Gallium has two stable isotopes, and the masses of Gallium 69 which is 60.11 percent abundant
and Gallium 71 (39.89 percent abundant) are 68.926 amu and 70.925 amu, respectively.
Do you know what respectively means?
It means that we've got two masses here and two atoms here.
So respectively means the first of these masses goes with the first atom mentioned and then
the second one of these masses goes with the second atom mentioned, so don't let that term
throw you off.
So that's what respectively means.
Anyway, calculate that average atomic mass of Gallium.
So to do this, we're going to want to take the mass of the first isotope, multiply it
by its percentage expressed as a decimal, and then we'll take the mass of the second
isotope, multiply it by its percent abundance expressed as a decimal and we'll add the two
of them together.
So we will start with Gallium 69.
So what's its mass?
It's the first one here so respectively we will use the first mass, it is 68.926 and
now we want to multiply this by Gallium 69 percent abundance but expressed as a decimal.
So we'll be moving the decimal place two spots to the left times 0.6011, that's the first
part.
Now we're going to want to do the same thing for Gallium 71.
So its mass is the second one here, 70.925 and multiply it by its percent abundance as
expressed as a decimal.
Move this place two to the left so we get 0.3989, multiply both of these together and
then add them up, what you're going to get is 69.72 amu for that average atomic mass
for Gallium.
If you wanted to just check your work, you could look Gallium up on the periodic table,
here's what it would look like, and underneath the element name is the average atomic mass
which matches what we just calculated.
Now very quickly, check this out.
We have two isotopes of Gallium, one weighs about 69 and the other weighs about 71 and
the mass is closer to 69 than it is to 71.
And that makes sense because there is more Gallium 69 (60 percent) as compared to Gallium
71 which is only about 40 percent abundant.
So it makes sense that our weighted average should be closer to this one that's more abundant
than into this one which we don't have as much of.
Rubidium has two isotopes: Rubidium 85 which has an atomic mass of 84.911 amu and Rubidium
87 with an atomic mass of 86.909 amu.
The atomic weight of Rubidium reported on the periodic table is 85.47 and in this question
when they say atomic weight they mean atomic mass, relative atomic mass, any of these terms
you can use interchangeably.
Based on this information, which of the isotopes of Rubidium is more abundant?
We're talking about is it Rubidium 85 or Rubidium 87 and how do you know which one is more abundant?
This is a thought question, we don't really have to any calculation and it revolves around
the idea of relative atomic mass, atomic weight.
So how does this relate to these two isotopes?
We have Rubidium 85 which weighs pretty close to 85 amu and then we have Rubidium 87 that
weighs pretty close to 87 amu.
So for these two things, the regular average if we had the exact same amount of both would
be right in the middle, it would be 86 amu but instead we can tell from here and from
the periodic table that the atomic mass of Rubidium 85, the weighted average isn't 86
but it is 85.47 amu.
This means that it's closer to the mass of Rubidium 85.
It's not in the middle and it's not close to 87, so that means that the weighted average
is telling us that we have more Rubidium 85 because this weighted average number is closer
to this.
So there's more of this that is pulling the weighted average number down so Rubidium 85
is more abundant because the atomic mass weighted average is closer to that than it is to this.
Magnesium has three stable isotopes.
Calculate its average atomic mass, using information in the chart below.
We've already done this with two isotopes but you can do this with as many isotopes
as you need, it's the same process throughout.
So let's start with Magnesium 24.
We're going to want to take its mass which is 23.985 and multiply it by its abundance
expressed as a decimal, 0.7899.
That was Magnesium 24, now we're going to go on to Magnesium 25, take its mass of 24.9586,
multiply that by its abundance as a decimal so 0.1000.
Okay and then finally Magnesium 26 with 25.983 times 0.110.
Ah, I fit it all on one line.
So we're going to do this math and we're going to end up with 24.31 amu which is the average
atomic mass and you can check yourself by looking it up on the periodic table and you
find that the reported atomic mass is the same as what we calculated here.