A proton and an antiproton annihilate, producing two photons. Fin...

Question

A proton and an antiproton annihilate, producing two photons. Find the energy, frequency, and wavelength of each photon (a) if the p and p are initially at rest and

Accepted Answer

Welcome back, everyone. We are making observations about muons. Now, muons are massive particles and a muon represented by negative E and an anti muon represented by positive E could transform into an electron and a positron. Now we are told that the massive particles will initially be at rest and we are tasked with finding three things here. One, what is going to be the energy of the electron and the antiparticle, what is going to be the frequency of each of those? And what is going to be the wavelength of each of those as well? On our left hand side here, we have all of our answer choices that it could be. So let's get down to it. Well, we know and are told that the mass of an electron is approximately 200 times less than the mass of a muon. So what we can say is that the mass of a muon is 200 times times the mass of the electron. Now, what we can do is we can draw a parallel to the mass energy of a muon. And we can say that the mass energy of a muon is times that of the rest mass energy of an electron. So what is this going to be? Well, what we get is that this is equal to times 0. mega electron volts giving us one oh 2.2 electron volts. Now, we are going to have that the energy of the anti muon is going to be the same. So the mass energy of the muon is equal to the mass energy of the anti muon. But we can bring this one step further. We have that the electron and positron have the same energy as each of our previous massive particles. So we can say that E M is equal to E A is equal to E E is equal to E P. Meaning that our energy or both our electron and our anti particle is simply going to be one oh 2.2 elect mega electron volts. Wonderful. Now let me go ahead and change colors here to move on to part two. How do we find frequency when we can use this? We can say that our energy of a particle is simply equal to planks constant times the frequency dividing both sides by planks constant. We can see that on the right hand side of our equation, we get frequency by itself. So we have that frequency is equal to our energy divided by planks constant. Let's go ahead and carry that out. What we get is one oh 2.2 mega electron volts mega electron volts or one point or one oh 2.2 times 10 to the six electron volts. Now, this is going to be divided by planks constant of 4. times 10 to the negative fifth electron volt seconds, which gives us a frequency of 2. times 10 to the 22nd earths. Wonderful. Now let me go ahead and change colors one more time so that we may go ahead and find the wavelength of each of our particles here. Now, our wavelength is simply going to be equal to the speed of light divided by our frequency. So what this gives us is three times 10 to the eighth divided by 2.47 times 10 to the 22nd giving us a uh wavelength of 1.21 times 10 to the negative 14th meters. So now we have found the energy of our particles, the frequency of our particles and the wavelength of our particles which corresponds to answer choice. A thank you all so much for watching. I hope this video helped. We will see you all in the next one.

A proton and an antiproton annihilate, producing two photons. Find the energy, frequency, and wavelength of each photon (a) if the p and p are initially at rest and

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