Uncertainty in Velocity of Particle b Solution

STEP 0: Pre-Calculation Summary
Formula Used
Uncertainty in Velocity given b = (Mass a*Uncertainty in position a*Uncertainty in velocity a)/(Mass b*Uncertainty in Position b)
Δvb = (ma*ΔxA*ΔvA)/(mb*ΔxB)
This formula uses 6 Variables
Variables Used
Uncertainty in Velocity given b - (Measured in Meter per Second) - Uncertainty in Velocity given b is the accuracy of the speed of particle.
Mass a - (Measured in Kilogram) - Mass a is the measure of the quantity of matter that a microscopic particle contains.
Uncertainty in position a - (Measured in Meter) - Uncertainty in position a is the accuracy of the measurement of microscopic particle A.
Uncertainty in velocity a - (Measured in Meter per Second) - Uncertainty in velocity a is the accuracy of the speed 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.
STEP 1: Convert Input(s) to Base Unit
Mass a: 2.5 Kilogram --> 2.5 Kilogram No Conversion Required
Uncertainty in position a: 20 Meter --> 20 Meter No Conversion Required
Uncertainty in velocity a: 200 Meter per Second --> 200 Meter per Second No Conversion Required
Mass b: 8 Kilogram --> 8 Kilogram No Conversion Required
Uncertainty in Position b: 15 Meter --> 15 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Δvb = (ma*ΔxA*ΔvA)/(mb*ΔxB) --> (2.5*20*200)/(8*15)
Evaluating ... ...
Δvb = 83.3333333333333
STEP 3: Convert Result to Output's Unit
83.3333333333333 Meter per Second --> No Conversion Required
FINAL ANSWER
83.3333333333333 83.33333 Meter per Second <-- Uncertainty in Velocity given b
(Calculation completed in 00.020 seconds)

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National Institute of Information Technology (NIIT), Neemrana
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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 Velocity of Particle b Formula

Uncertainty in Velocity given b = (Mass a*Uncertainty in position a*Uncertainty in velocity a)/(Mass b*Uncertainty in Position b)
Δvb = (ma*ΔxA*ΔvA)/(mb*ΔxB)

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 Velocity of Particle b?

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

How to calculate Uncertainty in Velocity of Particle b using this online calculator? To use this online calculator for Uncertainty in Velocity of Particle b, enter Mass a (ma), Uncertainty in position a (ΔxA), Uncertainty in velocity a (ΔvA), Mass b (mb) & Uncertainty in Position b (ΔxB) and hit the calculate button. Here is how the Uncertainty in Velocity of Particle b calculation can be explained with given input values -> 83.33333 = (2.5*20*200)/(8*15).

FAQ

What is Uncertainty in Velocity of Particle b?
The Uncertainty in velocity of particle b is defined as the accuracy of the speed of the particle in Heisenberg's Uncertainty Principle theory and is represented as Δvb = (ma*ΔxA*ΔvA)/(mb*ΔxB) or Uncertainty in Velocity given b = (Mass a*Uncertainty in position a*Uncertainty in velocity a)/(Mass b*Uncertainty in Position b). Mass a is the measure of the quantity of matter that a microscopic particle contains, Uncertainty in position a is the accuracy of the measurement of microscopic particle A, Uncertainty in velocity a is the accuracy of the speed of microscopic particle 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.
How to calculate Uncertainty in Velocity of Particle b?
The Uncertainty in velocity of particle b is defined as the accuracy of the speed of the particle in Heisenberg's Uncertainty Principle theory is calculated using Uncertainty in Velocity given b = (Mass a*Uncertainty in position a*Uncertainty in velocity a)/(Mass b*Uncertainty in Position b). To calculate Uncertainty in Velocity of Particle b, you need Mass a (ma), Uncertainty in position a (ΔxA), Uncertainty in velocity a (ΔvA), Mass b (mb) & Uncertainty in Position b (ΔxB). With our tool, you need to enter the respective value for Mass a, Uncertainty in position a, Uncertainty in velocity a, Mass b & Uncertainty in Position b 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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