Talia Rice II
Jan 10, 2025
The Heisenberg Uncertainty Principle – Chemistry Question PLEASE HELP! I’ve tried to work it out 4 times!?
A student is examining a bacterium under a microscope. The E. coli bacterial cell has a mass of 1.60 femtograms (fg), where 1 femtogram is equal to 10^-15 grams, and it is swimming at a velocity of 4.00 micrometers per second (µm/s), with an uncertainty in the velocity of 3.00%. E. coli cells are approximately 1 micrometer (µm) or 10^-6 meters in length. The student is supposed to observe the bacterium and make a drawing. However, having just learned about the Heisenberg Uncertainty Principle in physics class, the student expresses frustration, stating that the uncertainty in the bacterium’s position is larger than the microscope’s field of view, making it impossible to locate the bacterium.
What is the uncertainty of the position of the bacterium? Please express your answer numerically in meters. I understand the formula, but I’m unsure which numbers to use in the calculation.
1 Answers
The momentum of the bacteria is 4.10^-6*1.60.10^-18 = 6.4 10^-24 kgm/s
and the uncertainty is 3% of that: 1.92.10^-25
According to the uncertainty relations the product of the (minimal) uncertainty on position and momentum is hbar (‘normalized’ Planck’s constant) which is worth 1.05.10^-34 J s so the uncertainty in position here is 5.5.10^-10 m that is .0005 of the bacterium length and the claim of the student is completely unwarranted
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