Consider the Heisenberg uncertainty relation for energy and time deltaE delta t

Question

Consider the Heisenberg uncertainty relation for energy and time deltaEdeltat >=h/4pie where h is Planck's constant.

Apply this uncertainty relation to electron/positron pair production, a process by which an electron and positron can appear out of vacuum so long as the two particles exist for a time shorter than delta t. (A positron is the electron's antiparticle, having equal mass but opposite charge.) The two particle's are created moving apart with approximately equal and opposite velocities, but in a brief time (less than or equal to delta t) they pull each other back together and annhilate upon colliding. For electron/positron pair production, delta E is the uncertainty in the energy of the vacuum, which may vary by as much as the total energy of an electron/positron pair.

An electron and positron are created with speeds much less than c, so that the pair's total energy is approximately equal to their combined rest energy. What is the maximum time that the pair can exist, from when they are created out of vacuum to when they collide and annhilate?

Explanation / Answer

Here energy of electron E=mec2

energy of positron E=mpc2

and deltaE=mec2+mpc2

Now according Heisenberg uncertainty relation for energy and time deltaEdeltat >=h/4pie

putting the value of deltaE we will find the value of deltat.

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