Question

What is the uncertainty of the position of the bacterium? express your answer with the appropriate units?

Answer 1

For two un-related quantities, the Heisenberg uncertainty equations holds: the prduct of the two uncertainty quantities is greater than
`\hbar/2`
Example of unrelated quantities are position and momentum, energy and time.
Thus

`\Delta x*\Delta p \ \textgreater \ \hbar/2`
Knowing the speed of the bacteria the uncertainty in its position is

`\Delta x \ \textgreater \ \hbar/(2 \Delta p) =\hbar/(2mv)`