Every element has a characteristic atomic mass, because they each have a
different number of protons, neutrons, and electrons. Most of the time, you won't use
the actual masses of each element's atoms. Subatomic particles are so tiny - their
masses are so small that it would make problem-solving unwieldy. For instance,
the mass of a proton is 1.67 times 10 to the negative 24 grams. The mass of a
neutron is 1.68 times 10 to the negative 24 grams. And the mass of an
electron is 9.11 times 10 to the negative 28 grams. Adding and multiplying
numbers of those very small sizes is awkward, so instead of using the actual
mass of atoms and problems, chemists compare all atoms to one
standard atom. They picked carbon-12 as the standard. Carbon-12 is the isotope
of carbon with 6 protons and 6 neutrons. Carbon-12 is assigned a mass of exactly
12 unified atomic mass units or u. Some people write amu, or Daltons. Chemists
just defined a new unit for convenience. See, it's much easier to think and write
that carbon has a mass of 12 u, than to add up all the small masses of all of
its protons and neutrons and electrons, and write 2 times 10 to the negative 23
grams. It's just a lot easier to think in terms of whole numbers. So then helium is
about 4u, because a helium atom is about 1/3 the mass of a carbon atom.
12u divided by 3 equals 4u. Hydrogen, the smallest atom, is about 1 u, because
it's about 1/12 the size of a carbon atom. 12u divided by 12 equals 1u.
So why, when you look at the periodic table, does it not say exactly
12 for carbon's atomic mass? Because there is more than one kind of carbon. Remember
chemists assigned carbon-12 the mass of 12u.
But there are other isotopes of carbon: Carbon-13 which has six protons and
seven neutrons and Carbon-14 which has six protons and eight neutrons. If you
need a quick refresher on isotopes please watch our short 30 second
glossary video (link in description). Carbon-12 and carbon-13 are stable, but carbon-14 is radioactive,
so it is slowly decaying. Maybe you've heard of carbon-14 dating of fossils, but
that's a topic for another video.
On Earth, there's a lot of carbon-12, a
little bit of carbon 13 and a very small amount of carbon-14.
To find the average atomic mass of carbon, you take a weighted average of
these isotopes, based on their natural percent abundances. First, let's make a
table of the isotopes their masses and their percent abundances. I would look
these up. This isn't something you would know off the top of your head. The amount
of carbon-14 is so small - it's less than one thousandth of one percent of the
carbon present on earth - so it won't play a part in our weighted average. It's just
not significant enough to affect the mass if we go to two decimal places.
When we measure, and then round to two decimal places,
notice that the percentages of carbon-12 and carbon-13 add to 100 percent. So we
know we're okay disregarding the very small percentage of carbon-14.
Change the percent abundances to decimal fractions by dividing by 100 percent.
98.89 percent becomes 0.9889 and 1.11 percent
becomes 0.0111 Check your answer.
There are two types of carbon we're worried about here: let's call them A and B.
A weighted average will be decimal fraction A times mass A plus decimal
fraction B times mass B. That's 12 times 0.9889
plus 13 times 0.0111 which equals 12.0111
or about 12.01 unified atomic mass units. That
should be close to what you see on your periodic table.
Does this answer make sense to you?
Remember, most of the carbon on earth is carbon-12, and only a little
bit of it is carbon-13, so the weighted average should be really close to the
atomic mass of carbon-12. And it is! Just a tiny bit more than 12u, due to the
little bit of carbon-13, which is heavier.
Let's do one more example.
What is the average atomic mass of oxygen?
Here's a table of the isotopes of oxygen, with
their masses and their natural percent abundances.
The weighted average of the three isotopes - let's call them A, B, and C -
Will be decimal fraction A times mass A plus
decimal fraction B times mass B plus decimal fraction C times mass C
Convert the percentages to decimals fractions by dividing by 100 percent
0.9976 0.0004 0.002
The weighted average is 16 times 0.9976
plus 17 times 0.0004 plus 18 times 0.002
That equals 16.00044 or approximately 16.00 u
You may get a slightly different answer,
depending on how many decimal places you have in your percent abundances
measurement. Check your answer to see if it passes the "smell test." You know that
the most common isotope by far is oxygen-16, so the average atomic mass should be
really close to 16u... and it is!
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