Question

How would you find the relative atomic mass of magnesium if there is $1$ atom of Magnesium$- 24$ to every atom of Magnesium$- 25$?

Answer 1

Relative atomic mass is symbolised as ${A_r}$ and it is a physical quantity which can be defined as the ratio of average mass of atoms of chemical element in a given sample to atomic mass constant.
The atomic mass constant (symbol: mu) is defined as being $1/12\;$of the mass of a $carbon - 12$ atom. Since both quantities in the ratio are masses, the resulting value is dimensionless; hence the value is said to be relative.

Complete step-by-step answer: Relative atomic mass is the weighted arithmetic mean of masses of individual atoms ( which consist of their isotopes). There are two isotopes given of magnesium which are magnesium$- 24$ and magnesium$- 25$.
‘one atom of magnesium$- 24$ to every one atom of magnesium$- 25$ statement tells their abundances. Thus we get the idea here that both isotopes are equally contributing to the relative mass of magnesium. So now we find the relative atomic mass of magnesium with the help of atomic masses of its isotopes and their respective abundance.
${A_r} = \sum\limits_i {} (isotop{e_i} \times abundance{e_i})$
Magnesium$- 24$ will have the atomic mass of 24u. this means that it will have ${\mathbf{12}}$ protons and ${\mathbf{12}}$ neutrons. $u$ is known as the unified atomic mass unit and this unit is equal to the mass of one nucleon(proton or neutron)
Likewise, magnesium$- 25$ will have an atomic mass of $25{\text{ }}u$ because it contains ${\mathbf{12}}$ protons and ${\mathbf{13}}$neutrons.
This means that the relative atomic mass of magnesium will be
${A_r} = 24{\text{ }}u \times 50/100 + 25{\text{ }}u \times 50/100 = 1/2 \times 49{\text{ }}u = 24.5{\text{ }}u$

Note: This quantity can vary substantially between samples because the sample's origin (and therefore its radioactive history or diffusion history) may have produced unique combinations of isotopic abundances. There is a more specific quantity called the standard atomic weight symbolised by ${A_r}$ standard which can be used as an application of relative atomic mass values obtained from multiple different samples.