Calculating Percentage of Uncertainty in Momentum: Tips and Tricks

[CollectiveRocker]

How do you go about finding the percentage in the uncertainty of momentum, if you already know the momentum and delta momentum? I'm asking because both of them end up being the same; thus I'm wondering if I'm terribly wrong. Any advice?

 

[Tide]

To find the percentage change divide the change in momentum by the (starting) momentum and multiply by 100%. The change in momentum has units of momentum but the percentage change has no units so they are not the same.

 

[CollectiveRocker]

The thing which I've discovered is that when I use that formula, I only end up with 100% back again. Are delta p and p supposed to be the same? For I've taken the things I know, the uncertainty in position and charge, and rearranged them in order to solve for things which I don't know.

 

[CollectiveRocker]

Any ideas guys?

 

[NateTG]

How do you go about finding the percentage in the uncertainty of momentum, if you already know the momentum and delta momentum? I'm asking because both of them end up being the same; thus I'm wondering if I'm terribly wrong. Any advice?

Can you give some more context with this question? Specifically, is it about Quantum Mechanics and Heisenberg's Uncertainty Principle, or something else?

 

[CollectiveRocker]

It is about Heisenberg's Uncertainty Principle. We are given the uncertainty for the position of the 1 KeV electron, and we're asked to find the percentage of uncertainty in it's momentum. Now, I've already found the uncertainty of momentum. However, when I use that answer and solve for momentum, both mometum and the uncertainty in momentum are equal. Thus when I use the % formula: (delta p *100%)/p, I end up with 100% as my percentage. What am I doing wrong?

 

[NateTG]

Thus when I use the % formula: (delta p *100%)/p, I end up with 100% as my percentage. What am I doing wrong?

This is ceratinly not my area of expertise, but why do you think having the uncertainty equal to the momentum is an incorrect answer? From what I understand the uncertainty can be larger than the momentum as well.

 

[CollectiveRocker]

Doesn't that mean that my percentage in my uncertainty is 100%?

 

[dextercioby]

Doesn't that mean that my percentage in my uncertainty is 100%?

Why not??As far as the calculations u made are correct,then that should be it.But i'd like to see all the numbers,though.U say the KE of the electron is 1KeV.Please give us the uncertainty in distance.

Daniel.

 

[CollectiveRocker]

the uncertainty of position is .100 nm

 

[dextercioby]

the uncertainty of position is .100 nm

I'm sorry to say,that,but you screwed up the numbers.Did u use the correct (nonrelativistic) formula for the momentum in terms of the KE??If so,combined with Heisenberg formula u should be getting less than 1%.

Daniel.

 

[CollectiveRocker]

The formula for KE = (p^2)/2m
k = 2pi/lambda, and delta p = h/lambda

 

[NateTG]

I also get less than 1% uncertainty.

 

[CollectiveRocker]

with what formula

 

[dextercioby]

with what formula

Nope,delta p_x is given by the Heisenberg (not de Broglie) formula wrt to h and delta x

 

[CollectiveRocker]

for delta p do you get 6.626 * 10^-24?

 

[dextercioby]

for delta p do you get 6.626 * 10^-24?

Yes.This thread is getting annoyingly long. :tongue2:

 

[CollectiveRocker]

I'm sorry to keep on testing your patience. So then we solve for k using k = 2pi/lambda, because lambda = delta x, and I get 6.283 * 10^10

 

[dextercioby]

I'm sorry to keep on testing your patience. So then we solve for k using k = 2pi/lambda, because lambda = delta x, and I get 6.283 * 10^10

Pay attention.It's not difficult at all:
$$E=\frac{p^{2}}{2m}$$ From which $$p=\sqrt{2mE}$$.Plug in the numbers,and find the result.If u don't know,learn that
$$m=9.1\cdot 10^{-31} kg$$.

Express the enrgy in Joules,compute the momentum and from there,devide the number u got for $\Delta p$ through the number u got for "p" and express the final result in terms of procents.

Daniel.

 

[CollectiveRocker]

is the answer .08?

 

[CollectiveRocker]

It's ok, I've got it. Thank you for all your help and patience.