The Heisenberg Uncertainty Principle and bacteria

• plstevens
In summary, the student is examining a bacterium with a mass of 0.200 femtograms and a swimming speed of 4.00 microns per second with a 5.00% uncertainty. The student is unable to make a drawing due to the uncertainty principle, which states that the uncertainty in the position of the bacterium is greater than the microscope's viewing field. However, when applying the DeBroglie thesis and considering the bacterium's wavelength, the uncertainty can be calculated without relying on statistical mechanics.
plstevens
A student is examining a bacterium under the microscope. The bacterial cell has a mass of 0.200 (a femtogram is 10^-15) and is swimming at 4.00 microns per second, with an uncertainty in the speed of 5.00%. E.coli bacterial cells are around 1 micron, or 10^-6 meters in length. The student is each 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.

A. What is the uncertainty of the position of the bacterium? Answer should be in m.

i don't understand this at all and there's no examples in my book can someone just help me with this one?

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I do know that the standard rule is to show an attempt but there is no examples in my textbook. So, if someone could help me that would be greatly appreciated.

if you write up Heisenbergs uncertainty principle and plug in the numbers from the exercise you should see that the uncertainty principle is not so relevant for the bacteria.

Try to write up the equation and put in the numbers...

ok, is this how i should set this equation up?

(4*10^-6)(2*10^-15)(5.00%)>=h/4(phi)

equation

[(4*10^-6)(2*10^-19)(5.00%)]*x>=h/4(phi)

where 'x' is uncertainity in position of bacteria'[(4*10^-6)(2*10^-19)(5.00%)]' is uncertainity in momentum(velocity*mass*%uncertainity in momentum)

now acc to heinsberg equation
(uncertainity in momentum)*(uncertainity in position)>=h/4phi

I would instead look at the DeBroglie thesis... apply a wavelength to the bacterium and then show the wavelength and find uncertainty as based upon that... it gets you around statistical mechanics.

1. What is the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle is a fundamental principle in quantum mechanics that states that it is impossible to know the exact position and momentum of a particle simultaneously. In other words, the more accurately we know the position of a particle, the less accurately we can know its momentum, and vice versa.

2. How does the Heisenberg Uncertainty Principle apply to bacteria?

The Heisenberg Uncertainty Principle applies to all particles, including bacteria. Bacteria are made up of tiny particles, such as molecules and atoms, which follow the laws of quantum mechanics. This means that we cannot know the exact position and momentum of a bacterium at the same time.

3. Does the Heisenberg Uncertainty Principle affect how we study bacteria?

Yes, the Heisenberg Uncertainty Principle has implications for how we study bacteria. Since we cannot know the exact position and momentum of a bacterium, our measurements and observations of their behavior and properties will always have a degree of uncertainty.

4. How does the Heisenberg Uncertainty Principle impact our understanding of bacteria?

The Heisenberg Uncertainty Principle reminds us that there are limits to what we can know and measure in the microscopic world. This means that our understanding of bacteria is limited by the uncertainty inherent in quantum mechanics. However, scientists have developed techniques to minimize this uncertainty and improve our understanding of bacteria.

5. Can the Heisenberg Uncertainty Principle be applied to other aspects of biology?

Yes, the Heisenberg Uncertainty Principle can be applied to other aspects of biology, such as the behavior of cells and the structure of molecules. It is a fundamental principle of quantum mechanics that applies to all particles, including those found in living organisms.

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