Question

Magnesium has an atomic mass of 24.3. there are two isotopes of magnesium - one contains 12 neutrons and the other contains 13 neutrons in the nucleus. what is the fractional abundance of the one that contains 12 neutrons?

Answer 1

So what we know:
-Atomic Mass = Protons + Neutrons
-Atomic Number is the number of protons

Magnesium's atomic number is 12, so the natural occurring isotope for magnesium is Mg-12 (12 protons and 12 neutrons). Added up we have an atomic mass of 24 amu. Which means if we added one neutron in Mg-13, our atomic mass would be 25 amu.

We can use the equation:
(amu of isotope 1)x + (amu of isotop 2)(x-1) = Average atomic mass
where isotope 1 is the fractional abundance we're solving for.

Plugged in it looks like this:
24x + 25(1-x) = 24.3

Now to solve for x:
24x + 25 - 25x = 24.3
   -x + 25 = 24.3
        -x = -.7
         x = .7

So in this case, the fractional abundance of Mg-12 would be .7, or 70%.