Why is the atomic mass unit less than the mass of both a neutron and a proton?

Question

The atomic mass unit is $1.6605 \times 10^{-27}$ kg.

This is less than the mean of the masses of 6 protons and 6 neutrons.

How do we account for the lower mass ?

My understanding is that some of the mass is in the form of energy somewhere, in the bonding maybe or in the kinetic energy.

Can someone clarify where this mass is please ?

Binding a proton to a neutron releases energy. I've read that some gentleman named Albert Einstein figured out that this energy carries off the missing mass, $m=E/c^2$ is how he originally rendered it I think. — Oscar Lanzi, Jan 02 '21 at 07:53
Does this answer your question? Units of mass on the atomic scale — cngzz1, Jan 02 '21 at 10:13

score 1 · Accepted Answer · answered Jan 02 '21 at 22:30

The source of the discrepancy is the mass defect, which is described in the article below as :

The difference between the sum of the masses of the components and the measured atomic mass is called the mass defect of the nucleus. Just as a molecule is more stable than its isolated atoms, a nucleus is more stable (lower in energy) than its isolated components. Consequently, when isolated nucleons assemble into a stable nucleus, energy is released. According to Equation 4, this release of energy must be accompanied by a decrease in the mass of the nucleus.

The equation four referenced is just E=mc^2. When these nucleons form carbon-12, which is the reference isotope for the definition of the amu, the mass defect appears, as you mentioned, by conversion to binding energy.

https://chem.libretexts.org/Courses/Grand_Rapids_Community_College/CHM_120_-_Survey_of_General_Chemistry/2%3A_Atomic_Structure/2.07_Mass_Defect_-_The_Source_of_Nuclear_Energy

Why is the atomic mass unit less than the mass of both a neutron and a proton?

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