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56. (a) Calculate the energy released the neutron- induced fission reaction n + 235 U _ 92Kr ~ + 142Ba + 2n given m(92Kr) = 91.926269 u and m(142Ba) =141.916361 u _...

Question

56. (a) Calculate the energy released the neutron- induced fission reaction n + 235 U _ 92Kr ~ + 142Ba + 2n given m(92Kr) = 91.926269 u and m(142Ba) =141.916361 u _ (b) Confirm that the total number of nucleons and total charge are conserved in this reaction

56. (a) Calculate the energy released the neutron- induced fission reaction n + 235 U _ 92Kr ~ + 142Ba + 2n given m(92Kr) = 91.926269 u and m(142Ba) =141.916361 u _ (b) Confirm that the total number of nucleons and total charge are conserved in this reaction



Answers

(a) Calculate the energy released in the neutron-induced fission reaction
$n+^{235} \mathrm{U} \rightarrow^{92} \mathrm{Kr}+^{142} \mathrm{Ba}+2 n$
given $m\left(^{92} \mathrm{Kr}\right)=91.926269 \mathrm{u}$ and
$m\left(^{142} \mathrm{Ba}\right)=141.916361 \mathrm{u}$
(b) Confirm that the total number of nucleons and total charge are conserved in this reaction.

No problem. 45 in chapter gratitude in this problem, we are given our efficient again. This is a new Troy induced and the neutron reactive is plutonium to 13. I, Aniki, were so give four neutrons ended in student union and some burial. And first of it calculates the math loss during this process that I am Eco's the left off neutron plus a mess. Oh, plutonium and the minus a meth. I was drawn to him and then minus a mess. Oh, barium and some minor. It's a mess off your trunk. Tanks forth. Plug in the numbers. Here is a gift to a result. These two numbers are giving in the in the problem and this is from the website and here is from the appendix A. The result is 0.1938374 atomic mass. So the energy loss will be that I am times to see square. You know that one atomic mass times the sea squirrel is not handled on a 31.5 American electoral rolls. So in here for this amount all mess the energy released is one 88.56 mega electoral votes and I am part of beat. Asked us to the total number off your clothes and the total charge. If will is it conserved between these two sides. So first, the total track total number of new class neutron has no clue number one and plutonium to 39. On the right hand side, it's 19 6 plus 440 plastic for does e equal. Yes, this ecos 2 40 All right? Yes. And then the total charge. Neutron has charged zero on the pro. Tony, um, it has charged 0 94 And on the right hand side, this one has this'll. One has ah has atomic number old 54 the barium has atomic number off 56 to the Nico. No, I'm sorry. Is this, uh for strong Herot? Mead has atomic number or 38. So the ICO Yes. 94 cigar

So we're talking about the neutron, uh, induced fission of uranium. So this was given in the problem here? Ah, as were the masses. I went ahead and looked up the masses for uranium and the neutron as well. We simply need to just calculate the mass defect right. Mass defect is taking the masses of the product of the parent nuclei and then tracking off the daughter nuclei. When you do that, I get in the mass defect 0.19 in atomic mass units. I certainly like converting to the movies. So I get 177. Uh, M E v Persie squared right? And the problem mentions that this is about 6 may be higher than spontaneous fission, and that's pretty simple. This is a neutron induced, which means it needed help, right? So it has a higher activation energy to get there. So if you think about a reaction being able to go from here to here, right, spontaneous means it can get over this with just thermal barriers. But what we're saying is that there's another barrier that's taller and deeper, and it needed the energy from the neutron to be able to get over it. But when it does get over, it actually is paid off with a deeper well. So in this case, about 6 a.m. E V. Now the other thing that we want to check is to make sure everything was actually concerned. So let me get rid of these numbers down here. We get rid of everything and I want to check how many total protons there were on the left hand side. Right. Total protons at 92 rise just uranium and on the right hands in. Strontium is 38 and seen on is 54 ongoing. Behold, you get 92 on the total nuclear onside neutrons. Air one uranium is 2 38 So we have 239 now. The right hand side, we have 96 plus 1 40 plus three for the three new trunk and again to 39. So we are confirmed that everything is conserved

Problem afforded thrilling Chapter 32 This problem. We are going to calculate the energy release off nutrient pills to uranium. A fusion as official reaction is here. If you quit, is here one new trunk reactivity William, and the production is That's 14 IAM and Lena and three neutral. So to calculate its energy release that we need to calculate the mass close so that I am is the math in your trunk clocks, the math off uranium and the minor semester authority? Um, it's a minor Samat, Rosina and his own minus suey times on meth. Oh neutron, this ecos 0.190068 atomic Mass And then we know that for one atomic, a mass times C Square it's nice 31 point of Phi Omega electoral rolls. So the energy loss due to this um actually it's just tow good math loss times this number and this gives a result off 177 point 05 Maguy Electoral Waltz in part of beat Ask Otto Compare agrees that all spontaneous fission that a purely intact the book, the spontaneous fission gives ah energy release off about 171 megawatt awas so this vision is about a six mega electoral watt speakers. And this well, why's that, Director singling is because the meth follows a different. This one is has a bigger mess. Oh, so it has a bigger energy release. Another battle thing about it is because this is a new toy and used. It's a second order off this of this reaction. Actually, it's, uh, it's can be formed the in a cycle in the spontaneous sufficient there is neutral created. And then this neutral one you'd want singer activist uranium again. Don't give us this reaction. And I am policy to ask how to calculate the number on your clones and told her charge So first to lay the number or new plans on the left hand side is the neutral has a nuclear number or one on the uranium has two certainly night to 38 as it on the right hand side is 96 class 140 apply street Tuesday. ICO. Yes, the number is 23 and nine. And for the total charge, Toto, charge number Neutron has charged over Theo on the uranium is ah ah. Atomic number is 92 So is charge. Number is 92 on the right hand side of the fourth door, Tino is atomic. Number is 38 on for Xena is 54 4 Neutron zero to the eagle. Yes, pose equals 2 92

This question, we gotta find what is the energy release by this reaction, this new proficient or uranium to show Jim and seen on. So to find energy released, we need to find a cure value that is to find SD changing the messes off the knew. Quite what applied by C squared, changing a mess is simply taking the initial total Massive directives Subject it. Piety final mess off the products So we have less off uranium plus mess softie you, John subject by mass off de Shaun T Maso. See, you know and show off times theme ass off your truck. We have charged neutrons. That's all fine. And put not profiting by C squared and you get the answer. So the mess is already given on the right hand side here can find them from Appendix B. Sister, An atomic mass units. Right. We can use C square in the form off 91.5 MTV for you. Right, Which you say it more convenient form since we're doing for atomic mass units and can't get energy in terms off MTV. More conveniently so, the finance serve issued gets 1 to 6.5 every V by just substituting or devalues on the right answer into the equation.


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