An atom of magnesium has 12 neutrons, 12 protons and 12 electrons. The mass of an electron is `9.10938356*10^-31` kg, the mass of a proton is `1.6726231*10^-27` kg and the mass of a neutron is `1.6749286*10^-27` kg.
The mass of an atom is less than the total mass of the constituent particles. This decrease in mass is equivalent to the binding energy of the atom. The equation `E = m*c^2` gives the mass energy relation where E is the energy, m is the mass and c is the velocity of light. The binding energy of magnesium is 198.25 MeV.
One MeV is equal to `1.6022*10^-13` J. 198.25 MeV is equal to `3.176315*10^-11` J.
This is equivalent to a mass `3.176315*10^-11/(299792458)^2` = `3.534127063*10^-28` kg. The total mass of 12 electrons, protons and neutrons is `12*(9.10938356*10^-31+1.6726231*10^-27+1.6749286*10^-27)` = `4.018155166*10^-26` kg. Subtracting the mass equivalent of the binding energy gives `4.018155166*10^-26-3.534127063*10^-28` = `3.982813895*10^-26` kg.
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