Final answer:
Energy is released during the formation of a nucleus due to the conversion of mass to energy, explained by Einstein's equation E=mc². The mass of the resulting nucleus is less than the combined mass of its constituent nucleons, the difference being manifested as binding energy released during the process.
Step-by-step explanation:
According to Einstein's equation (E=mc²), mass can be converted into energy, which is a critical concept in understanding why energy is released when nuclei are formed. The formation of a nucleus from protons and neutrons involves the release of binding energy, which is the energy required to separate the nucleus into its constituent nucleons. This energy release is explained by the difference in mass between the combined nucleons and the newly formed nucleus. Since the resulting nucleus is lighter, the missing mass has been converted into energy, calculated using the equation E=mc², where m is the mass difference, and c is the speed of light.
The process of calculating the amount of energy released can be elucidated using the strategy where Δm (mass difference) is first determined between the parent nucleus and the products of the decay. The energy can then be found by applying Einstein's equation: the mass difference (in kilograms) multiplied by the speed of light squared (approximately 9 x 10¹⁶ m/s²) gives the amount of energy released in Joules.
For example, compared to the mass of individual nucleons, the mass of a nucleus is less due to the energy released in forming the nucleus: E₁ = (Δm) c². This is because energy has been expended to bind the nucleons together, thereby reducing the overall mass of the nucleus when compared to the sum of the separate nucleon masses.