How is mass converted into energy in nuclear reactions?

Mass is converted into energy in nuclear reactions through the process of nuclear fission or fusion.

In nuclear reactions, the principle of mass-energy equivalence, as stated by Albert Einstein's famous equation E=mc^2, is at play. This equation tells us that mass (m) can be converted into energy (E), with c being the speed of light in a vacuum.

In nuclear fission, the nucleus of an atom is split into two smaller nuclei. This process is usually initiated by the nucleus absorbing a neutron. The combined mass of the resulting nuclei is less than the original mass. This 'missing' mass has been converted into energy, which is released in the form of kinetic energy of the fission products and radiation.

Nuclear fusion, on the other hand, involves the combination of two light atomic nuclei to form a heavier nucleus. This process, which powers the sun and other stars, also results in a mass difference. The mass of the resulting nucleus is less than the combined mass of the original nuclei. Again, this 'missing' mass is converted into energy, which is released as light and heat.

In both fission and fusion, the amount of energy released is enormous because of the c^2 factor in Einstein's equation. The speed of light is a very large number, and squaring it makes the energy yield from a small amount of mass very significant. This is why nuclear reactions, despite involving tiny atomic particles, can produce a large amount of energy.

It's important to note that these nuclear reactions don't violate the law of conservation of energy. The energy isn't created out of nothing; it's converted from mass. Similarly, the law of conservation of mass isn't violated either, as the 'missing' mass isn't lost; it's converted into energy. This conversion is what makes nuclear reactions a powerful source of energy, but also what makes them potentially dangerous if not controlled properly.