Mass deficit and binding energy both have to do with holding the atom together. Binding energy increase when the atom is more stable because its is harder to break the atom apart. Mass deficit is the difference in mass between an atom that is intact versus an atom that is separate parts. Einstein figured out that atom weights more when its separated than it does when its intact.
To calculate mass deficit and binding energy is measure with E = mc2 where E equals the binding energy and m is the mass deficit.
1. Mass deficit is measured by mass of the whole atom- the mass of the atoms components (protons, neutrons). Since we know the mass of the element (30.994 amu), we need to figure out the number of protons and neutrons the element has. The element (P) has 15 protons and 16 neutrons (31 (molecular weight) -15 (atomic number)). We also know that the weight of the protons is 1.0081 amu and neutrons 1.0089.
16 protons (1.0081 proton/amu) + 15 neutron (1.0098/amu) =
16.1296 + 15.147 = 31.2766 amu
mass deficit = 31.2766-30.994
mass deficit = 0.2826 amu
2. Convert the mass deficit into kg (1 amu =`1.66x 10^-27) kg`
0.2826 amu x `1.66x 10^-27` kg = `4.69 x 10^-28 `
3. Convert the mass into energy using E = mc2 (c=2.9979x 10^8m/s)
E =`4.69E^-28 x (2.9979E^8 m/s)^2`
E = `4.22E^-11 `
4. Convert to nucleon (1MeV= `1.602E^-13)`
Binding energy = 6.753E-24 MeV/nucelon