The Heisenberg Uncertainty Principle Part A What is the uncertainty of the posit

Question

The Heisenberg Uncertainty Principle Part A What is the uncertainty of the position of the bacterium? Express your answer with the appropriate units. 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 10-15 g) and is swimming at a velocity of 9.00 m/s with an uncertainty in the velocity of 5.00%. E coli bacterial cells are around 1 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 hat 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. Hints Submit My Answers Give Up

Explanation / Answer

Given dv = 0.01*10^6 m/s

the uncertainty is:

dx = h/4pi*m*dv

h = (6.626*10^-34) (Planck Constant)

pi = 3.1416..

dv = 5% of original = 5/100*9 = 0.45 micrometer/s = 0.45*10^-6 m/s

m = mass of particle = mass of bacteria = 1.1*10^-15 g = 1.1*10^-18 kg

Substitute all data in equation:

dx = (6.626*10^-34)/((4*3.141592*1.1*10^-18)*( 0.45*10^-6))

dx = 1.0652*10^-10 m

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