If protons and neutrons
each weighed exactly 1 amu, and there was no change in mass when
the nucleus was formed, then the mass number of an isotope would
equal the sum of the masses of the protons and neutrons in amu,
or its atomic weight. This is not strictly true. Not only are protons
and neutrons slightly heavier than 1 amu, there is a small loss
in mass when they combine to form a nucleus.
This missing mass is converted to energy during the nucleus-forming
process and is lost by the atom. The nucleus cannot be taken apart
again unless the lost energy is resupplied to make up the full mass,
that is, the mass of the initial protons and neutrons. This missing
energy represents the binding energy of the nucleus, or the energy
that holds the nucleus together.
Nevertheless, for approximate calculations we can think of the atomic
weight of an isotope as being approximately equal to the sum of
its protons and neutrons, or to its mass number.