Question

Heisenburgs Uncertainty Principle.
I keep getting the wrong answer and it is driving me crazy.

Using Heisenbergs uncertanty priciple, calculate the uncertanty in the position of a) A 1.50-mg mosquito moving at a speed of 1.40 m/s if the speed is known to within 0.01 m/s; and b) which I will try to figure out on my own if I fully understand this one.

The following post will show what I have done.

Answer 1

\[h=6.626*10^{−34}\]
\[Δx=h/(4π∗Δp)\]
\[m=1.5mg=1.5∗10^{-6}kg\]
\[Δv=1.4m/s±0.01m/s=1.40∗10^{-2}\]

I would assume, here that I have everything and it should just be plug and chug, however I am not getting the correct answer and do not know why.

Answer 2

Simply \(\Delta v=0.01 \;m/s \)

Answer 3

Even using that I still have the wrong answer...

Answer 4

To one sig fig, it is correct... let me ask a few questions...

Answer 5

So, the speed that is given at 1.4 m/s is not used or even needed, just the uncertanty in the speed itself. And this will find the uncertanty in position correct?

Answer 6

and that the mass should always be in kg? and velocity should always be in m/s, right?

Answer 7

Check with your textbook. There are different definitions of "\(\Delta\)something" and they can lead to slightly different expressions of Heisenberg's inequalities by a factor 2 or a factor \(\pi\).

Answer 8

Correct for kg and m/s.

Answer 9

"So, the speed that is given at 1.4 m/s is not used or even needed, just the uncertanty in the speed itself. And this will find the uncertanty in position correct?"

- Correct!

Answer 10

This is a Chem book, not very well defined in this area. Going though my Physics book would be overkill with the chapters I would have to go back through. (Which I plan on doing prior to the next Chem class)

Answer 11

That is strange that is is only the uncertanty that we need, and not the actual speed itself. This helps clear things up a bit. Thanks!!

Answer 12

You're welcome :))