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Question 10: Why the annihilation of an electron and positron creates a pair of photons a d not a single photon?


When a particle and its antiparticle meet they annihilate (destroy, kill, eat up) each other and a pair of photons is formed. Therefore, when electron meets positron, they both disappear and a pair of photons is formed.

We know that in any process the momentum before and after the process remains conserved. Similarly, total sum of mass energy is equal to the energies of the photon after annihilation of electron and positron. Now if m0 is the mass of electron and positron and f is frequency of the photons, then m0c2 + m0c2 = hf + hf ⇒ 2m0c2 = 2hf ⇒ m0c2 = hf ⇒ hf = 9.11 * 10-31 * (3*108)2 = 0.51 MeV

Similarly, the momentum before and after are also conserved.

0 + 0 = hf/c + (- hf/c) ⇒ hf/c = hf/c

Thus, to satisfy these laws, two photons ate emitted in opposite directions.


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