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How to calculate the energy released during fusion?

Mar 7, 2018

Depending on how the information is given to you:

If the masses are given in terms of $u$:
"Mass change"=(1.67*10^-27)("Mass of reactants"-"Mass of products")
If the masses are given in terms of $k g$:
"Mass change"=("Mass of reactants"-"Mass of products")

This may seem strange, but during nuclear-fusion, the products are lighter than the reactants, but only by a small amount. This is because the heavier nuclei need more energy to keep the nucleus together, and to do so, need to convert more of their mass into energy. However, iron-56 has the highest energy-per-nucleon value of all nuclei, so fusion to nuclei beyond this will lead to a decrease in mass.

The relationship between energy and mass is given by:
$E = {c}^{2} \Delta m$, where:

• $E$ = energy ($J$)
• $c$ = speed of light (~3.00*10^8ms^-1)
• $\Delta m$ = change in mass ($k g$)

$E \approx {\left(3.00 \cdot {10}^{8}\right)}^{2} \cdot \text{Mass change}$

However, if you want to be more accurate:
$E = {\left(299 792 458\right)}^{2} \cdot \text{Mass change}$