# Calculating binding energy from mass defect

I am trying to wrap my head around the relationship between binding energy and mass defect. I have read that the difference between the binding energies of the products and reactants of a nuclear equation is equal to the energy equivalent of the mass defect. Using this, along with exact masses of a proton, electron and deuteron I have calculated the following:

mass difference = 7.49089 x 10^-31 kg

Converting this mass to energy via E = mc^2

E = 6.732476 x 10^-14 J = 0.420208 MeV

This value is far from the value I have managed to find on the internet, which states that the binding energy of deuteron is approximately 2.2 MeV.

Am I wrong in my knowledge that the binding energy is equivalent to the mass defect, or is there some other explanation for the disparity in the binding energy I calculated and the value found on the internet?

## 1 Answer

It'll be clearer if you first list the particles (with their mass) that a deuteron contains. Deuteron is a deuterium's nucleus which contains a proton and a neutron (not electron, although outside a nucleus, a neutron further decays to form a proton, electron and antineutrino. However, for now it's enough to consider just a neutron).

From wikipedia you can find easily the mass of these three particles:

M$$_\text{proton} = 938.272$$ MeV/$$c^2$$

M$$_\text{neutron} = 939.565$$ MeV/$$c^2$$

M$$_\text{deuteron} = 1875.612$$ MeV/$$c^2$$

With a simple arithmetic:

M$$_\text{proton}$$ $$+$$ M$$_\text{neutron}$$ $$-$$ M$$_\text{deuteron}$$ $$= 938.272 + 939.565 - 1875.612 = 2.237$$ MeV/$$c^2$$, which is the number you're looking for.