Creating/Destroying Electron-Positron Pairs: Time Limit?

[S1CkFiSh]

The rest energy of an electron is 0.511 MeV = 8.2 x10-14 J. A positron is an electron with positive charge and the same rest energy. Within what time interval can we create and destroy an electron-positron pair without worrying about the conservation of energy? h = 6.626 × 10-34 J s.

 

[tiny-tim]

Hi S1CkFiSh!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[kerimek]

I can provide a response to this question by applying the principles of conservation of energy and the uncertainty principle in quantum mechanics.

Firstly, the creation and destruction of electron-positron pairs involve the conversion of energy into matter and vice versa. This process must adhere to the law of conservation of energy, which states that energy cannot be created or destroyed, only converted from one form to another. Therefore, any time interval in which we create and destroy an electron-positron pair must also conserve the total energy of the system.

Secondly, the uncertainty principle in quantum mechanics states that there is a fundamental limit to the precision with which certain pairs of physical properties, such as position and momentum, can be known simultaneously. In this case, the uncertainty in energy and time are related by the equation ΔEΔt ≥ h/4π, where h is the Planck constant.

Applying these principles, we can calculate the maximum time interval in which we can create and destroy an electron-positron pair without violating the conservation of energy. Using the given values, we can rearrange the uncertainty principle equation to solve for Δt, which gives us a time interval of approximately 4.3 x 10^-22 seconds.

This means that within this time interval, the uncertainty in energy will be small enough for the creation and destruction of an electron-positron pair to occur without worrying about the conservation of energy. However, it is important to note that this is a theoretical calculation and in practice, there may be other factors that could affect the actual time interval.