The neutral pion decays by $\pi$⁰ $\rarr$2 $\lambda$.The rest mass of the neutral pion is 135 MeV/c².What is the energy of each of the photons if the pion is at rest when it decays? A) 270 MeV B) 135 MeV C) 67.5 MeV D) 1.02 MeV E) This decay cannot happen.

Question

Quizplus · Accepted Answer

In this decay, the neutral pion at rest decays into two photons. By conservation of momentum, the total momentum of the two photons must be equal and opposite, since the initial momentum of the pion was zero. Therefore, if we know the energy of one of the photons, the energy of the other photon is simply the rest of the energy of the pion minus the energy of the first photon.

The rest energy of the pion is given as 135 MeV/c^2. Since the pion is at rest, all of this energy will be converted into the energy of the two photons. Since there are two photons, each photon will have half of this energy:

E(photon) = 135 MeV / 2 = 67.5 MeV

Therefore, the correct answer is (C).

The Neutral Pion Decays By π\piπ 0 →\rarr→ 2 λ\lambdaλ The Rest Mass of the Neutral Pion Is 135 MeV/c2

The Neutral Pion Decays By $\pi$ ⁰ $\rarr$ 2 $\lambda$ The Rest Mass of the Neutral Pion Is 135 MeV/c²