Evaluate the minimum energy required to separate a proton from a nucleus containing Z protons and N neutrons. Let M_ Z, N denote the mass of an atom with Z protons and N neutrons in the nucleus, and M_H denote the mass of a hydrogen atom. This energy is termed the proton-separation energy.

Step-by-step solution

The separation of a proton from a nucleus with Z protons and N neutrons can be represented as: Nucleus (Z, N) Nucleus (Z-1, N) + proton The minimum energy required for this process is the proton-separation energy, given by the mass difference between the products and the reactant: E = [m_ nuc (Z-1, N) + m_p - m_ nuc (Z, N)] c^2 The nuclear mass m_ nuc can be expressed in terms of the atomic mass M by subtracting the mass of the electrons: m_ nuc (Z, N) = M_ Z, N - Z m_e m_ nuc (Z-1, N) = M_ Z-1, N - (Z-1) m_e Subst