Question

A student is examining a bacterium under the microscope. The E. coli bacterial cell has a mass of m = 1.80 fg (where a femtogram, fg, is 10−15g) and is swimming at a velocity of v = 8.00 μm/s , with an uncertainty in the velocity of 3.00 % . E. coli bacterial cells are around 1 μm ( 10−6 m) in length. The student is supposed to observe the bacterium and make a drawing. However, the student, having just learned about the Heisenberg uncertainty principle in physics class, complains that she cannot make the drawing. She claims that the uncertainty of the bacterium's position is greater than the microscope's viewing field, and the bacterium is thus impossible to locate. Part A What is the uncertainty of the position of the bacterium

Answer 1

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