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Problem 40 Hard Difficulty

Consider two reactions:
$(1) \mathrm{n}+\frac{2}{3} \mathrm{H} \rightarrow_{1}^{3} \mathrm{H}$
(2) $_{1}^{1} \mathrm{H}+_{1}^{2} \mathrm{H} \rightarrow_{2}^{3} \mathrm{He}$
(a) Compute the Q values for these reactions. Identify whether each reaction is exothermic or endothermic. (b) Which reaction results in more released energy? Why? (c) Assuming the difference is primarily due to the work done by the electric force, calculate the distance between the two protons in
helium - 3.

Answer

a. \text { exothermic }
b. \text { first reaction }
c. 1.8810^{-15} \mathrm{m}

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Video Transcript

number 40 were given these two nuclear reactions, and we want to find Q for both of us. So I looked at the mass of each of these pieces in the back, the book in the appendix and just a regular neutron as a massive 1.0, eight, 665 this hydrogen two point 014 102 And then this heavy heist room 3.16 Oh, for nothing as well. Go ahead into the other room while shoe. Um, this hydrogen 1.0, seven 8 to 5. This one. So is that one 2.14102 And this helium The re point. 016 Oh so nine so far. But if I q, I'm going to just find the difference in the masses before and after. So basically, I'm gonna add these two and subtract that one. Have I got 0.0, six, 718 And that would be in use. We're gonna convert that now to energy equivalence. I know there's 931.5 mega electron bowls. I know you. So I get that the energy will be six point 258 Mega electron volts for this one, you do the same thing down here. These were the same slogan and add them. Subtracted this and they get the difference in mass is going to be a point. Oh, 58 98 Do my conversion. You cancel, and I'm gonna have 5.494 mega electron volts for this one. I'm gonna ask, which are the X A thermic endo. Thermic. They both have a positive number. So they're going to XO thermic both of them. Let him ask which one is more? Um, yeah. Which one releases more energy? Core system's gonna be this one. Some drill, That error there releases more energy. I'm gonna arrest him. Look. Why? Well, if you look at it, this is this nucleus. There's two protons, so, you know, protons repel each other. It's gonna take work to hold those together. So that's why this one has more energy released and then were to find out how far apart these protons are in this helium. Well, if I subtracted these, that's the difference. You That's what's holding this together. So I'm subtracting that something in that minus patch and I get the difference is the point 764 mega electron volts. And that's going to be the work holding those together. Um, so I can think of it is the work is equal to the electric potential energy. So the work I know is this point 764 mega electron rules and P. I remember listening to K something charge of the one the charge of the other than the distance between them. So Okay, nighttime stay overnight. Charge of one charge of the other, the birth proton. So I'm just take that and square it. So the charge of a proton the same was approaching a charge of an electron 1.60 times 10 like in 19. Remember, I'm squaring that before the both Q divided by the distance between him. And that's what I'm trying to find clinical t. Remember, this is gonna turn out to be in jewels, though. And this was in mega electron volts. So I'm going to a conversion over here on this side. Oh, remember the one point. Basically the charge, um, of the electron. But I have to account for the mega. So another power six. So this is gonna be 1.60 times. 10 to the negative. 13th. It's money, jewels or in an a mega electron volts. Maybe I'll put my units in here. So this is Jules. This is Mega Electron Volts. This is how many jewels, Aaron? One mega electron role. So Meg Electron volts canceled and the city in jewels Also. So now I just solve this equation for the D you take this times this squared divided by that times. That and then no equal. My d I get it. 1.885 times. Temple negative 15th meters. Really small number like I was expecting.

University of Virginia
Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

Marshall S.

University of Washington

Farnaz M.

Other Schools

Zachary M.

Hope College