Answer:
Δx ≥ 1.22 *10^-10m
Explanation:
Step 1: Data given
The E. coli bacterial cell has a mass of 1.80 fg ( = 1.80 * 10^-15 grams = 1.80 * 10^-18 kg)
Velocity of v = 8.00 μm/s (= 8.00 * 10^-6 m/s)
Uncertainty in the velocity = 3.00 %
E. coli bacterial cells are around 1 μm = 10^−6 m in length
Step 2: Calculate uncertainty in velocity
Δv = 0.03 * 8*10^-6 m/s =2.4 * 10^-7 m/s
Step 3: Calculate the uncertainty of the position of the bacterium
According to Heisenberg uncertainty principle,
Δx *Δp ≥ h/4π
Δx *mΔv ≥ h/4π
with Δx = TO BE DETERMINED
with m = 1.8 *10^-18 kg
with Δv = 2.4*10^-7
with h = constant of planck = 6.626 *10^-34
Δx ≥ 6.626*10^-34 / (4π*(1.8*10^-18)(2.4*10^-7))
Δx ≥ 1.22 *10^-10m