Astudent is examining a bacterium under the microscope. the e. coli bacterial cell has a mass of m = 0.900 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 3.00 % . 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? express your answer with the appropriate units.

9.73 x 10⁻¹⁰ m

Explanation:

According to Heisenberg uncertainty principle

Uncertainty in position x uncertainty in momentum ≥ h / 4π

Δ X x Δp ≥ h / 4π

Δp = mΔV

ΔV = Uncertainty in velocity

= 2 x 10⁻⁶ x 3 / 100

= 6 x 10⁻⁸

mass m = 0.9 x 10⁻¹⁵ x 10⁻³ kg

m = 9 x 10⁻¹⁹

Δp = mΔV

= 9 x 10⁻¹⁹ x 6 x 10⁻⁸

= 54 x 10⁻²⁷

Δ X x Δp ≥ h / 4π

Δ X x  54 x 10⁻²⁷ ≥ h / 4π

Δ X = h / 4π x 1 /  54 x 10⁻²⁷

=

= 9.73 x 10⁻¹⁰ m

low freq = 100 mhz

low wavelength =101.7m

length = 3x10^8/freq

bacteria that live on the ocean floor are sustained by phytoplankton. phytoplankton, microscopic marine photosynthetic organisms, have a vastly significant role to play not only in the marine food web of which they’re part of, but also on a more global scale. despite their infinitely small size in comparison to other marine organisms, these tiny creatures occupy an immensely important ecological niche: they are the foundation of the marine food web, and as primary producers, play key roles in supporting all other organisms in the marine environment, as well as in the regulation of the earth’s climate through the sequestration of carbon, oxygen production, and other related processes. phytoplankton account for roughly half of all global primary productivity; therefore, their significance extends far beyond the marine environment alone. there is an intriguing sense of irony in the realization that these tiny living beings that often live out their existence unnoticed and undetected by the rest of the world, have such a far-reaching impact on the lives of virtually all other living organisms on the planet, particularly on those in the marine environment. the world that we have become accustomed to has been and is continuously shaped by the workings of these miniscule yet vital “plants of the sea”.

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