Uncertainty in Momentum Calculator

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✖Uncertainty in Position is the accuracy of the measurement of particle.ⓘ Uncertainty in Position [Δx]

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✖Uncertainty in Momentum is the accuracy of the momentum of particle.ⓘ Uncertainty in Momentum [Δp]

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Formula

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Uncertainty in Momentum

Formula

`"Δp" = "[hP]"/(4*pi*"Δx")`

Example

`"1.5E^-36kg*m/s"="[hP]"/(4*pi*"35m")`

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Uncertainty in Momentum Solution

STEP 0: Pre-Calculation Summary

Formula Used

Uncertainty in Momentum = [hP]/(4*pi*Uncertainty in Position)
Δp = [hP]/(4*pi*Δx)
This formula uses 2 Constants, 2 Variables

Constants Used

[hP] - Planck constant Value Taken As 6.626070040E-34 Kilogram Meter² / Second
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Uncertainty in Momentum - (Measured in Kilogram Meter per Second) - Uncertainty in Momentum is the accuracy of the momentum of particle.
Uncertainty in Position - (Measured in Meter) - Uncertainty in Position is the accuracy of the measurement of particle.

STEP 1: Convert Input(s) to Base Unit

Uncertainty in Position: 35 Meter --> 35 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Δp = [hP]/(4*pi*Δx) --> [hP]/(4*pi*35)

Evaluating ... ...

Δp = 1.50653114305588E-36

STEP 3: Convert Result to Output's Unit

1.50653114305588E-36 Kilogram Meter per Second --> No Conversion Required

FINAL ANSWER

1.50653114305588E-36 ≈ 1.5E-36 Kilogram Meter per Second <-- Uncertainty in Momentum

(Calculation completed in 00.004 seconds)

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Created by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

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Verified by Pragati Jaju

College Of Engineering (COEP), Pune

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< 23 Heisenberg's Uncertainty Principle Calculators

Mass b of Microscopic Particle in Uncertainty Relation

Go Mass b = (Mass a*Uncertainty in position a*Uncertainty in velocity a)/(Uncertainty in Position b*Uncertainty in Velocity b)

Mass of Microscopic Particle in Uncertainty Relation

Go Mass a = (Mass b*Uncertainty in Position b*Uncertainty in Velocity b)/(Uncertainty in position a*Uncertainty in velocity a)

Uncertainty in Position of Particle a

Go Uncertainty in position a = (Mass b*Uncertainty in Position b*Uncertainty in Velocity b)/(Mass a*Uncertainty in velocity a)

Uncertainty in Position of Particle b

Go Uncertainty in Position b = (Mass a*Uncertainty in position a*Uncertainty in velocity a)/(Mass b*Uncertainty in Velocity b)

Uncertainty in Velocity of Particle a

Go Uncertainty in velocity a = (Mass b*Uncertainty in Position b*Uncertainty in Velocity b)/(Mass a*Uncertainty in position a)

Uncertainty in Velocity of Particle b

Go Uncertainty in Velocity b = (Mass a*Uncertainty in position a*Uncertainty in velocity a)/(Mass b*Uncertainty in Position b)

Uncertainty in Position given Uncertainty in Velocity

Go Uncertainty in Position = [hP]/(2*pi*Mass*Uncertainty in Velocity)

Angle of Light Ray given Uncertainty in Momentum

Go Theta = asin((Uncertainty in Momentum*Wavelength of Light)/(2*[hP]))

Mass in Uncertainty Principle

Go Mass = [hP]/(4*pi*Uncertainty in Position*Uncertainty in Velocity)

Uncertainty in Velocity

Go Uncertainty in Velocity = [hP]/(4*pi*Mass*Uncertainty in Position)

Uncertainty in Momentum given Angle of Light Ray

Go Uncertainty in Momentum = (2*[hP]*sin(Theta))/Wavelength

Wavelength given Uncertainty in Momentum

Go Wavelength = (2*[hP]*sin(Theta))/Uncertainty in Momentum

Uncertainty in Position

Go Uncertainty in Position = [hP]/(4*pi*Uncertainty in Momentum)

