Let M_A be the atomic mass of an isotope _Z^A X . If m_H is the mass of a hydrogen atom, m_p is the mass of a proton, m_n is the mass of a neutron, and m_e is the mass of an electron, the nuclear binding energy of the isotope is correctly expressed as:

Step-by-step solution

The nuclear binding energy is given by B.E. = m c^2 , where m is the mass defect. The mass defect in terms of the nuclear mass M_ nuc is: m = Z m_p + (A-Z)m_n - M_ nuc The nuclear mass can be found from the atomic mass M_A by subtracting the mass of the Z orbital electrons: M_ nuc = M_A - Z m_e Similarly, the mass of a proton is the mass of a hydrogen atom minus the mass of its electron: m_p = m_H - m_e Substituting these expressions into the mass defect equation: m = Z(m_H - m_e) + (A-Z)m_n - (M_A - Z m_e) m = Z m