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Problem 20 Medium Difficulty

A reaction that has been considered as a source of energy is the absorption of a proton by a boron - 11 nucleus to produce three alpha particles:
$$
_{1}^{1} \mathrm{H}+\frac{11}{5} \mathrm{B} \rightarrow 3\left(_{2}^{4} \mathrm{He}\right)
$$
This reaction is an attractive possibility because boron is easily obtained from Earth’s crust. A disadvantage is that the protons and boron nuclei must have large kinetic energies for the reaction to take place. This requirement contrasts to the initiation of uranium fission by slow neutrons. (a) How much energy is released in each reaction? (b) Why must the reactant particles have high kinetic energies?

Answer

a. 8.68 $\mathrm{MeV}$
b. The proton and the boron nucleus are both positively charged and thus require sufficient kinetic energy to overcome the coulomb repulsion between the nuclides

Discussion

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

Farnaz M.

Other Schools

Meghan M.

McMaster University

Video Transcript

discussion. The first part we are looking at. What is the energy released by this particular fusion reaction involving 100 new kite Wi Fi borrowing? 11. You're going to give us tree alpha particles, right? Which I actually have new cuts. So the energy releases given S t cured number Q factor just financed. E changing mess multiplied by C square. Changes men. Sorry. The changing Messi is defined as he minutes off the ensure reactant subjected by the mass off the final products. And this will give us tea amount off mess There was actually committed into energy, which would give us the energy released. Right. So we we need meself t hydrogen, right? Thus mess off the boron click subtracted by three times d mess off the far particle. Want to bite by sea script miss off the 100 trend. If we can look that up online, it should be around one point. She was who? Seven. Fine. Yes. Lt. Brian 11. Yes, 11.2 short. Nine is your secure. And that's the message. Tee off a particle This for my church to six year tree. You? No, de very off c square. We're gonna use 91.494 MTV for you since you're working way for 20 mass units. So it's small computer, putting it to co creator. We should get it 0.68 MTV. The reason why? Ah, the question stated, a large amount of kinetic energy is required for direction. Think places because get our both our reckons they are both positively charged. Randy nucleus are positively church, and it is, well, we know that positive. The charged particles will repel each other right due to cologne, repulsion and such. A lunch amount off energy is required toe force them close enough to each other by going against Thekla. Repulsion in orderto get the nucleus closing after fuse right. That's when the almost like touching, and that is a very large, mild, off low energy that is quiet to overcome. Unlike looking at the uranium to 35 with neutrons because neutrons are neutral, so there's no cologne repulsion involved, and so you're inefficient. It's actually requires less less energy in order to proceed

National University of Singapore
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

Farnaz M.

Other Schools

Meghan M.

McMaster University