Final answer:
The energy released in the hypothetical proton decay reaction p → π⁰ + e⁺ is given by the mass-energy equivalence principle and is represented by the formula: mₚ c² - mₐ⁰ c² - mᴇ c².
Step-by-step explanation:
The amount of energy released if a proton were to decay via the conjectured reaction p → π⁰ + e⁺ can be calculated using the mass-energy equivalence principle E = mc², where E is the energy, m is the mass, and c is the speed of light.
The mass of the initial proton must be greater than the combined mass of the decay products for energy to be released. The correct expression for the energy released would thus be the difference in mass-energy between the initial proton and the decay products.
Hence, the formula for energy released is option (b): mₚ c² - mₐ⁰ c² - mᴇ c², where mₚ is the mass of the proton, mₐ⁰ is the mass of the neutral pion (π⁰), and mᴇ is the mass of the electron (e⁺).
The energy released in the decay of a proton via the reaction p→π⁰+e⁺ is given by the equation mₚc² - m_π⁰c² - mₑc², where mₚ is the mass of the proton, m_π⁰ is the mass of the neutral pion, and mₑ is the mass of the positron (electron).
Using this equation, we can calculate the energy released in this decay.