# Uncertainty in the position of a particle, and momentum question

1. Feb 26, 2009

### Zit501

Hi all,

I just can't wrap my head around this one. It should be fairly easy, but i'm lost!

1. The problem statement, all variables and given/known data
Suppose that the uncertainty in the position of a particle is of the order of its de Broglie wavelength. Show that in this case the uncertainty in its momentum is of the order of it's momentum.

2. Relevant equations

Not 100% sure...

Delta x is similar to the wavelength
Delta p is similar to Plancks constant over wavelength
Therefore delta x delta p are similar to Plancks constant

3. The attempt at a solution
Well I can see how delta x and delta p can be related together to the wavelength, but after that I'm lost.

Any help much appreciated! I'm a B.Sc Mechanical Engineer doing an entry level nuclear physics course and I'm holding on... just.

2. Feb 26, 2009

### CompuChip

Yes, so you almost got it.

$$\Delta x \sim \lambda$$
If the uncertainty relation is near the minimum value, then
$$\Delta x \Delta p \sim \hbar$$

So what is $\Delta p$ then. What is $\lambda$ in terms of p?