Uncertainty in Position Solution

STEP 0: Pre-Calculation Summary
Formula Used
Position Uncertainty = [hP]/(4*pi*Uncertainty in Momentum)
Δxp = [hP]/(4*pi*Δp)
This formula uses 2 Constants, 2 Variables
Constants Used
[hP] - Planck constant Value Taken As 6.626070040E-34
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Position Uncertainty - (Measured in Meter) - Position Uncertainty is the accuracy of the measurement of particle.
Uncertainty in Momentum - (Measured in Kilogram Meter per Second) - Uncertainty in Momentum is the accuracy of the momentum of particle.
STEP 1: Convert Input(s) to Base Unit
Uncertainty in Momentum: 105 Kilogram Meter per Second --> 105 Kilogram Meter per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Δxp = [hP]/(4*pi*Δp) --> [hP]/(4*pi*105)
Evaluating ... ...
Δxp = 5.02177047685292E-37
STEP 3: Convert Result to Output's Unit
5.02177047685292E-37 Meter --> No Conversion Required
FINAL ANSWER
5.02177047685292E-37 5E-37 Meter <-- Position Uncertainty
(Calculation completed in 00.004 seconds)

Credits

Created by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
Akshada Kulkarni has created this Calculator and 500+ more calculators!
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 given UP = (Mass a*Uncertainty in position a*Uncertainty in velocity a)/(Uncertainty in Position b*Uncertainty in Velocity b)
Uncertainty in Velocity of Particle a
Go Uncertainty in Velocity given 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 given b = (Mass a*Uncertainty in position a*Uncertainty in velocity a)/(Mass b*Uncertainty in Position b)
Mass of Microscopic Particle in Uncertainty Relation
Go Mass in UR = (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)
Angle of Light Ray given Uncertainty in Momentum
Go Theta given UM = asin((Uncertainty in Momentum*Wavelength of Light)/(2*[hP]))
Mass in Uncertainty Principle
Go Mass in UP = [hP]/(4*pi*Uncertainty in Position*Uncertainty in Velocity)
Wavelength given Uncertainty in Momentum
Go Wavelength given Momentum = (2*[hP]*sin(Theta))/Uncertainty in Momentum
Uncertainty in Position given Uncertainty in Velocity
Go Position Uncertainty = [hP]/(2*pi*Mass*Uncertainty in Velocity)
Uncertainty in Velocity
Go Velocity Uncertainty = [hP]/(4*pi*Mass*Uncertainty in Position)
Uncertainty in Momentum given Angle of Light Ray
Go Momentum of Particle = (2*[hP]*sin(Theta))/Wavelength
Uncertainty in Position
Go Position Uncertainty = [hP]/(4*pi*Uncertainty in Momentum)
Uncertainty in Momentum
Go Momentum of Particle = [hP]/(4*pi*Uncertainty in Position)
Uncertainty in Energy
Go Uncertainty in Energy = [hP]/(4*pi*Uncertainty in Time)
Angle of Light Ray given Uncertainty in Position
Go Theta given UP = asin(Wavelength/Uncertainty in Position)
Wavelength of Light Ray given Uncertainty in Position
Go Wavelength given PE = Uncertainty in Position*sin(Theta)
Uncertainty in Time
Go Time Uncertainty = [hP]/(4*pi*Uncertainty in Energy)
Uncertainty in Position given Angle of Light Ray
Go Position Uncertainty in Rays = Wavelength/sin(Theta)
Early Form of Uncertainty Principle
Go Early Uncertainty in Momentum = [hP]/Uncertainty in Position
Uncertainty in momentum given uncertainty in velocity
Go Uncertainity of Momentum = Mass*Uncertainty in Velocity
Wavelength of Particle given Momentum
Go Wavelength given Momentum = [hP]/Momentum
Momentum of Particle
Go Momentum of Particle = [hP]/Wavelength

Uncertainty in Position Formula

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

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 Position?

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

How to calculate Uncertainty in Position using this online calculator? To use this online calculator for Uncertainty in Position, enter Uncertainty in Momentum (Δp) and hit the calculate button. Here is how the Uncertainty in Position calculation can be explained with given input values -> 5E-37 = [hP]/(4*pi*105).

FAQ

What is Uncertainty in Position?
The Uncertainty in position formula is defined as the accuracy of the measurement of the particle in Heisenberg's Uncertainty Principle theory and is represented as Δxp = [hP]/(4*pi*Δp) or Position Uncertainty = [hP]/(4*pi*Uncertainty in Momentum). Uncertainty in Momentum is the accuracy of the momentum of particle.
How to calculate Uncertainty in Position?
The Uncertainty in position formula is defined as the accuracy of the measurement of the particle in Heisenberg's Uncertainty Principle theory is calculated using Position Uncertainty = [hP]/(4*pi*Uncertainty in Momentum). To calculate Uncertainty in Position, you need Uncertainty in Momentum (Δp). With our tool, you need to enter the respective value for Uncertainty in Momentum 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 Position Uncertainty?
In this formula, Position Uncertainty uses Uncertainty in Momentum. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Position Uncertainty = [hP]/(2*pi*Mass*Uncertainty in Velocity)
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