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When a star has exausted its hydrogen fuel, it may fuse other nuclear fuels. At temperatures above , helium fusion can occur. Write the equations for the following process, (a) Two alpha particles fuse to produce a nuclear A and a gamma ray. What is nuclear A (b) Nucleus A absorbs an alpha particle to produce a nuclear B and a gamma ray. What is nucleus B? (c) Find the total energy released in the reactions given in parts (a) and (b).

Note: The mass of  

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Sumant
SumantLv10
27 Mar 2021

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Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

The Sun is powered by nuclear fusion. In each chain reaction, four hydrogen nuclei fuse together to become a single helium nucleus. The total combined mass of the individual hydrogen nuclei before the reaction is greater than the mass of the helium nucleus. The mass lost as a result of this chain reaction is turned into energy according to Einstein’s famous equation, E = mc2 (Chapter 39). Consider the first part of the chain reaction in which two hydrogen nuclei (each a single proton) fuse. Figure P8.56A shows the potential energy curve of a two-proton system. The energy in this graph is given in keV, where “eV” is the abbreviation for the unit electron-volt and 1 eV = 1.6 × 10−19 J. When the protons are more than about 2 fm (2 × 10−15 m) apart, the potential energy is positive. When the protons are close together, the potential energy is negative, and the protons are fused. Figure P8.56B shows a close-up of the potential energy curve when the protons are far apart.

  1. a. What is the minimum mechanical energy required for the two protons to fuse? Give your answer in keV.
  2. b. The mechanical energy of an average two-proton system in the Sun is around 2 keV. What is the minimum distance between the protons in such a system?
  3. c. Explain why it seems impossible for fusion to take place in the Sun. Note: Of course, fusion must take place in the Sun. Although it seems impossible according to classical mechanics, quantum mechanics (Part VI) makes fusion possible. According to quantum mechanics, the seemingly impossible is merely improbable, and even events with a low probability of occurrence may still happen. Because there are so many protons in the Sun, there is a good chance that at any moment many of them will fuse.

Chapter 8, Problem 56PQ, The Sun is powered by nuclear fusion. In each chain reaction, four hydrogen nuclei fuse together to

A nuclear reaction is represented by an equation similar to theequation for a chemical reaction. An example of a nuclear reactionis the decay of radium into radon by the emission of an alphaparticle (a helium nucleus). The equation for this reactionis

^{226}_{\ 88}{\rm Ra}\; \rightarrow \, ^{222}_{\ 86}{\rmRn}+\;^4_2{\rm He}.

The superscript preceding each element indicates the nucleon numberof that particular nucleus (total number of protons and neutrons).The subscript indicates the charge of the nucleus, which is equalto the atomic number for nuclei. Nuclear reactions frequentlyinvolve electrons (sometimes called beta rays) and photons(sometimes called gamma rays). Electrons, which have nucleon number0 and charge -1, are represented in equations as either ^{\ \;0}_{-1}\beta or ^{\ \; 0}_{-1}{\rm e}. Photons are represented as^{0}_{0}\gamma to emphasize that they have no nucleon number andcarry no charge.

In nuclear reactions, several conservation laws are usuallysufficient to determine the products or reactants. One of these isconservation of nucleon number. The total number of neutrons andprotons in all of the reactants must be the same as the totalnumber of protons and neutrons in the products. Although protonsand neutrons sometimes change into one another, neither can simplydisappear. Another important conservation law is conservation ofcharge. The net charge of the reactants must be the same as that ofthe products.

Notice that, in our equation for the decay of radium, the sum ofthe nucleon numbers on each side is 226 and the sum of the chargeson each side is 88. If you knew everything in this equation exceptthe isotope of radon produced, you could simply subtract 4 from 226to find the nucleon number required to make the nucleon number ofthe products equal the nucleon number of the reactants. Similarly,if you knew everything in this equation except for the identity ofthe product element, you could simply subtract 2 from 88 and thenlook in a periodic table to find that the element with atomicnumber 86 is radon.

In parts A and B consider the decay of radon by alpha particleemission:

^{222}_{\ 86}{\rm Rn}\;\rightarrow\;X +\,^{4}_{2}{\rm He}.

a. What is the nucleon number of the element X?
Express your answer as an integer.

b. What is the atomic number (nuclear charge) of the elementX?
Express your answer as an integer.

n parts C and D consider the decay of Potassium-43 into calcium-43via the following reaction:

^{43}_{19}{\rm K} \rightarrow ^{43}_{20}{\rm Ca}+\,X.

c. What is the charge of the emitted particle X?
d. is not visible yet

E. An isotope of potassium with a half-life of roughly one billionyears is often used in radioactive dating. This isotope decaysthrough electron capture, the process of drawing an electron intothe nucleus. What is the chemical symbol for the element thatresults from this process? The equation for the reaction is

^{40}_{19}{\rm K}+\,^{\ \;0}_{-1}{\rm e}\rightarrow \,?.
Express your answer as a chemical symbol (e.g., Na forsodium).

f. The reaction energy of a reaction is the amount of energyreleased by the reaction. It is found by determining the differencein mass between the reactants and products and then using E=mc^2 toconvert the lost mass into the released energy.

Look again at the equation for the decay of radium (Ra), given inthe introduction. Use the following table of masses to determinethe reaction energy of this reaction.
Nucleus or particle Mass in atomic mass units
radium-226 226.025402
radon-222 222.017571
alpha particle 4.002602
Express your answer in joules to three significant figures.

please answer fully... thank you

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