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Problem 18 Hard Difficulty

Another series of nuclear reactions that can produce energy in the interior of stars is the cycle described below. This cycle is most efficient when the central temperature in a star is above $1.6 \times 10^{7} \mathrm{K}$ . Because the temperature at the center of the Sun is only $1.5 \times 10^{7} \mathrm{K}$ , the following cycle produces less than 10$\%$ of the Sun's energy. (a) A high-energy proton is absorbed by 12 $\mathrm{C}$ . Another nucleus, $A,$ is produced in the reaction, along with a gamma ray. Identify nucleus $A$ . (b) Nucleus A decays through positron emission to form nucleus $B$ . Identify nucleus $B$ . (c) Nucleus $B$ absorbs a proton to produce nucleus C and a gamma ray. Identify nucleus $C$ . (d) Nucleus $C$ absorbs a proton to produce nucleus $D$ and a gamma ray. Identify nucleus $D .$ (e) Nucleus $D$ decays through positron emission to produce nucleus $E$ . Identify nucleus $E$ (f) Nucleus $E$ absorbs a proton to produce nucleus $F$ plus an alpha particle. What is nucleus $F ?$ Note: If nucleus $F$ is not $1^{12} \mathrm{C}-$ that is, the nucleus you started with - you have made an error and should review the sequence of events.

Answer

a. $^{13}_{7} N$
b.$_{6}^{13} C$
c. $_{7}^{14} N$
d. $_{7}^{15} N$
e. $_{8}^{15} O$
f. $^{12}_{6} C$

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Video Transcript

in this question, we are given a series off your reactions that Cohen son and keep in various or no new clients there. We want toe identify. So I've written down the various equations They were mobilized in the question after the under new guys are labeled over here A, B, C or the re on two F. And so the general method they're gonna use to identify the I know knew quite is to use the conservation off nuclear number and conservation off proton numbers. So in a reaction, the total proto number shouldn't change. And he told her nuclear number shouldn't change as well. So they must be equal or the left hand side and the right hand side. Now they start off 51st equation at the top. The total total number on the left answer is six past 76 plus one, which is seven. So the proton about the right hand side must be seven is well right. The total brother number since camera ready told contributes any portal number put on a bill from a must be seven same thing. 50 nuclear number defense Ice shop Last one which is studying so a must have 13. You can't. Now to identify the element. We're gonna look up the periodic table and usti proton number to identify Weiss D Element. So he probably number seven anyone's must be nitrogen. So this is nitrogen. 30. So you come please. Thes I tortured teen. I would give it that natural Turned 13 on a course. Positron que So it means a positron. If a neutrino that comes along 50 positron and then we have our don't be total proton away. Seven. So be master six protons. You can't number is 13. So be must've Tina's well camped A periodic table for anyone with six protons must be covered. So peace carbon t using the same method. All right? No, we haven't. I don't see over here myself. A total proton above six plus one, which is seven. You can't number must be 40 And so this is a natural same thing seven plus one proton number. But we ate 14 plus one Proton number must be sorry. Nuclear number must be 50 Captain periodic table. This must be oxygen because yes, it protons This is oxygen. 15 eight on the left hand side eight protons. So what you write and site. You must be seven 50 Nuclear number since on 11 size 15 as well. So campy periodic table. This is a natural trend. 15 Lastly, nitrogen 15. Given that undergo, say, alpha decay. So Elfatih key has its a helium UK we for neutrons and protons. So we take seven total, right? And so, uh, if must have so I d this excuse to include, say, pro talks, right? I missed rt caught on over here. Absorb. See Proton. All right, and then it put uses f personnel for Baikal. Next. What is the correct equation? Total proton number is eight over here. So if America takes away two of the proton number, so it must be six total nuclear number is 16 when you write your 16 minus four, this is chalk. And so the element f must be a carbon chop. So we have actually come full circle. Right? Come on. A show for pierce again from the initial reactors to the final product to the X kind of like e, uh, catalyst for this particular reaction

National University of Singapore
Top Physics 103 Educators
Elyse G.

Cornell University

Marshall S.

University of Washington

Farnaz M.

Other Schools

Jared E.

University of Winnipeg