Question

How to calculate the energy released during fusion?

Answer 1

Hint: To determine the answer to this question we should know what fusion reactions are. Fusion is the combination reaction of lighter elements to give the stable heavier elements. The energy required to break the nucleus into individual components, protons, and neutrons is known as binding energy.

Complete answer:
In nuclear fusion, the smaller nuclei having mass numbers less than $60$ are combined to a heavier more stable nuclei. This reaction is known as fusion. The nuclei having mass number less than $60$ are unstable.
The amount of energy released when a heavy nuclei forms from lighter nuclei is known as binding energy. The formula of binding energy of nucleus is as follows:
$\text{B}\text{.E}\text{.}\text{ = }\mathrm{\Delta }m{\text{c}}^2$
Where,
B.E. is the binding energy of the nucleus
$\mathrm{\Delta }m$ is the mass defect
c is the speed of light whose value is $3\times {10}^8$ m/s.
An example of fusion reaction is shown as follows:
$\text{4}{}_{\text{1}}^{\text{1}}\text{H}\to {}_2^4\text{H}\text{ + }{}_{+1}^0\beta \text{ + }\text{energy}$
The exact mass of the nucleus is never equal to the sum of the mass of protons and neutrons of that nucleus. The mass of the nucleus is slightly less than the sum of the exact mass of protons and neutrons of that nucleus. This difference is known as mass defect.
Mass defect in kilogram = mass of reactant – mass of product
When we determine the mass defect in an amu unit then we have to multiply the mass defect with $1.67\times {10}^{-27}$ .
Therefore, the energy released during fusion is calculated by the $\text{B}\text{.E}\text{.}\text{ = }\mathrm{\Delta }m{\text{c}}^2$ formula.

Note:Fusion reactions take place at very high temperature. The reaction in which the mass of the product is greater than the mass of the reactant is known as an endergonic reaction. Fusion is an endergonic reaction. The mass defect is negative for fusion reaction. The energy also comes into negative for fusion reactions. The negative sign shows the release of energy.