Uncertainty in Position of Particle a Calculator

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Heisenberg's Uncertainty Principle

Bohr's Atomic Model

Compton Effect

De Broglie Hypothesis

Distance of Closest Approach

Important Formulas on Bohr's Atomic Model

Photo Electric Effect

Planck Quantum Theory

Rutherford Scattering

Schrodinger Wave Equation

Sommerfeld Model

Structure of Atom

✖Mass b is the measure of the quantity of matter that a microscopic particle contains.ⓘ Mass b [m_b]			+10% -10%
✖Uncertainty in Position b is the accuracy of the measurement of microscopic particle B.ⓘ Uncertainty in Position b [Δx_B]			+10% -10%
✖Uncertainty in Velocity b is the accuracy of the speed of microscopic particle B.ⓘ Uncertainty in Velocity b [Δv_B]			+10% -10%
✖Mass a is the measure of the quantity of matter that a microscopic particle contains.ⓘ Mass a [m_a]			+10% -10%
✖Uncertainty in velocity a is the accuracy of the speed of microscopic particle A.ⓘ Uncertainty in velocity a [Δv_A]			+10% -10%

✖Uncertainty in position a is the accuracy of the measurement of microscopic particle A.ⓘ Uncertainty in Position of Particle a [Δx_A]

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Formula

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Uncertainty in Position of Particle a

Formula

`"Δx"_{"A"} = ("m"_{"b"}*"Δx"_{"B"}*"Δv"_{"B"})/("m"_{"a"}*"Δv"_{"A"})`

Example

`"36m"=("8kg"*"15m"*"150m/s")/("2.5kg"*"200m/s")`

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Uncertainty in Position of Particle a Solution

STEP 0: Pre-Calculation Summary

Formula Used

Uncertainty in position a = (Mass b*Uncertainty in Position b*Uncertainty in Velocity b)/(Mass a*Uncertainty in velocity a)
Δx_A = (m_b*Δx_B*Δv_B)/(m_a*Δv_A)
This formula uses 6 Variables

Variables Used

Uncertainty in position a - (Measured in Meter) - Uncertainty in position a is the accuracy of the measurement of microscopic particle A.
Mass b - (Measured in Kilogram) - Mass b is the measure of the quantity of matter that a microscopic particle contains.
Uncertainty in Position b - (Measured in Meter) - Uncertainty in Position b is the accuracy of the measurement of microscopic particle B.
Uncertainty in Velocity b - (Measured in Meter per Second) - Uncertainty in Velocity b is the accuracy of the speed of microscopic particle B.
Mass a - (Measured in Kilogram) - Mass a is the measure of the quantity of matter that a microscopic particle contains.
Uncertainty in velocity a - (Measured in Meter per Second) - Uncertainty in velocity a is the accuracy of the speed of microscopic particle A.

STEP 1: Convert Input(s) to Base Unit

Mass b: 8 Kilogram --> 8 Kilogram No Conversion Required
Uncertainty in Position b: 15 Meter --> 15 Meter No Conversion Required
Uncertainty in Velocity b: 150 Meter per Second --> 150 Meter per Second No Conversion Required
Mass a: 2.5 Kilogram --> 2.5 Kilogram No Conversion Required
Uncertainty in velocity a: 200 Meter per Second --> 200 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Δx_A = (m_b*Δx_B*Δv_B)/(m_a*Δv_A) --> (8*15*150)/(2.5*200)

Evaluating ... ...

Δx_A = 36

STEP 3: Convert Result to Output's Unit

36 Meter --> No Conversion Required

FINAL ANSWER

36 Meter <-- Uncertainty in position a

(Calculation completed in 00.004 seconds)

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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 of Particle a Formula

Uncertainty in position a = (Mass b*Uncertainty in Position b*Uncertainty in Velocity b)/(Mass a*Uncertainty in velocity a)
Δx_A = (m_b*Δx_B*Δv_B)/(m_a*Δv_A)

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 of Particle a?

Uncertainty in Position of Particle a calculator uses Uncertainty in position a = (Mass b*Uncertainty in Position b*Uncertainty in Velocity b)/(Mass a*Uncertainty in velocity a) to calculate the Uncertainty in position a, The uncertainty in position of particle a is defined as the accuracy of the measurement of the particle in Heisenberg's Uncertainty Principle theory. Uncertainty in position a is denoted by Δx_A symbol.

How to calculate Uncertainty in Position of Particle a using this online calculator? To use this online calculator for Uncertainty in Position of Particle a, enter Mass b (m_b), Uncertainty in Position b (Δx_B), Uncertainty in Velocity b (Δv_B), Mass a (m_a) & Uncertainty in velocity a (Δv_A) and hit the calculate button. Here is how the Uncertainty in Position of Particle a calculation can be explained with given input values -> 36 = (8*15*150)/(2.5*200).

FAQ

What is Uncertainty in Position of Particle a?

The uncertainty in position of particle a is defined as the accuracy of the measurement of the particle in Heisenberg's Uncertainty Principle theory and is represented as Δx_A = (m_b*Δx_B*Δv_B)/(m_a*Δv_A) or Uncertainty in position a = (Mass b*Uncertainty in Position b*Uncertainty in Velocity b)/(Mass a*Uncertainty in velocity a). Mass b is the measure of the quantity of matter that a microscopic particle contains, Uncertainty in Position b is the accuracy of the measurement of microscopic particle B, Uncertainty in Velocity b is the accuracy of the speed of microscopic particle B, Mass a is the measure of the quantity of matter that a microscopic particle contains & Uncertainty in velocity a is the accuracy of the speed of microscopic particle A.

How to calculate Uncertainty in Position of Particle a?

The uncertainty in position of particle a is defined as the accuracy of the measurement of the particle in Heisenberg's Uncertainty Principle theory is calculated using Uncertainty in position a = (Mass b*Uncertainty in Position b*Uncertainty in Velocity b)/(Mass a*Uncertainty in velocity a). To calculate Uncertainty in Position of Particle a, you need Mass b (m_b), Uncertainty in Position b (Δx_B), Uncertainty in Velocity b (Δv_B), Mass a (m_a) & Uncertainty in velocity a (Δv_A). With our tool, you need to enter the respective value for Mass b, Uncertainty in Position b, Uncertainty in Velocity b, Mass a & Uncertainty in velocity a 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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