Question

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

Short answer

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

Define nuclei

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

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.