Question

What is the uncertainty of the position of the bacterium?

Express your answer with the appropriate units.

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A student is examining a bacterium under the microscope. The E. coli bacterial cell has a mass of m = 1.10 fg (where a femtogram, fg, is 10−15g) and is swimming at a velocity of v = 9.00 μm/s , with an uncertainty in the velocity of 7.00 % . 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.

Answer 1

According to the Heisenberg's uncertainty principle the exact position() and the exact momentum() of a particle are difficult to find with great accuracy.

Where = = uncertainty of position

= planck's constant

= uncertainty of momentum =

= mass of bacteria = 1.10fg =

= uncertainty of velocity =  

Velocity of bacteria =

The uncertainty in velocity =

Therefore uncertainty in velocity

Uncertainty in the position =

Therefore the uncertainty in the position =