Uncertainty in Momentum

Go Uncertainty in Momentum = [hP]/(4*pi*Uncertainty in Position)

Uncertainty in Energy

Go Uncertainty in Energy = [hP]/(4*pi*Uncertainty in Time)

Uncertainty in Time

Go Uncertainty in Time = [hP]/(4*pi*Uncertainty in Energy)

Angle of Light Ray given Uncertainty in Position

Go Theta = asin(Wavelength/Uncertainty in Position)

Wavelength of Light Ray given Uncertainty in Position

Go Wavelength = Uncertainty in Position*sin(Theta)

Uncertainty in Position given Angle of Light Ray

Go Uncertainty in Position = Wavelength/sin(Theta)

Early Form of Uncertainty Principle

Go Uncertainty in Momentum = [hP]/Uncertainty in Position

Uncertainty in momentum given uncertainty in velocity

Go Uncertainty in Momentum = Mass*Uncertainty in Velocity

Wavelength of Particle given Momentum

Go Wavelength = [hP]/Momentum

Momentum of Particle

Go Momentum = [hP]/Wavelength

Uncertainty in Momentum Formula

Uncertainty in Momentum = [hP]/(4*pi*Uncertainty in Position)
Δp = [hP]/(4*pi*Δx)

What is Heisenberg's Uncertainty Principle?

Heisenberg's Uncertainty Principle states that ' It is impossible to determine simultaneously, the exact position as well as momentum of an electron'. It is mathematically possible to express the uncertainty that, Heisenberg concluded, always exists if one attempts to measure the momentum and position of particles. First, we must define the variable “x” as the position of the particle, and define “p” as the momentum of the particle.

Is Heisenberg’s Uncertainty Principle noticeable in All Matter Waves?

Heisenberg’s principle is applicable to all matter waves. The measurement error of any two conjugate properties, whose dimensions happen to be joule sec, like position-momentum, time-energy will be guided by the Heisenberg’s value.
But, it will be noticeable and of significance only for small particles like an electron with very low mass. A bigger particle with heavy mass will show the error to be very small and negligible.

How to Calculate Uncertainty in Momentum?

Uncertainty in Momentum calculator uses Uncertainty in Momentum = [hP]/(4*pi*Uncertainty in Position) to calculate the Uncertainty in Momentum, The Uncertainty in momentum formula is defined as the accuracy of the momentum of the particle in Heisenberg's Uncertainty Principle theory. Uncertainty in Momentum is denoted by Δp symbol.

How to calculate Uncertainty in Momentum using this online calculator? To use this online calculator for Uncertainty in Momentum, enter Uncertainty in Position (Δx) and hit the calculate button. Here is how the Uncertainty in Momentum calculation can be explained with given input values -> 1.5E-36 = [hP]/(4*pi*35).

FAQ

What is Uncertainty in Momentum?

The Uncertainty in momentum formula is defined as the accuracy of the momentum of the particle in Heisenberg's Uncertainty Principle theory and is represented as Δp = [hP]/(4*pi*Δx) or Uncertainty in Momentum = [hP]/(4*pi*Uncertainty in Position). Uncertainty in Position is the accuracy of the measurement of particle.

How to calculate Uncertainty in Momentum?

The Uncertainty in momentum formula is defined as the accuracy of the momentum of the particle in Heisenberg's Uncertainty Principle theory is calculated using Uncertainty in Momentum = [hP]/(4*pi*Uncertainty in Position). To calculate Uncertainty in Momentum, you need Uncertainty in Position (Δx). With our tool, you need to enter the respective value for Uncertainty in Position and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Uncertainty in Momentum?

In this formula, Uncertainty in Momentum uses Uncertainty in Position. We can use 3 other way(s) to calculate the same, which is/are as follows -

Uncertainty in Momentum = Mass*Uncertainty in Velocity
Uncertainty in Momentum = [hP]/Uncertainty in Position
Uncertainty in Momentum = (2*[hP]*sin(Theta))/Wavelength

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