hP]^2)/(8*Mass of Particle*Length of 1D Box^2) to calculate the Energy of Particle in 1D Box, The Energy of Particle residing in nth Level in 1D Box formula is defined as the quantized energy values that the particle can take in an energy level. Energy of Particle in 1D Box is denoted by E_n symbol.

How to calculate Energy of Particle residing in nth Level in 1D Box using this online calculator? To use this online calculator for Energy of Particle residing in nth Level in 1D Box, enter Energy Levels in 1D Box (n), Mass of Particle (m) & Length of 1D Box (a) and hit the calculate button. Here is how the Energy of Particle residing in nth Level in 1D Box calculation can be explained with given input values -> 1.5E+19 = (5^2*[hP]^2)/(8*9E-31*1.2E-10^2).

FAQ

What is Energy of Particle residing in nth Level in 1D Box?

The Energy of Particle residing in nth Level in 1D Box formula is defined as the quantized energy values that the particle can take in an energy level and is represented as E_n = (n^2*[hP]^2)/(8*m*a^2) or Energy of Particle in 1D Box = (Energy Levels in 1D Box^2*[hP]^2)/(8*Mass of Particle*Length of 1D Box^2). Energy Levels in 1D Box 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 1D Box gives us the dimension of the box in which the particle is kept.

How to calculate Energy of Particle residing in nth Level in 1D Box?

The Energy of Particle residing in nth Level in 1D Box formula is defined as the quantized energy values that the particle can take in an energy level is calculated using Energy of Particle in 1D Box = (Energy Levels in 1D Box^2*[hP]^2)/(8*Mass of Particle*Length of 1D Box^2). To calculate Energy of Particle residing in nth Level in 1D Box, you need Energy Levels in 1D Box (n), Mass of Particle (m) & Length of 1D Box (a). With our tool, you need to enter the respective value for Energy Levels in 1D Box, 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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