Chapter 19, Problem 19.17P

Interpretation Introduction

Interpretation:

Calculation of the amount of energy released for the fusion reaction.

Concept Introduction:

Nuclear fusion is defined as a nuclear reaction in which two or more nuclei combine to form one or more atomic nuclei of higher atomic number. Large amount of energy is released on fusion reaction. The difference in masses of reactants and products in nuclear fusion reaction gives information about this energy. This difference in energy actually arises from the difference in binding energy before and after the reaction.
Now, binding energy is the energy required to bind the nucleons in the nucleus, i.e. , this amount of energy is supplied, the nucleus will break into free nucleons.
Binding energy and mass difference is related by:
$\text{Binding Energy (B}\text{.E) = }\Delta M\times c^2$ , where $\text{ΔM}$ is the mass difference in amu, c is the speed of light in ${\text{m s}}^{-1}$ and B.E is obtained in $\text{eV}$.
We know that, $\text{1}\text{amu=1}{\text{.66053904 × 10}}^{\text{-27}}\text{ kg}$ and ${\text{1 J= 1 kg m}}^{\text{2}}{\text{ s}}^{\text{-2}}$

  $\begin{array}{l}\therefore \text{ B}\text{.E =1}{\text{.66053904 × 10}}^{\text{-27}}{\text{) kg × (3×10}}^{\text{8}}{\text{m}}^{\text{2}}{\text{s}}^{\text{-2}})\\ \text{}=4.9816\times {10}^{-19}\text{J}\\ \Rightarrow \text{B}\text{.E= (}4.9816\times {10}^{-19}\times \Delta M\text{) J}\end{array}$

Given:

  $\text{Mass of a }\text{H}\text{=1}\text{.00783 u}$

  $\text{Mass of a }\text{H}\text{=2}\text{.01410 u}$

  $\text{Mass of a }\text{H}\text{=3}\text{.01613 u}$