Final answer:
The binding energy per nucleon for the atom with 9¹⁹F is 8.79 MeV/nucleon. Therefore, the correct answer is (b) 8.79 MeV/nucleon.
Step-by-step explanation:
The binding energy per nucleon for the atom with 9¹⁹F is determined by dividing the total nuclear binding energy by the number of nucleons. The mass of the atom is given as 18.99840 amu. To calculate the binding energy, we need to convert the mass defect into energy.
The binding energy is calculated as mass defect × c², where c is the speed of light (3.00 × 10^8 m/s) squared. The binding energy per nucleon is determined by dividing the binding energy by the number of nucleons.
Given that the binding energy is 492 MeV and the number of nucleons is 56, the binding energy per nucleon can be calculated as 492 MeV / 56 nucleons = 8.79 MeV/nucleon.
Therefore, the correct answer is (b) 8.79 MeV/nucleon.
The nucleus of 19F contains 9 protons and 10 neutrons, giving a total mass of 19 amu if there were no binding energy. The mass defect Δm is the difference between this value and the actual measured atomic mass, Δm = 19 amu - 18.9984 amu = 0.0016 amu.
The binding energy (E) can be calculated using Einstein's equation, E = Δm × c2, where c is the speed of light. However, it is conventional in nuclear physics to use the conversion factor 1 amu = 931 MeV/c2, therefore E = 0.0016 amu × 931 MeV/amu.
To find the binding energy per nucleon, this value is then divided by the total number of nucleons (protons + neutrons), Enucleon = E/19 nucleons.