# The Heisenberg Uncertainty Principle

1. Mar 2, 2008

### 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?

Last edited: Mar 2, 2008
2. Mar 3, 2008

### plstevens

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

3. Mar 3, 2008

### greisen

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...

4. Mar 3, 2008

### plstevens

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

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

5. Jul 14, 2011

### darkxponent

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

6. Jul 21, 2011

### That Neuron

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.