The products of a nuclear reaction usually have a different mass than the reactants. Why?

A nuclear reaction involves a change in an atom's nucleus and often leads to the transformation of one element into another. During such reactions, like fission where a nucleus splits or fusion where nuclei combine, a tiny fraction of mass is not lost but converted into an enormous amount of energy. This process is fundamental in stars, including the sun, where hydrogen nuclei fuse into helium and release energy that eventually reaches Earth as sunlight.
To vividly illustrate this, consider a metaphor: if a lump of clay (representing the mass of reactants) is re-shaped into a sculpture (representing the mass of products), there might seem to be a difference in size or form, but the amount of clay remains constant. In nuclear reactions, the 'clay' essentially changes its form from mass to energy.

The laws of conservation are cornerstones of physics, acting as the universal rules for the consistency of certain quantities. Within an isolated system, these laws state that total mass, energy, charge, and other fundamental properties remain constant, regardless of the processes occurring within the system. These laws are essential in understanding not only mechanics but also thermal dynamics, electromagnetism, and, crucially, nuclear physics. In the context of a nuclear reaction, the law of conservation of mass-energy ensures that the mass-energy before and after a reaction is the same, even though mass may convert into energy or vice versa.

The equation \( E=mc^2 \) is the iconic representation of mass-energy equivalence put forth by Albert Einstein. Here, \( E \) represents energy, \( m \) represents mass, and \( c^2 \) is the square of the speed of light in vacuum. This simple yet profound equation tells us that mass can be seen as a concentrated form of energy. Consequently, when mass is transformed into energy during nuclear reactions, the resulting energy follows this relationship. One may think of it as a universal currency exchange rate between mass and energy, wherein even a tiny amount of mass can be equivalent to a massive amount of energy because the speed of light squared is a significantly large number.

Nuclear physics is the branch of physics that deals with the constituents and interactions of atomic nuclei. It encompasses the study of nuclear reactions, radiation, and the principles governing the complex behavior of subatomic particles. Discoveries in nuclear physics have led to various applications, from nuclear energy production to medical imaging techniques like PET scans. It relies on theories and concepts from quantum mechanics and special relativity, utilizing sophisticated experiments and computational models to understand phenomena such as radioactive decay and nuclear fusion that power stars.