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 your post above.
To find the uncertainty in the position of the fly given its velocity uncertainty, we need to use the Heisenberg's uncertainty principle equation Δx * Δp = h/(4π).
First, let's calculate the uncertainty in momentum (Δp) of the fly. The uncertainty in velocity (Δv) can be obtained by multiplying the velocity (v) by the percentage uncertainty (u) (Δv = v * u). Substituting the values, we get:
Δv = 3.219 m/s * 0.01273 = 0.04104 m/s
The momentum (p) of the fly can be calculated by multiplying its mass (m) by its velocity (v):
p = m * v = 0.001409 kg * 3.219 m/s = 0.004534 kg·m/s
Now, we can rearrange the Heisenberg's uncertainty principle equation to solve for the uncertainty in position (Δx):
Δx = (h/(4π)) / Δp
Substituting the values:
Δx = (6.626 x 10^(-34) J·s / (4π)) / 0.004534 kg·m/s
Δx ≈ 1.442 x 10^(-33) m
Therefore, the uncertainty in the position of the fly would be approximately 1.442 x 10^(-33) meters.