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Energy input is required to fuse medium-mass nuclei, such as iron or cobalt, into more massive nuclei. Explain why.

Short Answer

Expert verified

There is no energy release because heavier nuclei have lower binding energy than their constituents. So, it requires energy input for the nuclear reaction.

Step by step solution

01

Define nuclei

A focal point around which additional elements are organised or assembled.

02

Explanation

Examine why energy is required for the fusion of medium mass nuclei (such as cobalt or iron). We have extra energy that we call the binding energy when elements fuse or fission because of the mass difference between final nuclei and constituent nuclei, which is defined as,

\(\begin{aligned} BINDING\,\,ENERGY &= \left( {\Delta m} \right){c^2}\\ &= \left( {\left( {Z{m_p} + N{m_n}} \right) - {m_{tot}}} \right){c^2}\end{aligned}\)

As a result, the missing mass in heavier nuclei is proportional to the binding energy in the two medium mass nuclei. One can observe from the book's Figure\({\rm{31}}{\rm{.27}}\)that medium-sized nuclei have the maximum binding energy of all the nuclei. As a result, heavier nuclei fused from medium mass nuclei have lower binding energy than the two nuclei from which they were created. As a result, because the binding energy of a heavier nucleus is lower than the binding energy of two component medium mass nuclei, the energy will not be released. We must inject energy into this nuclear reaction since there is no extra energy in this scenario.

Therefore, as heavier nuclei have lower binding energy than their components, there is no energy release, hence energy input is required for the nuclear reaction to occur.

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Most popular questions from this chapter

Calculate the energy output in each of the fusion reactions in the proton-proton cycle, and verify the values given in the above summary.

The power output of the Sun is \(4 \times {10^{26}}{\rm{ }}W\).

(a) If \(90\% \) of this is supplied by the proton-proton cycle, how many protons are consumed per second?

(b) How many neutrinos per second should there be per square meter at the Earth from this process? This huge number is indicative of how rarely a neutrino interacts, since large detectors observe very few per day.

(a) What temperature gas would have atoms moving fast enough to bring two \(^{\rm{3}}{\rm{He}}\) nuclei into contact? Note that, because both are moving, the average kinetic energy only needs to be half the electric potential energy of these doubly charged nuclei when just in contact with one another.

(b) Does this high temperature imply practical difficulties for doing this in controlled fusion?

(a) Calculate the energy released in the neutron-induced fission (similar to the spontaneous fission in Example\(32.3\)) \(n{ + ^{238}}U{ \to ^{96}}Sr{ + ^{140}}Xe + 3n\), given \(m{(^{96}}Sr) = 95.921750{\rm{ }}u\) and \(m{(^{140}}Xe) = 139.92164{\rm{ }}u\).

(b) This result is about \(6{\rm{ }}MeV\) greater than the result for spontaneous fission. Why?

(c) Confirm that the total number of nucleons and total charge are conserved in this reaction.

Verify that the total number of nucleons, total charge, and electron family number are conserved for each of the fusion reactions in the carbon cycle given in the above problem. (List the value of each of the conserved quantities before and after each of the reactions.)

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