Question

 The atomic mass of \( ^{16}O \) is 16.0000 amu. Calculate its binding energy per nucleon. Mass of electron = 0.00055 amu, mass of proton = 1.007593 amu, mass of neutron = 1.008982 amu, and 1 amu = 931 MeV. 
 

Hint:

The binding energy of a nucleus is a measure of how stable the nucleus is; more binding energy indicates a more stable nucleus.

Answer 1

- Step 1: Calculate the mass defect The mass of the oxygen atom is given as 16.0000 amu. For the calculation, we assume that oxygen has 8 protons and 8 neutrons (since \( ^{16}O \) is the isotope with a mass number 16). The total mass of the nucleons is: \[ \text{Total mass} = (8 \times \text{mass of proton}) + (8 \times \text{mass of neutron}) + (\text{mass of electron}) \] \[ = (8 \times 1.007593) + (8 \times 1.008982) + (8 \times 0.00055) = 16.152744 \, \text{amu}. \] Now, the mass defect \( \Delta m \) is: \[ \Delta m = (\text{Total mass of nucleons}) - (\text{Atomic mass}) = 16.152744 - 16.0000 = 0.152744 \, \text{amu}. \] - Step 2: Calculate the binding energy To find the binding energy, we use the equivalence \( E = \Delta m \cdot c^2 \), where 1 amu = 931 MeV. \[ \text{Binding energy} = 0.152744 \times 931 = 142.5 \, \text{MeV}. \] - Step 3: Calculate binding energy per nucleon Since the oxygen nucleus contains 16 nucleons, the binding energy per nucleon is: \[ \text{Binding energy per nucleon} = \frac{142.5}{16} = 8.91 \, \text{MeV}. \]