Problem: By looking at the uncertainty of the bacterium's position, did the student have a valid point? A student is examining a bacterium under the microscope. The E. coli bacterial cell has a mass of m = 1.20 fg (where a femtogram, fg, is 10-15g) and is swimming at a velocity of v = 7.00 μm/s , with an uncertainty in the velocity of 6.00 % . 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.What is the uncertainty of the position of the bacterium? Express your answer with the appropriate units.

FREE Expert Solution

Recall that Heisenberg’s Uncertainty Principle states that we cannot accurately determine both the position and velocity of an electron. This means we can only know either one at any given time

Mathematically, this is expressed as:

$\overline{){\mathbf{\Delta x}}{\mathbf{·}}{\mathbf{\Delta p}}{\mathbf{\ge }}\frac{\mathbf{h}}{\mathbf{4}\mathbf{\pi }}}$

where:

h = Planck’s constant (6.626 × 10–34 kg • m2/s)

Δx = uncertainty in position (in m)

Δp = uncertainty in momentum (in kg • m/s)

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Problem Details

By looking at the uncertainty of the bacterium's position, did the student have a valid point? A student is examining a bacterium under the microscope. The E. coli bacterial cell has a mass of m = 1.20 fg (where a femtogram, fg, is 10-15g) and is swimming at a velocity of v = 7.00 μm/s , with an uncertainty in the velocity of 6.00 % . 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.

What is the uncertainty of the position of the bacterium? Express your answer with the appropriate units.