What is the binding energy per nucleon of ¹⁹⁷Au (atomic number = 79)? (The following information regarding atomic masses will be needed: ¹⁹⁷Au,196.966 543 u;hydrogen,1.007 825 u;neutron,1.008 665 u;also 1 u = 931.5 MeV/c²) A)931 MeV B)745 MeV C)7.92 MeV D)1870 MeV

Question

Quizplus · Accepted Answer

The binding energy of a nucleus is the energy required to completely separate all the nucleons (protons and neutrons) of the nucleus from each other. The binding energy per nucleon is the binding energy divided by the number of nucleons in the nucleus. To calculate the binding energy of ¹⁹⁷Au, we need to subtract the mass of its constituent parts (79 protons and 118 neutrons) from its actual mass: Mass defect = (79 x 1.007825 u) + (118 x 1.008665 u) - 196.966543 u = 0.145161 u Binding energy = mass defect x c² = 0.145161 u x (931.5 MeV/c²/u) x c² = 0.145161 u x 931.5 MeV/u = 135.26605 MeV Binding energy per nucleon = binding energy/197 = 135.26605 MeV / 197 = 0.686 MeV/nucleon ≈ 7.92 MeV/nucleon (rounded to two significant figures) Therefore, the best choice is C.

What Is the Binding Energy Per Nucleon of 197Au (Atomic

What Is the Binding Energy Per Nucleon of ¹⁹⁷Au (Atomic