# Pair Production in Vacuum

#### Phyisab****

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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?

Last edited:

Homework Helper

#### 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 .

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