estimate how long the electron and positron can exist before annihilating.

You are performing research on quantum fluctuations in empty space. In one type of fluctuation, an electron– positron pair (Section 44.2) appears in empty space. This process appears to violate the conservation of energy principle, since the rest energy of the particles has been created from nothing. According to Equation 39.24, however, this violation of conservation of energy can exist as long as the particles annihilate with each other in a time interval consistent with the energy–time version of the uncertainty principle. You employ this principle to estimate how long the electron and positron can exist before annihilating.