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Princeton University

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Problem 67 Hard Difficulty

Consider the fusion reaction $^{2}_{1}H$ + $^{2}_{1}H \rightarrow ^{3}_{2}He + ^{1}_{0}n$. (a) Estimate the barrier energy by calculating the repulsive electrostatic potential energy of the two $^{2}_{1}H$ nuclei when they touch. (b) Compute the energy liberated in this reaction in MeV and in joules. (c) Compute the energy liberated $per$ $mole$ of deuterium, remembering that the gas is diatomic, and compare with the heat of combustion of hydrogen, about $2.9 \times 10^{5} J/mol$.

Answer

(a)$0.48 \mathrm{MeV}$
(b)$5.239 \times 10^{-13} \mathrm{J}$
(c)$3.155 \times 10^{11} \mathrm{J} / \mathrm{mol}$

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Video Transcript

is this question reward He considers a fusion reaction up for hydrogen for 200 atoms into a huge in madam in a Utah. So we want to first calculates the Barrow energy by calculating the repulsive electrostatic petition was a touch. So it's just, um we need to use the cooler energies. So, uh, za radius a hydrogen atom can be phoned buys a very first equation off this chapter. This isn't two months search. So this, if we remember this is a constant is this is atomic Alexa. Total wage In terms of atomic numbers, she's the last start. So this is going to give us a radius Offices. Adam just want one for one times 10 to 0 to 15 meters Wednesday to Adam's touch. They are is there really are two reduces support, but we're going to assume that they'll some part of it, is going to overlap, but don't want to disappoint. So the electrostatic energy is going to be 1.4 pipes from what e squared over. R, this is just a constant. This is ah, in actual 1.6 10 to 10 to the negative 19. So the regis we found things out. Paris case, Um oh, actually, use to reduce is because when they touch their to reduce a support so there's going to be nine times 10 to the lies you turn meter squared over C squared times. Ah, the electoral is 1.6 times turn to electric lighting. Coolum slur over two times of radios is 1.51 times 10 to the subject of two meter. So this is going to give us an energy of 7.65 attempts to selective 14 job or in terms of MTV is little point. But for eight MTV. So that is for part A. And then we can look at Kirby. Heartbeat wants us to look at us. Energy liberated. Is this reaction e m b b and that the jurors? So this is this case when you two calculates the change of mess. So Delta M is going to be is a mess. The two times a mess. Hydrogen, um, some trucked. It's a mass off human. Subtract. It's a mess of a nitrogen, says Mess is going to be 3.51 several times, 10 to the negative three U. So this course and again we know each you is 931 25. My home judge, Sir, do you want with five MTV? So if we use this converted factor, Super 10 times turned 2 to 3. Huge arms 131. Fun, um, TV for you. We're going to see such a total number off energy. It's just a lot of energy that just produces three point 270 on TV. So that's what part B, um, and I think we are. It does not ask us to compute. Oh, it was awesome to compute this age are. So if we convert an e vite a chore, we can find that US 3.270 m B B is equivalent you 5.239 times 10 to the negative searching job. Very last part us us to find the energy per more. And we need to remember that discusses die atomic. Um, so each at each mark you're actually continues to Adams is and we want you compare this energy to was a combustion off hydrogen. So let us compute, um, someone of energy promoter. So for each reaction, we have 200 nucleus, So each more of your room has 6.22 times 10 to 23. Office up. Carter Carter is constant that many modern cures. So that has that many parents. That's the same number of pairs of molecules. So we really we will have 6.22 times 10 to Z 23 reactions for each more off during because, well, Durham has two Adams and then to Adam's form a reaction. So and then each of these hair were produced a lot of energy of what we found. Five wins over Tuesday nine times 10 to 0 to 13 job. So each more were produced, 3.155 times changes 11 job tomorrow and also approval. And we can see this energy is more Sam Miller time starters and the energy we get firms are combustion off, more off haji guests

Princeton University
Top Physics 103 Educators
Elyse G.

Cornell University

LB
Liev B.

Numerade Educator

Zachary M.

Hope College

Aspen F.

University of Sheffield