Hi I\'m working on the following problems and I don\'t understand how to solve t

Question

Hi I'm working on the following problems and I don't understand how to solve them.
1) A student is examining a bacterium under the microscope. The E. coli bacterial cell has a mass of m = 0.600 fg (where a femtogram, fg, is 1015g) and is swimming at a velocity of v = 7.00 m/s , with an uncertainty in the velocity of 2.00 % . 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.
What is the uncertainty of the position of the bacterium?
2)An electron traveling at 5.0×105 m/s has an uncertainty in its velocity of 1.11×105 m/s .
What is the uncertainty in its position?

Explanation / Answer

1) Given

dv = 7 x 10^-6 m/s x 0.02 = 1.4 x 10^-7 m/s

h = planck's constant

m = 0.6 x 10^-18 kg

and using below equation with dx as uncertainty in position,

dx = h/4pim(dv)

     = 6.626 x 10^-34/4 x 3.14 x 0.6 x 10^-18 x 1.4 x 10^-7

     = 6.28 x 10^-10 m

2) dv = 1.11 x 10^5 m/s

m = 9.11 x 10^-31 kg

we get,

uncertainty in position dx as,

dx = 6.626 x 10^-34/4 x 31.4 x 9.11 x 10^-31 x 1.11 x 10^5

     = 5.22 x 10^-10 m

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