Heisenberg's uncertainty principle can be expressed mathematically as Δx*Δp = h/4π, where Δx and Δp denote the uncertainty in position and momentum respectively and h is Planck's constant. What would be the uncertaintry in the position of a fly (mass = 0.001409 kg) that was traveling at a velocity of 3.219 m/s if the velocity has an uncertainty of 1.273%?
See the (your) post under Andy above with a slightly different %error on velocity.
To calculate the uncertainty in the position of a fly using Heisenberg's uncertainty principle, you need to determine the uncertainty in momentum first. Let's break down the steps:
Step 1: Find the uncertainty in momentum (Δp)
To find the uncertainty in momentum, we need to calculate the percentage uncertainty in velocity and then use it to calculate the uncertainty in momentum.
Given:
Mass of the fly (m) = 0.001409 kg
Velocity of the fly (v) = 3.219 m/s
Percentage uncertainty in velocity = 1.273%
To calculate the uncertainty in velocity (Δv), we apply the percentage uncertainty:
Uncertainty in velocity (Δv) = (percentage uncertainty / 100) * velocity
Using the given values:
Δv = (1.273 / 100) * 3.219 = 0.041 m/s
Next, we find the uncertainty in momentum (Δp) using the equation:
Δp = mass (m) * uncertainty in velocity (Δv)
Δp = 0.001409 kg * 0.041 m/s ≈ 5.776 x 10^(-5) kg∙m/s
Step 2: Calculate the uncertainty in position (Δx)
According to Heisenberg's uncertainty principle:
Δx * Δp = h / (4π)
Rearranging the equation, we can solve for Δx:
Δx = (h / (4π)) / Δp
In this case:
h = Planck's constant = 6.626 x 10^(-34) J∙s
π = 3.14159
Substituting the values:
Δx = (6.626 x 10^(-34) J∙s / (4 * 3.14159)) / (5.776 x 10^(-5) kg∙m/s)
Calculating Δx:
Δx ≈ 2.840 x 10^(-30) meters
Therefore, the uncertainty in the position of the fly is approximately 2.840 x 10^(-30) meters.