Homework Help: Quantum Phenomena question

1. The problem statement, all variables and given/known data
Hi, I'm fairly new to these forums and I'm stuck on a problem. Just wondered if anyone could give me any hints or tips on how to get started on the following question:
An unstable particle produced in a high-energy collision has a mass of m and an uncertainty in mass that is p of the particle's mass. Estimate the liftime of the particle.


2. Relevant equations

I am assuming this question has something to do with Heisenbergs Uncertainty Principle. i.e
[tex] \Delta x*\Delta p >= \hbar [/tex] where p is momentum and x is some distance
From the information given I assume I have to use the above formula to get:
[tex] \Delta x*(p/m)*v >= \hbar [/tex] ....? where p/m is the uncertainty in the mass described in the question

3. The attempt at a solution
As I said at the begining I don't really know how to get started on this question, and thus the derived relationship above is all I have managed to come up with thus far. I am begining to think that this question requires me to calculate the energy of the particle by calculating the minimum uncertainty on the momentum (i.e (p/m)*V). If the equation that I have formulated so far is correct, what am I supposed to use for delta x? From the information given I cannot see any way to deduce this. Any indication on whether im on the right lines here or any other help would be very much appreciated. Thanks in advance, Kam.

 

Can anyone please give me an idea whether I am heading in the right direction here, or indicate to me that I need to show more working before anyone will assist me further? Thanks.

 

Ok I will take on board what you have said and I will try and solve this problem. I did not know that the uncertainty principal could be related to time and energy. Thank you for your help :)

 

Ok so I now have the equation [tex] \Delta t \Delta E = \hbar [/tex]
I have used the equation E = mc^2 and substituted the values into the Heisenberg equation to get:
[tex] \Delta t = hm/(2 \pi c^2 p) [/tex]
However mastering physics is saying that this answer is incorrect :(

 

Hi, I used the value p/m for the mass as I assumed this would represent the ratio of the uncertainty of the mass to the actual mass of particle. When I divide through by (p/m)c^2 (In the Heisenberg equation) doesn't the m go to the top? Or have I got my relationship between p and m wrong, should the uncertainty in the mass be p*m not p/m? Thanks.

[EDIT Problem solved, thanks!]