The atomic mass of beryllium-9 can be calculated using the mass-energy equivalence principle, which states that the binding energy of an atomic nucleus is equivalent to the mass defect of the nucleus. The mass defect is the difference between the actual mass of the nucleus and the sum of the masses of its individual protons and neutrons.
To calculate the atomic mass, we need to convert the binding energy from joules to electron volts (eV), as it is commonly expressed in atomic and nuclear physics. The conversion factor is 1 eV = 1.60218 × 10^-19 J.
First, we convert the binding energy to eV:
9.3182 × 10^-12 J × (1 eV / 1.60218 × 10^-19 J) ≈ 5.8105 × 10^7 eV
Next, we determine the mass defect using Einstein's mass-energy equation:
Binding Energy = Mass Defect × (Speed of Light)^2
5.8105 × 10^7 eV = Mass Defect × (3.00 × 10^8 m/s)^2
Mass Defect = 5.8105 × 10^7 eV / (9 × 10^16 m^2/s^2)
Mass Defect ≈ 6.456 × 10^-10 kg
Finally, we subtract the mass defect from the sum of the masses of the individual protons and neutrons in beryllium-9 to find the atomic mass. The atomic mass unit (u) is defined as 1/12th the mass of a carbon-12 atom.
Atomic Mass = (4 protons × mass of a proton) + (5 neutrons × mass of a neutron) - Mass Defect
Atomic Mass ≈ (4 × 1.007276 u) + (5 × 1.008665 u) - 6.456 × 10^-10 kg / (1.66054 × 10^-27 kg/u)
Atomic Mass ≈ 8.99843 u
Therefore, the atomic mass of beryllium-9 is approximately 8.99843 atomic mass units (u) when the nuclear binding energy of its atom is 9.3182 × 10^-12 J.