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Problem 42 Hard Difficulty

Two protons approach each other with 70.4 MeV of kinetic energy and engage in a reaction in which a proton and a positive pion emerge at rest. What third particle, obviously uncharged and therefore difficult to detect, must have been created?

Answer

Neutron

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

LB
Liev B.

Numerade Educator

Zachary M.

Hope College

Jared E.

University of Winnipeg

Video Transcript

for this question given that two protons collectively shot a hit on each of them have kinetic energy off 70.4 MTV and you collect to give rise to treat it from pie coz right Proton pi positive pie own Israel Lestienne Unknown X particle. They want 100 5 26 So first off, using conservation of momentum we know that since both protons are coming hit on with same energy, the total momentum or this system is zero right? Totally momento. So the final mental this system must be zero s well and we are given that the Proton and Peyron came out at rest right you much at rest between moving. And that means that the X must be not moving as well to allow the total momentum system to remain zero. So this must be at rest this smell. And so in order to identify what this particle is, we can simply look at what is the rest energy off this portico by using conservation off energy so total energy and start must be questioned. Totaled energy in the final reactors, right? So energy in issue with Bt mass energy off the protons wants right by two plus two times off the K off the protons. Frank, you quit this toe. The final energy, which is simply the rest, Mrs off the proton, the pie own positive Pion and our unknown X. Okay, so the rest mass energy off proton. What a piece Square just given ass Night tree eight point tree everybody. So you can calculate what is the rest? Energies. So the rest energies for the real Sony for the pion over here, that is one treat, nine 0.6 Hemi V. And so from here we just need to substitute the values in. Maybe quit Bolf equations, and then we can find what? He's a mix square. By rearranging the equation, a little bit should be able to bring this were to the left. That site gets Peace Square right off course. The kinetic energy over here still times off the 70.4. Just 240.8 TV. Oh, I answer for this. You should gets 99 0.5 g right and so distressed energy. My given that the an additional fact that ah, by conservation off burial number, we have plus one last one over here barrel numbers is this plus one, This is zero. So x must be a plus one for myself plus 1 40 Berra number. So you must be a very on infect. It must So from this. But go rest energy. It can either be a neutron or anti neutron. But since it is burial not boys plus one, it must be a you try. Right, So Particle X is a neutrons.

National University of Singapore
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

LB
Liev B.

Numerade Educator

Zachary M.

Hope College

Jared E.

University of Winnipeg