# Why is the mass number an integer but the relative atomic mass is not?

Jul 22, 2018

Well the mass number refers to a given $\text{nuclide...}$

#### Explanation:

A nuclide is a specific isotope, which of course has specific ${Z}_{\text{the atomic number}}$, and a SPECIFIC number of neutrons. The sum of both these numbers is necessarily precise AND integral (why so?.. because we cannot have half a neutron or two thirds a proton, these are discrete fundamental particles).

On the other hand, the $\text{relative atomic mass}$ is the weighted average of the isotopic masses compared to the mass of a ""^12C isotope, whose nucleus contains 6 protons (necessarily, why so), and 6 neutrons.

By way of example, the element boron has $Z = 5$, and has an isotopic distribution of 20%  ""^10B, and 80%  ""^11B, and their weighted average is $10.81$, which is the relative atomic mass, and the mass we would use if we calculated the formula mass of a boron-containing compound. And clearly this mass number CAN BE non-integral.

And so the $\text{relative atomic mass}$ is DIMENSIONLESS...and given the isotopic distribution common to most elements, it is NON-INTEGRAL. As a tip read the Periodic Table beside you now. This should be available in most exams of chemistry and fyziks, and a bit of study now will pay big dividends...