A student is examining a bacterium under the microscope. The E. coli bacterial c

Question

A student is examining a bacterium under the microscope. The E. colibacterial cell has a mass of m = 0.400 fg (where a femtogram, fg, is 1015g) and is swimming at a velocity of v = 8.00 m/s , with an uncertainty in the velocity of 4.00 % . E. coli bacterial cells are around 1 m( 106 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.

Please show your work, so I can understand how to do this problem.

Explanation / Answer

Heisenberg uncertainty principle

dp * dx = h/4pi

here dp = uncertainity in momentum

and dx = uncertainity in position

given

v = 8micro m/s = 8 x 10^-6 m/s

uncertainity in velocity = 4%

m = 0.400 x 10^-18 kg

dp = mdv = 0.400 x 10^-18 * 0.04 x 8 x 10^-6

dx = h/4pi*dp

dx = 4.12 x 10^-10 m = 41.2 nm = 4.12 A

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