Q.Define the atomic mass unit (u). Given that $1\ \text{u} = 1.660539\times10^{-27}\ \text{kg}$, show that its energy equivalent is close to $931.5\ \text{MeV}$.

Nuclear and atomic masses, when expressed directly in kilograms, come out as extremely inconvenient numbers (of order $10^{-25}$ kg or smaller), so nuclear physics instead uses a purpose-built unit called the atomic mass unit, symbol u. One atomic mass unit is defined as exactly one-twelfth of the mass of a single atom of the most abundant naturally occurring isotope of carbon, $^{12}_{6}C$:

Using this unit, key particle and atomic masses become simple, easily remembered numbers close to whole integers: the neutron's mass is 1.008665 u, the proton's mass is 1.007276 u, the hydrogen atom's mass is 1.007825 u, and by definition the mass of $^{12}_{6}C$ is exactly 12 u.

It is important to keep in mind that a mass quoted "for" a nucleus (or, more usually, "for" an atom) in atomic mass units is nearly always the atomic mass - the nucleus plus its full complement of orbiting electrons - rather than the bare nuclear mass alone; to isolate the true nuclear mass, the combined mass of the atom's $Z$ electrons must be subtracted from the tabulated atomic mass. Atomic masses are measured experimentally with an instrument called the Bainbridge mass spectrometer.

When a periodic table quotes "the" atomic mass of an element without singling out any particular isotope, that number is actually a weighted average over every isotope that occurs naturally, each isotope weighted by its own percentage abundance - for example, chlorine's familiar periodic-table value of 35.453 u is the abundance-weighted average of its two natural isotopes, $^{35}Cl$ (75.77% abundant, mass 34.96885 u) and $^{37}Cl$ (24.23% abundant, mass 36.96593 u), and is therefore not the actual mass of any single real chlorine atom.

Because 1 u corresponds, via Einstein's $E=mc^2$, to an energy of almost exactly 931 MeV ($1\ \text{u}\approx14.94\times10^{-11}\ \text{J}\approx931$ MeV), the atomic mass unit also serves as the standard bridge between mass-defect calculations and binding-energy calculations throughout nuclear physics.