A student is examining a bacterium under the microscope. The E. coli bacterial cell has a mass of = 1.60 fg (where a femtogram, fg, is 10^-15 g) and is swimming at a velocity of v= 4.00 um/s, with an uncertainty in the velocity of 3.00 % . E. coli bacterial cells are around 1 (um 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.

What is the uncertainty of the position of the bacterium?

Express your answer numerically in meters.

i know the formula but i don’t know which numbers to plug in

you are wrong. the answer i got was 2.75 x 10^-9 but it says im wrong

nevermind i got the answer

### 1 Answer

The momentum of the bacteria is 4.10^-6*1.60.10^-18 = 6.4 10^-24 kgm/s

and the uncertainty is 3% of that: 1.92.10^-25

According to the uncertainty relations the product of the (minimal) uncertainty on position and momentum is hbar (‘normalized’ Planck’s constant) which is worth 1.05.10^-34 J s so the uncertainty in position here is 5.5.10^-10 m that is .0005 of the bacterium length and the claim of the student is completely unwarranted