Final answer:
The energy released from the annihilation of an electron and a positron at rest is 2m_e c², and the correct answer is B. (2m_e c²).
Step-by-step explanation:
When a positron and an electron meet, they annihilate each other, converting their entire mass into energy.
According to Einstein's famous equation E = mc², where m is the mass and c is the speed of light, the energy released from one electron-positron pair is 2mec², as both particles have the same mass me.
Therefore, because they are assumed to be at rest initially, the correct answer is B. (2me c²).