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

Oct 22, 2015

$\text{24.5 u}$

#### Explanation:

The idea here is that the question provided you with all the information you need to find the relative atomic mass of magnesium, but it did so in a tricky way.

The first thing to notice that you're only given two isotopes, magnesium-24 and magnesium-25.

The second thing to notice is that the question also gives you their abundances. The phrase

one atom of magnesium-24 to every one atom of magnesium-25

tells you that both isotopes contribute equally to the relative mass of magnesium, or, in other words, both isotopes have a 50% abundance.

Now, the relative atomic mass of an element can be found by using the atomic masses of its isotopes and their respective abundance

A_"r" = sum_i("isotope"_i xx "abundance"_i)

In your case, magnesium-24 will have an atomic mass of $\text{24 u}$ because it contains 12 protons and 12 neutrons. Here $u$ represents the unified atomic mass unit and is equal to the mass of one nucleon (proton or neutron).

Likewise, magnesium-25 will have an atomic mass of $\text{25 u}$ because it contains 12 protons aqnd 13 neutrons.

This means that the relative atomic mass of magnesium will be

A_"r" = "24 u" xx 50/100 + "25 u" * 50/100 = 1/2 xx "49 u" = color(green)("24.5 u")