Question

A student is examining a bacterium under the microscope. The E. coli bacterial cell has a mass of m = 1.80 fg (where a femtogram, fg, is 10−15g) and is swimming at a velocity of v = 2.00 μm/s , with an uncertainty in the velocity of 5.00 % . 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. Part A What is the uncertainty of the position of the bacterium

Answer 1

By Heisenberg uncertainty principle

(1)

is uncertainty in position , ( m ) uncertainty in momentum

is uncertainty in velocity. h is planck's constant = 6.626 10-34 J.s

now, given mass of bacetrial cell = 1.80 fg = 1.80 fg

= 1.80 10-15 g

= 1.80 10-15 g

= 1.80 10-18 Kg.

Velocity of bacetrial cell = 200 / s

= 2.00 / s  

= 2.00 10-6m /s

now, uncetainty in velocity is 5.00%

so,   = 2.00 10-6 m /s  

= 1.00 10-7 m/s

now putting the values in Eq. 1

  

or, 1.80 10-18 1.00 10-7  =

or , 1.80 10 -25 = (6.626 10-34 / 43.14)

or, 1.80 10 -25  = 5.275 10-35

or, = 5.275 10-35 /1.80 10 -25  

or, = 2.93 10-10 m

therefore ,  uncertainty of the position of bacterium is 2.93 10-10 m