Why does magnesium have an atomic mass of 24.3 instead of 24 or 25?

For magnesium, #Z#, the atomic number, #=# #12#. That is there are 12 protons, 12 fundamental, massive, positively charged particles in the nucleus. #Z# of course determines the nuclear identity. However, within the nucleus, there may be 12, or 13, or 14, NEUTRONS; massive, neutrally charged, nuclear particles, that also do contribute to nuclear stability, but not to chemistry (#Z# has already determined that!).

The weighted average of the individual isotopes is the atomic mass quoted on the Periodic Table. Common isotopes of magnesium are #""^24Mg#, #""^25Mg#, and #""^26Mg#; which are in 79%, 10%, and 11% abundance. The weighted average of these isotopes sum to 24.3 amu. There are a few other, less abundant isotopes, but these don't concern is very much due to their rarity.

Capisce?

In an exam you are sometimes given details of a few common isotopes, and then asked to quote an atomic mass. The weighted average is simply the the SUM of the individual isotopes WEIGHTED according to their isotopic abundance. For the figures above we could do the sum:

#"Average mass"# #=# #0.78xx24+0.10xx25+0.11xx26# #=# #24.3# as required. Most elements have a number of common isotopes.