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

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Energy of Particle in 1D Box is defined as the discrete energy values that a particle can have residing in a level. Check FAQs

E n = \frac{n^{2} \cdot {[hP]}^{2}}{8 \cdot m \cdot a^{2}}

E_n - Energy of Particle in 1D Box?n - Energy Levels in 1D Box?m - Mass of Particle?a - Length of 1D Box?[hP] - Planck constant?

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

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Here is how the Energy of Particle residing in nth Level in 1D Box equation looks like with Values.

Here is how the Energy of Particle residing in nth Level in 1D Box equation looks like with Units.

Here is how the Energy of Particle residing in nth Level in 1D Box equation looks like.

660.7642 = \frac{5^{2} \cdot {6.6E-34}^{2}}{8 \cdot 9E-31 \cdot {1.2}^{2}}

660.7642eV = \frac{5^{2} \cdot {6.6E-34}^{2}}{8 \cdot 9E-31kg \cdot {1.2A}^{2}}

660.7642 = \frac{5^{2} \cdot {6.6E-34}^{2}}{8 \cdot 9E-31 \cdot {1.2}^{2}}

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

Follow our step by step solution on how to calculate Energy of Particle residing in nth Level in 1D Box?

FIRST Step Consider the formula

E n = \frac{n^{2} \cdot {[hP]}^{2}}{8 \cdot m \cdot a^{2}}

Next Step Substitute values of Variables

∴

E n = \frac{5^{2} \cdot {[hP]}^{2}}{8 \cdot 9E-31kg \cdot {1.2A}^{2}}

Next Step Substitute values of Constants

∴

E n = \frac{5^{2} \cdot {6.6E-34}^{2}}{8 \cdot 9E-31kg \cdot {1.2A}^{2}}

Next Step Convert Units

∴

E n = \frac{5^{2} \cdot {6.6E-34}^{2}}{8 \cdot 9E-31kg \cdot {1.2E-10m}^{2}}

Next Step Prepare to Evaluate

∴

E n = \frac{5^{2} \cdot {6.6E-34}^{2}}{8 \cdot 9E-31 \cdot {1.2E-10}^{2}}

Next Step Evaluate

∴

E n = 1.05866136610208E-16J

Next Step Convert to Output's Unit

∴

E n = 660.764165288794eV

LAST Step Rounding Answer

∴

E n = 660.7642eV

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

Variables

Constants

Energy of Particle in 1D Box

Energy of Particle in 1D Box is defined as the discrete energy values that a particle can have residing in a level.

Symbol: E_n

Measurement: EnergyUnit: eV

Note: Value can be positive or negative.

Formulas to find Energy of Particle in 1D Box

Energy Levels in 1D Box

Energy Levels in 1D Box are the quantised levels where the particle may be present.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Energy Levels in 1D Box

Mass of Particle

Mass of Particle is defined as the energy of that system in a reference frame where it has zero momentum.

Symbol: m

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Mass of Particle

Length of 1D Box

Length of 1D Box gives us the dimension of the box in which the particle is kept.

Symbol: a

Measurement: LengthUnit: A

Note: Value should be greater than 0.

Formulas to find Length of 1D Box

Planck constant

Planck constant is a fundamental universal constant that defines the quantum nature of energy and relates the energy of a photon to its frequency.

Symbol: [hP]

Value: 6.626070040E-34

Other formulas in Particle in 1 Dimensional Box category

Go Number of Nodes for particle in 1D Box

N = (n - 1)

Go Zero Point Energy of Particle in 1D Box

Z.P.E = \frac{{[hP]}^{2}}{8 \cdot m \cdot {(a)}^{2}}

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

Energy of Particle residing in nth Level in 1D Box evaluator 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 evaluate 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 evaluate Energy of Particle residing in nth Level in 1D Box using this online evaluator? To use this online evaluator 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.

FAQs on Energy of Particle residing in nth Level in 1D Box

What is the formula to find Energy of Particle residing in nth Level in 1D Box?

The formula of Energy of Particle residing in nth Level in 1D Box is expressed as Energy of Particle in 1D Box = (Energy Levels in 1D Box^2*[hP]^2)/(8*Mass of Particle*Length of 1D Box^2). Here is an example- 1.5E+19 = (5^2*[hP]^2)/(8*9E-31*1.2E-10^2).

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

With Energy Levels in 1D Box (n), Mass of Particle (m) & Length of 1D Box (a) we can find Energy of Particle residing in nth Level in 1D Box using the formula - Energy of Particle in 1D Box = (Energy Levels in 1D Box^2*[hP]^2)/(8*Mass of Particle*Length of 1D Box^2). This formula also uses Planck constant .

Can the Energy of Particle residing in nth Level in 1D Box be negative?

Yes, the Energy of Particle residing in nth Level in 1D Box, measured in Energy can be negative.

Which unit is used to measure Energy of Particle residing in nth Level in 1D Box?

Energy of Particle residing in nth Level in 1D Box is usually measured using the Electron-Volt[eV] for Energy. Joule[eV], Kilojoule[eV], Gigajoule[eV] are the few other units in which Energy of Particle residing in nth Level in 1D Box can be measured.

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

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

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

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

Other formulas in Particle in 1 Dimensional Box category

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

FAQs on Energy of Particle residing in nth Level in 1D Box

Variable Name