Question

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

Short answer

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

Step-by-step solution

Define nuclei

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

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.