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# Worked example: Atomic weight calculation

## Video transcript

- [Instructor] We have, listed here... We know that carbon 12 is the most common isotope of carbon on Earth. 98.89% of the carbon
on Earth in carbon 12. And we know that, by definition, its mass is exactly 12 atomic mass units. Now that's not the only
isotope of carbon on Earth. There are other isotopes. The next most frequent one is carbon 13. 1.11% of the carbon on Earth is carbon 13. And we can experimentally find that its mass is 13.0034 atomic mass units. So, these numbers that we have here, just as a review, these are atomic mass. These are atomic mass. And so, what we're gonna
think about, in this video, is how do they come up with
the atomic weight number that they'll give you on a
periodic table like that? So, atomic weight. Where does that come from? Well, in the video on atomic
weight and on atomic mass, we see that the atomic weight
is the weighted average of the atomic masses of the various isotopes of that element. So, to find this roughly 12.01, we take the weighted
average of these two things. And what do we weight it by? We weight it by how common
that isotope actually is. So, what we wanna do is, we could take 98.89%
and multiply it by 12. And I'll rewrite this
percentage as a decimal. So it'll be 0.9889 times 12. And, to that, we are going to add... We are going to add 1.11% times 13.0034. So, as a decimal, that's
going to be 0.011. That's 1.11% is 0.011, oh, 111. And I'm gonna multiply that
times 13.0034 atomic mass units. So, what does that give us? Let's get our calculator out here. So, we are going to have 0.9889 times 12 is equal to 11.8668. And, to that, we are going to add... We are going to add 0.0111 times 13.0034. And I know it's going to do
this multiplication first because it's a calculator knows
about order of operations. And so, that's all going to be,
as you can see, 12.01113774, which, if you were to round
to the hundredths place, is how this atomic weight was gotten. So that's that. There you go. That's how we calculate atomic weight. So, I can write this
as approximately 12.01. It's the weighted average
of the atomic masses. Now, another thing that
you might want to note is, what's the difference between
carbon 12 and carbon 13? Carbon 12, this right
over here, is six protons. The six protons are what make it carbon, so both of these will have six protons. And the difference is in the neutrons. This right over here has
six neutrons, six neutrons. And this, right over here, is gonna have one more
neutron, seven neutrons. So, when you look at the
difference in atomic mass, notice the change is... Looks like it's plus
1.0034 atomic mass units. So, from this, you can say, "Hey, look, if I add a neutron... Plus one neutron. Plus one neutron. It's roughly equal to
an atomic mass unit." It's not exactly an atomic mass unit, but, roughly speaking,
in a lot of very broad, high-level terms, you can kind of view it as being very close to
one atomic mass unit. And the same thing is true of protons. Anyway, hopefully you now
have an appreciation for the difference between atomic
mass, which is the mass, and atomic weight, which
is the weighted average of the various isotopes
of that element on Earth, how to calculate it, and roughly what the mass of a neutron is.