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Why does the fusion of light nuclei into heavier nuclei release energy?

Short Answer

Expert verified

The reason for energy release is that heavier nuclei have more binding energy.

Step by step solution

01

Define nuclei

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

02

Explanation

Let’s look at why energy is released when light nuclei fuse with heavy nuclei. The term "fusion" refers to the joining of two smaller nuclei to create a larger nucleus. To begin solving this problem, one must first determine the binding energy, which is the amount of energy necessary to totally breakdown it into protons and neutrons. The rest mass, which can offer the difference, can be used to calculate the nucleus's binding energy. \({\rm{E = (}}\Delta {\rm{m)}}{{\rm{c}}^{\rm{2}}}\)is known to be the rest mass.

When the elements are separated, they have a different mass than when they are mixed together. When two light nuclei combine to form heavier nuclei, there is an energy release. The mass difference is equivalent to the mass of the\(\Delta m = BINDING\,\,ENERGY/{c^2}\)once again. Following that, we obtain the mass difference formula, which is,

\(\Delta {\rm{m = (Z}}{{\rm{m}}_{\rm{p}}}{\rm{ + N}}{{\rm{m}}_{\rm{n}}}{\rm{) - }}{{\rm{m}}_{{\rm{tot}}}}\)

And then just add the speed of light (which corresponds to the Einstein formula for the rest mass) to get the binding energy,

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

And the size of the binding energy is determined by the order of this mass difference. One can see how binding energy varies for different elements in relation to the number of nucleons\({\rm{BE/A}}\)in figure\({\rm{31}}{\rm{.27}}\)from the book. Following the image again, lighter nuclei have lower binding energies and greater mass per nucleon.

As a result of the merger of these two lighter nuclei into one heavier nucleus, nuclei with less mass per nucleon and higher binding energy will occur.

Therefore, it will result in energy release if energy is preserved.

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The activities of \(^{131}I\) and \(^{123}I\) used in thyroid scans are given in Table \({\rm{32}}{\rm{.1}}\) to be 50 and \(70\mu Ci\), respectively. Find and compare the masses of \(^{131}I\)and \(^{123}I\) in such scans, given their respective half-lives are \({\rm{8}}{\rm{.04\;d}}\)and \({\rm{13}}{\rm{.2\;h}}\). The masses are so small that the radioiodine is usually mixed with stable iodine as a carrier to ensure normal chemistry and distribution in the body.

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(a) Estimate the years that the deuterium fuel in the oceans could supply the energy needs of the world. Assume world energy consumption to be ten times that of the United States which is \(8 \times {10^9}J/y\) and that the deuterium in the oceans could be converted to energy with an efficiency of \(32\% \). You must estimate or look up the amount of water in the oceans and take the deuterium content to be \(0.015\% \) of natural hydrogen to find the mass of deuterium available. Note that approximate energy yield of deuterium is \(3.37 \times {10^{14}}J/kg\).

(b) Comment on how much time this is by any human measure. (It is not an unreasonable result, only an impressive one.)

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