Animated Solution for Physics - Atoms and Nuclei: Binding energy per nucleon versus mass number curve for nuclei is shown in figure. $W$, $X$, $Y$ and $Z$ are four nuclei indicated on the curve. The process that would release energy is

Have you ever wondered what makes a nuclear reaction tick? Why do some nuclei split apart while others fuse together, releasing massive amounts of energy in the process? The secret lies in a simple yet profound concept: Binding Energy.

Imagine a nucleus as a tightly packed group of protons and neutrons. To pull them apart, you need to supply energy. Conversely, when these nucleons come together to form a nucleus, they release energy. This released energy is called the binding energy. The higher the binding energy per nucleon ($BE/A$), the deeper the potential well the nucleons are in, and the more stable the nucleus is.

In our problem, we are given a graph of Binding Energy per nucleon ($BE/A$) versus Mass Number ($A$). We have four nuclei: $Z$, $Y$, $X$, and $W$.

To find out if a nuclear process releases energy, we need to check a simple condition: The total binding energy of the products must be greater than the total binding energy of the reactants.

Let's calculate the total binding energy ($BE$) for each nucleus by multiplying its $BE/A$ with its mass number $A$:

$B{E}_Z=30\times 5.0=150$ MeV

$B{E}_Y=60\times 8.5=510$ MeV

$B{E}_X=90\times 8.0=720$ MeV

$B{E}_W=120\times 7.5=900$ MeV

Now, let's test the given options one by one.

Option (a): $Y\to 2Z$ The reactant $Y$ has a total energy of $510$ MeV. The products, two $Z$ nuclei, have a total energy of $2\times 150=300$ MeV. Since $300<510$, energy is absorbed, not released.

Option (b): $W\to X+Z$ The reactant $W$ has an energy of $900$ MeV. The products $X$ and $Z$ have a combined energy of $720+150=870$ MeV. Again, $870<900$, so energy is absorbed.

Option (c): $W\to 2Y$ The reactant $W$ has an energy of $900$ MeV. The products, two $Y$ nuclei, have a total energy of $2\times 510=1020$ MeV.

Wow! Here, $1020>900$. The products have a higher total binding energy than the reactants. This means the system has moved to a more stable state, and the excess energy is released to the surroundings!

Option (d): $X\to Y+Z$ The reactant $X$ has an energy of $720$ MeV. The products $Y$ and $Z$ have a combined energy of $510+150=660$ MeV. Since $660<720$, energy is absorbed.

The only process that satisfies our condition is $W\to 2Y$. This is a classic example of nuclear fission, where a heavier, less stable nucleus splits into two lighter, more stable nuclei, releasing a tremendous amount of energy.

Always remember: Nature loves stability. Any process that moves a system towards the peak of the binding energy curve (higher $BE/A$) will spontaneously release energy!