The neutral ${}^{27}_{13}$ Al atom has a mass of 26.981539 u; a neutral hydrogen atom has a mass of 1.007825 u; a neutron has a mass of 1.008665 u; and a proton has a mass of 1.007277 u.What is the binding energy per nucleon for ${}^{27}_{13}$ Al? (1 u = 931.5 MeV/c²)

Question

Quizplus · Accepted Answer

The binding energy per nucleon can be calculated by first determining the mass defect, then converting that to energy, and finally dividing by the number of nucleons. For ${}^{27}_{13}$Al, the mass of the nucleons (13 protons and 14 neutrons) if they were separate is $13 \times 1.007277 \, \text{u} + 14 \times 1.008665 \, \text{u}$. The actual mass of ${}^{27}_{13}$Al is 26.981539 u. The mass defect is the difference between these two values. Converting the mass defect to energy using $1 \, \text{u} = 931.5 \, \text{MeV/c}^2$ gives the total binding energy. Dividing this energy by the total number of nucleons (27) gives the binding energy per nucleon, which is approximately 8.3 MeV, making choice A correct.

The Neutral 1327{}^{27}_{13}1327​ Al Atom Has a Mass of 26 1327{}^{27}_{13}1327​ Al? (1 U = 931

The Neutral ${}^{27}_{13}$ Al Atom Has a Mass of 26 ${}^{27}_{13}$ Al? (1 U = 931