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Binding Energy of a nucleus can be found using the formula $$E = \Delta m\,c^2$$

Here, $\Delta m$ is the mass defect of the nucleus. Now, in a nuclear fusion reaction, we combine two lighter elements into a heavier element. But in this reaction, the total mass of initial two elements is greater than the heavier element. So some mass $\Delta m$ is converted to energy. But shouldn't this released energy ($\Delta m\,c^2$) go into forming the binding energy for the nucleus? But then why energy is still released into the surroundings?

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Nuclear binding energy is the energy that has to be added to a nucleus in order to separate it into its constituent protons and neutrons. Another way of thinking about it is that it is the net energy that would be released if you pushed a bunch of protons and neutrons together so tightly than the short range strong nuclear force combined them into a nucleus.

Since the binding energy is always positive, the mass of a nucleus is smaller than the sum of the masses of its individual nucleons. So binding energy is sometimes referred to as the mass defect or mass deficit of a nucleus.

The key number is the average binding energy per nucleon. This is a minimum value for hydrogen (which has zero binding energy since its nucleus is a single proton), increases from hydrogen up to iron, and then decreases again for elements further along the periodic table than iron (this is a slight simplification - there is a chart of the actual shape of the curve here).

So if you fuse two nuclei that are lighter than iron, the mass defect of the fused nucleus is greater than the mass defect of the original nuclei. Since the mass defect goes up, the mass of the combined nucleus is smaller than the combined masses of the original nuclei, and the “missing” mass is released as energy. Similarly, if you split or fission a nucleus that is heavier than iron the mass defect also goes up, and energy is released.

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  • $\begingroup$ the mass of the combined nucleus is smaller than the combined masses of the original nuclei, and the “missing” mass is released as energy . Yes, and shouldn't this same "missing" mass convert into binding energy for holding the combined nuclei together? $\endgroup$
    – Jdeep
    Aug 25 at 9:04
  • $\begingroup$ @ Jdeep No. The mass defect is the binding energy. You don't have to add more energy when you fuse light nuclei - instead some of the binding energy present in the original nuclei is "repaid" and released into the environment. If you owe your brother two loans of \$25 each but he agrees to cancel the whole debt if you repay him \$30 then you are \$20 better off than you were before. $\endgroup$
    – gandalf61
    Aug 25 at 10:46
  • $\begingroup$ IMHO, it'd be less confusing if it were called the "unbinding energy". $\endgroup$
    – PM 2Ring
    Aug 25 at 10:55

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