Answer:
The average binding energy per nucleon of [tex]^{24} _{12} Mg[/tex] is 8.00 MeV/nucleon
Explanation:
Here we have the molar mass of [tex]^{24} _{12} Mg[/tex] is 23.985042 amu
The mass of a proton [tex]m_p[/tex] = 1.007276 amu
The mass of a neutron [tex]m_n[/tex] = 1.008665 amu
From the notation, 1 Mg = has 12 protons and 12 neutrons
Therefore, we find the binding energy as follows;
[tex]E_{bind}[/tex] = 12 × (1.007276) amu + 12 × (1.008665) amu - 23.985042 amu
[tex]E_{bind}[/tex] = 24.191292 amu - 23.985042 amu = 0.20625 amu
1 amu = 931 MeV
Therefore, 0.20625 amu = 0.20625 amu × 931 MeV = 192.01875 MeV
The average binding energy per nucleon in [tex]^{24} _{12} Mg[/tex] which has 24 nucleons, is thus;
[tex]E_{bind (ave)}[/tex] = 192.01875 MeV ÷ 24 = 8.00078 MeV/nucleon ≈ 8.00 MeV/nucleon.
