Questão 9 Unicamp 2020: Física moderna

Nuclear fusion is a reaction in which atomic nuclei merge to form the nucleus of a new atom. The mass of the new atom’s nucleus is lower than the sum of the merging nuclei’s masses, a difference that is released as energy.

This is, for instance, the reaction that occurs in the Sun.

The energy released during fusion can be calculated by the equation \(E = \Delta m c^2\), where \(\Delta m\) is the difference between the initial and final masses in the reaction, and \(c\) is the speed of light. When calculating the aforementioned energy, nucleus mass can be conveniently quantified using the atomic mass unit (u), which is roughly equivalent to 900 MeV (\(1\ \text{u} \rightarrow 900\ \text{MeV}\)). Consider the hypothetical nuclear fusion reaction \(^{222}X + {}^{4}Y \rightarrow {}^{221}Z\). Note that the masses of \(^{222}X\), \(^{4}Y\), and \(^{221}Z\) are 222 u, 4 u, and 221 u, respectively. The amount of energy released in this reaction is