How does nuclear fission differ from nuclear fusion? Why are both of these processes exothermic?

Nuclear fission involves splitting an atom's nucleus into smaller parts, often resulting in the creation of new elements. Picture a heavy nucleus such as Uranium-235, which upon capturing a neutron, becomes heavy and excited, leading it to become unstable. This instability causes the nucleus to divide, typically into two smaller nuclei and possibly releasing more neutrons that can trigger a chain reaction. During this process, a significant amount of energy is produced, which is fundamentally used in nuclear reactors to generate electricity.

The relevance of nuclear fission in generating electricity cannot be overstated. It holds the key to powering vast electrical grids without the direct emission of greenhouse gases, which is a step towards combating climate change.

In contrast to nuclear fission, nuclear fusion combines lighter atomic nuclei to form a heavier nucleus. The process occurs under extreme conditions of temperature and pressure where nuclei come so close that nuclear forces overcome their electrostatic repulsion, bonding them together. The most familiar example of nuclear fusion is the sun, where hydrogen nuclei merge to form helium, emitting immense energy that provides light and heat to our planet.

This fusion process is hoped to be replicated on Earth to create an abundant, clean energy source. While research in creating a controlled fusion environment continues, the potential of fusion energy promises an enormous energy output with minimal radioactive waste compared to fission.

Exothermic processes release energy to the surroundings, often in the form of heat. Both nuclear fission and fusion are prime examples of such processes. In fission, the energy comes from the splitting of a heavy nucleus, while in fusion, it is the result of combining light nuclei. Importantly, the energy released in these nuclear reactions is much larger than that from chemical reactions, such as the combustion of fossil fuels.

An understanding of exothermic reactions is critical in fields ranging from astrophysics to energy engineering, as it explains not just the workings of stars but also the principles behind modern nuclear power generation.

Mass-energy equivalence, epitomized by Einstein's famous equation, \( E=mc^2 \), reveals that mass and energy are two forms of the same thing and can be converted into each other. In the context of nuclear reactions, some of the mass 'disappears' as it is transformed into energy. This is observable in both fission and fusion processes as the mass of the resulting elements is slightly less than the mass of the original atoms. The difference in mass, known as the mass defect, accounts for the vast amounts of energy released during nuclear reactions.

This extraordinary insight into the interplay of mass and energy underpins not only our understanding of nuclear processes but also vast areas of modern physics, such as particle physics and cosmology. It also is the principle exploited in nuclear power generation and weaponry, illustrating the profound impact of theoretical physics on practical technological developments.