Question

A student is examining a bacterium under the microscope. The E, coli bacterial cell has a mass of m = 1.90 fg (where a femtogram, fg. is 10^-15 g) and is swimming at a velocity of upsilon = 9.00 mu m/s, with an uncertainty in the velocity of 5.00%. E. coli bacterial cells are around 1 mu m (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 posit on is greater than the microscope's viewing field, and the bacterium is thus impossible to locate. What is the uncertainly of the position of the bacterium? Express your answer with the appropriate units.

Answer 1

According to Heisenberg Uncertainty Principle,

Δx * Δv = h/(4*pi*m)

Here:

velocity = 9.00 um/s = 9.00*10^-6 m/s

Δv = 5.00% of 9.00*10^-6 m/s

Δv = 5.00*9.00*10^-6 / 100

Δv = 4.50*10^-7 m/s

also,

m = 1.90 fg = 1.90*10^-15 g = 1.90*10^-18 Kg

Now use:

Δx * Δv = h/(4*pi*m)

Δx * (4.50*10^-7 ) = (6.626*10^-34)/(4*3.14* 1.90*10^-18)

Δx * (4.50*10^-7 ) = 2.775*10^-17

Δx = 6.17*10^-11 m

Answer: 6.17*10^-11 m

or

61.7 pm