How long would an electron-positron pair exist for?

[ZedCar]

Homework Statement

How long would an electron-positron pair exist for in "the vacuum" [of space]?

To create an electron-positron pair requires at least 2mc^2 = 1.6 x 10^-13 J

Homework Equations

ΔEΔt ~ (h-bar)/2

The Attempt at a Solution

Δt ~ (h-bar)/2ΔE
Δt ~ (1.05 x 10^-34) / (2 x 1.6 x10^-13)
Δt ~ 3.28 x 10^-22 s

 

[Spinnor]

How big is the box you put them in? The more room the particles have to roam the smaller the chance they will "meet".

 

[ZedCar]

How big is the box you put them in? The more room the particles have to roam the smaller the chance they will "meet".

There is no reference to this in the question.

It just mentions that "the vacuum" is teaming with virtual particles which blink in and out of existence. Then asks How long would an electron-positron pair exist for in "the vacuum" [of space]?

 

[Antiphon]

I would suppose more than 14 billion years if they started out on opposite sides of the 14-billion light-year wide universe.

 

[frogjg2003]

I'm getting 3.22 instead of 3.28. If you're posting because your answer is wrong, that might be why. Try using more digits in your calculations.
I'm also guessing that you aren't supposed to consider that the electron and positron have kinetic energy as well as mass energy, otherwise you would have to take that into account, but no information has been given to you.

 

[ZedCar]

I'm getting 3.22 instead of 3.28. If you're posting because your answer is wrong, that might be why. Try using more digits in your calculations.
I'm also guessing that you aren't supposed to consider that the electron and positron have kinetic energy as well as mass energy, otherwise you would have to take that into account, but no information has been given to you.

Thanks frogjg2003.

Even though we're getting slightly different results which is probably due to using a different number of figures in the calculation, is the formula which I'm using correct?

There is no other info given, so nothing else has to be taken into account.

The reason I ask is because the lecturer provided on the board the following solution:

Electron pair requires at least 2mc^2=1.02MeV of energy
Δt ~ (h-bar)/ΔE
Δt ~ (1.05 x 10^-34) / (1.02 x 1.6 x 10^-13)
Δt ~ 6.4 x 10^-22 s

 

[Spinnor]

...

The reason I ask is because the lecturer provided on the board the following solution:

Electron pair requires at least 2mc^2=1.02MeV of energy
Δt ~ (h-bar)/ΔE

...

Is there a factor of 2 missing above? Δt ~ (h-bar)/ΔE

 

[ZedCar]

Is there a factor of 2 missing above? Δt ~ (h-bar)/ΔE

Yes, there is a factor of 2 missing.

It would appear the lecturer has done this intentionally.

bossman27 in another thread:
https://www.physicsforums.com/showthread.php?p=4124901&posted=1#post4124901

has informed me that excluding the factor of two is Heisenbergs original formula.