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Problem 23 Medium Difficulty

A neutral pion at rest decays into two photons according to
$$
\pi^{0} \quad \rightarrow \quad \gamma+\gamma
$$
Find the energy, momentum, and frequency of each photon.

Answer

$E = 67.5 \text{MeV}, p = 67.5 \text{MeV/c}, f = 1.63 \times 10^{22}\text{Hz}$

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Top Physics 103 Educators
Elyse G.

Cornell University

Zachary M.

Hope College

Aspen F.

University of Sheffield

Meghan M.

McMaster University

Video Transcript

this question, given a neutral pion that is initially at rest the case into 24 taunts by the conservation of momentum. Since the initial momentum is zero, right, it's at rest. The fundamental must be zero s Well, so the momentum off both photons must be equal and opposite, right? No, that can so each other out. And since D energy office photon is given esteem a winter multiply piety speed off light. We know that energy off the photons must be de saint, right? Since you have the same momentum. So the same energy and this energy must be or from the rest energy off our pion. Right? So because that's the only energy dead it has, it's at rest. So no kinetic energy. And so I only has his own rest energy to convert to energy. It's rest miss converts into energy. So the energy that is being converted over here is a mess off the pie on Times Square that is close to one tree, five MTV. And since the energy is equally shed between these two photons, the energy off a photon because to want to fight back by two to 67.5 MTV to find what is to you. Momentum. We take this equation e equals PC, so you will see speed off night. So this is 67.5 MTV. Percy. So this is a unit for momentum that this quite convenient When we are dealing with small values, off energies to find a frequency now in huts, you have to convert the energy. All right, so energy off the photo on its goes to hitch f hitches. Thanks, Constable. Private, if you can see so, eh? Physical. So you hitch. But before he actually cooperate this the energy has to reconnoiter into juice. So we take 67.5 movie What, whereby 600 power When this 13 juice per MTV This will give us juice damage right by plank's constant and we get the final into it hurts just 1.6 tree time stamp party to goods

National University of Singapore
Top Physics 103 Educators
Elyse G.

Cornell University

Zachary M.

Hope College

Aspen F.

University of Sheffield

Meghan M.

McMaster University