Animated Solution for Physics - Atoms and Nuclei: Statement I Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion. Statement II For heavy nuclei, binding energy per nucleon increases with increasing Z while for light nuclei, it decreases with increasing Z.

The Binding Energy Curve

Have you ever wondered why some elements, like Iron, are incredibly stable and abundant, while others, like Uranium, are radioactive and prone to falling apart? The answer lies in one of the most beautiful and revealing graphs in all of physics: the Binding Energy per Nucleon curve.

This curve plots the binding energy per nucleon ($E_{bn}$) against the mass number ($A$). Think of it as a map of nuclear stability. The higher a nucleus sits on this curve, the more tightly bound its nucleons are, and the more stable the nucleus is.

If you look at the curve, you will notice it has a distinct peak around a mass number of $A=56$. This corresponds to the isotope ${}^{56}\text{Fe}$ (Iron-56). Iron-56 is the king of the hill; it has the highest binding energy per nucleon, making it the most thermodynamically stable nucleus in the universe. Every other nucleus, whether lighter or heavier, 'wants' to be like Iron.

The Two Paths to Stability

This desire to reach the Iron peak drives the two most powerful energy-releasing processes known to humanity.

Nuclear Fission: Look at the heavy nuclei on the far right of the curve, such as ${}^{238}\text{U}$. Because they are far past the peak, their binding energy per nucleon is relatively low. If a heavy nucleus splits into two lighter, medium-sized fragments, those new fragments will have mass numbers closer to 56. This means they move up the curve. Moving up the curve implies an increase in stability and a loss of total mass (mass defect), which is converted into a massive amount of kinetic energy according to $E=\Delta m{c}^2$.

Nuclear Fusion: Now look at the far left of the curve, where the very light nuclei like Hydrogen and Helium reside. They also have low binding energy per nucleon. If we force these light nuclei to combine (fuse) into a heavier nucleus, the resulting nucleus again moves up the curve towards the Iron peak. Just like in fission, this increase in binding energy per nucleon results in a massive release of energy.

Therefore, Statement I is absolutely correct: Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion.

Now let's critically examine Statement II, which makes claims about the slope of the curve.

First, it claims that for heavy nuclei, the binding energy per nucleon increases with increasing $Z$ (and consequently, increasing $A$). If we look at the right side of the peak ($A>56$), the curve clearly slopes downwards. As nuclei get heavier, the long-range electrostatic repulsion between protons begins to overwhelm the short-range strong nuclear force, causing the binding energy per nucleon to decrease. The statement has this completely backwards.

Second, it claims that for light nuclei, the binding energy per nucleon decreases with increasing $Z$. Looking at the left side of the curve ($A<56$), we see a steep upward climb (ignoring the local spikes for highly stable alpha-particle structures like ${}^4\text{He}$ and ${}^{12}\text{C}$). As light nuclei get heavier, the strong nuclear force dominates, and the binding energy per nucleon generally increases. Again, the statement is backwards.

Because both parts of Statement II contradict the physical reality shown by the Binding Energy curve, Statement II is false.

By simply visualizing the Binding Energy per nucleon curve, we can confidently deduce that Statement I is true and Statement II is false. The correct option is (b).