How Accurate is the Uncertainty in the Lifetime of Electron-Positron Pairs?

[Phyisab****]

Homework Statement

What is the uncertainty in the life time of an electron and positron produced in a vacuum?

Homework Equations

$$\Delta E\Delta t=\frac{\hbar}{2}$$

The Attempt at a Solution

$$\Delta E\approx1.6\times10^{-13}J$$

$$\Delta t\geq\frac{\hbar}{2\Delta E}\approx 3ps$$

(edited for Tex)
This is the solution my professor had to this problem in his notes, but I am quite sure that the final answer of 3ps is a typo. I believe that Delta t is more like 3 x 10^-22 s. Can anyone clear this up for me?

 

[Dick]

Your answer seem right to me.

 

[Phyisab****]

Thanks! I had read over this part of the notes this morning right before the final exam. This problem ended up being on the exam. I could not for the life of me figure out why my answer was not 3ps .

 

[phsopher]

WolframAlpha is a fast way to check.