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Problem 36 Easy Difficulty

Consider the reaction $_{92}^{285} \mathrm{U}+_{0}^{1} \mathrm{n} \rightarrow_{57}^{148} \mathrm{La}+_{35}^{87} \mathrm{Br}+_{0}^{1} \mathrm{n}.$ (a) Write the conservation of relativistic energy equation symbolically in terms of the rest energy and the kinetic energy, setting the initial total energy equal to the final total energy. (b) Using values from Appendix B, find the total mass of the initial particles. (c) Using the values given below, find the total mass of the particles after the reaction takes place. (d) Subtract the final particle mass from the initial particle mass. (e) Convert the answer to part (d) to MeV, obtaining the kinetic energy of the daughter particles. Neglect the kinetic energy of the reactants. Note: Lanthanum-148 has atomic mass 147.932 236 u; bromine - 87 has atomic mass 86.920 711 19 u.

Answer

a) $K E_{i}+m_{i} c^{2}=K E_{f}+m_{f} c^{2}$
b) 236.052588$u$
c) 235.861612$u$
d) 0.190976$u$
e)

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Video Transcript

{'transcript': "this question were given that a nucleus initially is at rest and that it spontaneously splits into two different fragments minutes and one and two. And they carry away some form of kinetic energy. And we want to show what is the infection off the total kinetic energy carry away by the different messes and one of them too. So we're gonna use two different conservation loss and that it would be conservation of momentum and conservation off energy. So conservation of energy tells us that total energy total kinetic energy. Let's be close to Kennedy Energy off the first Miss us. I can't stand it. You're the second miss by conservation of momentum, right? We know that initial momentum is zero. So the final momentum must also be cereal. And that will mean that the magnitude off the momentum off mess one must be a course to magnitude off went off, mess to, Since they are both actually moving opposite directions, their actual momentum has opposite signs. So but the magnitude off the momentum are equal, right? Must be equal in order for them to cancel out. Let's just label this magnitude s p right, p just No, we can relate. STI kinetic energies too. Damn momentum. Right key one go says p one square to m one. Okay. Also equals to peace. Go with someone. Que two is p two square over two and two Was there close to p scale. What's went to and to find so we can find affection, right? This will be key one plus key to and substituting the values in. So we see that I say common factor off piece Grey over two for both the denominator. Andy, you burrito So we can cancel. Veto gets one over and one one plus 1/2. We multiply both the numerator and denominator by m one times m two gets to for two. Plus what? Yeah, this is whole final answer. We do the same acting with K two, right? But Noah skip a few steps. Very similar, except that now the numerator is and one if we get a final answer. So now we're gonna use this creature to co create well rt kinetic energies and evil Asti for the nuclear fission. Off uranium to 36 are united 236 sweets up to throw me and also continue 179 So you want four night? So now we want to find why Steve Disintegration Energy First the decision could is your energy humanistic? You value you take the mass defect want right by C Square the best effect is phoned by taking the massive director. How do you mess with the initial nuclear That is really into 36 Every subject that with the mess off the Fisher and products just for protein and letting them no more to play by C square This is Grace given us night tree One point for tie four m v v Poor You should get 177 MTV. This is our disintegration energy. So in order to find d kinetic energy, we're assuming that the total kinetic energy istea que value right. You assume disease our total kinetic energy and so we can find what iss Oh, mess. Maybe using either one off the equation either K on all k two, because it doesn't matter. So connecting under to approve me given s total kitty energy Well, to play by myself to you for the body total mess off t victims Amedi put ducks So we have faulty you Master required can use the menses in terms of the other white mess units. Right? Since we're only taking you a short so the units will cancel out we get 112 0.0 MTV for the kinetic energy. For me, co Katie Energy off netting. Um, we can simply take the total energy u minus. A weighty, kinetic energy of protein, Right, Because of conservation of energy. So we should get 65.4 and TV now to get a speed, we know that kinetic energy is given as half. Empty square. Sophie? Yes. Two K over em. Take a square root of it. So just to be clear, the kinetic energy will have to be in terms off Jews. So you have to convert the M E V to juice. So I just wait Example for probie rectal. This is equal two times off. One too. Every multiplying debts by 1.6 time said power minus 13 Jews Po MVV This will cooperate to juice that he mess off roominess given s seven seven. You were accommodated two kilograms a spell and you should get 1.5 feet. I was 10 involved seven meters per second we do the same thing except me. Chesty energy. And you also changed the mass. All right. Debbie should get you. Don't see for that. Tell you to be nine point tree. Sorry, it 9.2 the state About six. Just a second."}

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