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Problem 19 Medium Difficulty

Assume a deuteron and a triton are at rest when they fuse according to the reaction
$$
_{1}^{2} \mathrm{H}+_{1}^{3} \mathrm{H} \rightarrow_{2}^{4} \mathrm{He}+_{0}^{1} \mathrm{n}+17.6 \mathrm{MeV}
$$
Neglecting relativistic corrections, determine the kinetic energy acquired by the neutron.

Answer

$\text{KE}_{n}=14.1 \text{MeV}$

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Marshall S.

University of Washington

Jared E.

University of Winnipeg

Meghan M.

McMaster University

Video Transcript

for this question, we are looking at a duty on entry tomb that actually fused together to form a human for and a neutron. We are given that the energy released by this reaction the Q value is 17.6 MBD. Now this energy goes into the kinetic energy, writes off both the human and neutron. And so this must be equals two D kinetic energy controlling plus kinetic energy or for helium, for which is in off a particle, not to find ways to kinetic energy off the neutron. We need to utilize the conservation off momentum. We were given that the initial reactions actually fused 20 at rest. Which means that the initial momentum, my total momentum off the system must be zero. And so, by conservation of momentum, do you final final momentum off the system after the fusion must also be cereal. And what this meat is that he momentum off the helium must be equal and opposite to the momentum off our neutron. Right. In order to cancel each other out and to give ah, the total momentum, the census, um, to be zero right now. Since we are neglecting relativistic corrections, you can use the Costco equation for momentum. That is peace. Gray over to em. All right. No, We can put in right rearranging to get P P s. It goes to to end key square root X grow the entire thing. So it creating this too we should get Ah, soapy off helium. Might a mental here will be two times demands off Union. All right, well, for particle. Never Just yourself are in states times d k e off Effa his course to D two times Mess off the neutron times k off neutron it and so can simplify this ml far k how far this goes to and key off. Oh, in other words, since you want to find what it so penitential each often neutron Nerys, arrange kinetic energy off. L far terms off indented energy off neutron terrace for here. And we can substitute this. Go unquestioned too. Uh, creature in the worship right to interest in conservation of momentum regarding the kinetic energy and acute value. And we should gets key off neutron close. And for l four times key off. So basically key or future on, you re infected at all. He's animal farm course. 2017.6 every fee and then is given s what point she was your 8665 you ml fa is given this four points was your 26 year tree you so we can find this ratio very actually putting into calculator every and want to that to get our this factor here in every day by this factor over to the right hand side. Final answer for key off neutron is 14.1 every V.

National University of Singapore
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Marshall S.

University of Washington

Jared E.

University of Winnipeg

Meghan M.

McMaster University