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

• Phyisab****
In summary, the uncertainty in the life time of an electron and positron produced in a vacuum is approximately 3 x 10^-22 seconds, which is calculated using the equation Delta E x Delta t = hbar/2. The final answer of 3ps in the given solution is most likely a typo. WolframAlpha can be used to verify the answer.
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?

Last edited:

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 .

## 1. What is pair production in vacuum?

Pair production in vacuum is a phenomenon in which a high-energy particle, such as a photon, spontaneously transforms into a pair of particles, typically an electron and a positron, in the absence of any other particles or external fields.

## 2. How does pair production in vacuum occur?

In pair production, a high-energy photon interacts with the vacuum and creates a virtual particle-antiparticle pair. These virtual particles then become real and separate, resulting in the production of two new particles.

## 3. What is the significance of pair production in vacuum?

Pair production in vacuum is a fundamental process in quantum field theory and is essential to our understanding of the behavior of particles at the subatomic level. It has also been observed in high-energy particle collisions and has important applications in areas such as astrophysics and medical imaging.

## 4. Is pair production in vacuum possible in all types of vacuum?

No, pair production in vacuum can only occur in a true vacuum, also known as a perfect vacuum, which is a space devoid of all matter and radiation. In other types of vacuum, such as a low-pressure gas, there are still particles present that can interfere with the process.

## 5. Can pair production in vacuum result in particles other than electrons and positrons?

Yes, while the most common result of pair production in vacuum is an electron and a positron, it is also possible for other particle-antiparticle pairs to be produced, such as muons and antimuons. The specific particles produced depend on the energy of the initial photon and the properties of the vacuum in which the process occurs.

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