Counting Atomic Particles and Atoms
Now that we “know about” sub-atomic particles, we want to be able
to account for them. The following terms are useful and must be
memorized:
Atomic Number (Z): The number of protons in the nucleus of
an atom. Also the sequence number of the element on the periodic
table.
Mass Number: Since protons and neutrons are about the same
mass (we will call the mass number of them “1”) and electrons have a
mass of nearly “0” by comparison, we define the mass number as
P+N.
Thus, for any SINGLE atom (as opposed to all of the atoms of a
given element), we can identify the element name, the atom’s name,
the symbol for an atom, number of protons, number of neutrons,
number of electrons, atomic number, and mass number. The
following chart will help understand these:
atomic #
symbol protons neutrons electrons
(Z)
Element
atom name
hydrogen
hydrogen - 1
1
1
hydrogen
hydrogen - 2
2
1
H
hydrogen
hydrogen - 3
3
1
H
nitrogen
nitrogen - 15
15
7
H
N
1
1
1
7
0
1
2
8
Complete this chart given the two values shown:
tin
tin tin - 120
50
Sn
120
50
Sn
120
50
Sn
50
1
1
1
7
50
50
1
1
1
7
mass #
(P+N)
1
2
3
15
120
50
70
120
Final answer below:
tin
tin - 120
50
70
50
50
120
You will also be required to calculate average atomic masses,
because the elements have isotopes of various masses. If you want to
convert the mass of a sample of an element to the number of atoms,
you will need a conversion factor that includes the average mass of
the element’s atoms. In order to get the average atomic mass, you
will need to know (be given) the relative abundance of each isotope
in nature. For example:
Suppose that naturally occurring neon was composed of three
isotopes…neon-20, neon-21, and neon-22. Furthermore,
scientists have learned (discovered, measured, etc) that 90.9% of
neon is neon-20, 0.30% is neon-21, and 8.8% is neon-22. What
is the weighted average mass of neon atoms?
First, if there were only 3 atoms, the average would be:
(20+21+22)/2 = 21
But this makes no sense. There are not just 3 atoms, and most of
the atoms that do exist are neon-20. The weighted average
should be close to 20! Do it this way:
Isotope
weight
% abundance
contribution
neon-20
20.00
x
90.9%
=
neon-21
21.00
x
0.30%
=
0.063
neon-22
22.00
x
8.8%
=
1.936
18.18
average relative mass of neon atoms = 20.179
= 20.18 amu
Where amu = atomic mass units
And 1 amu = exactly 1/12 the mass of a carbon-12 atom or
1 carbon-12 atom has a mass of exactly 12 amu.
If we simply decide (make up, yank out of thin air, etc) that 1 carbon12 atom has a mass of 12 amu, then we can compare all other atoms
of all the other elements to it and assign atomic masses to them also.
They are called “relative atomic masses, because the their assigned
mass is relative to the mass of a carbon-12 atom.
Thus, the periodic table lists the average relative atomic mass of each
element. You can use it to learn that the average carbon atom has a
mass of 12.011 amu and the average chlorine atom has a mass of
35.453 amu.
Unfortunately, this does not help us go to the stock room and weigh
out 17 carbon atoms, since no scale commercially available can
weigh something so tiny. We need to weigh out very large numbers
of atoms to have a useful amount and we need to measure in grams.
So we simply decide (make up, yank out of thin air, etc) another
useful definition:
1 mole = the exact number of 12C atoms in exactly 12 g of 12C.
We can’t actually count this because the number is so big and
because it is not possible to obtain exactly 12 g of carbon. But it has
been measured and it turns out that:
1 mole = 6.022 x 1023 That is a REALLY big number.
This value was chosen, because it is so very, very convenient. It
means that when I read the periodic table and find that 1 average
carbon atom has a mass of 12.011 amu, then I also know that 1 mole
of average carbon atoms has a mass of 12.011 g. Or if I have 12.011
g of carbon atoms, then I have 1 mole or 6.022 x 1023 carbon atoms.
1 mol C = 12.011 g C
Finally, we have a way to convert the mass of a sample to the number
of atoms. For example:
How many atoms is 23.54 g of carbon?
Answer:
23.54 g C 1 mole C
x
 1.960 mole C
1
12.011g C
Another example:
What is the mass of 7.25 moles of copper?
Answer:
7.25 mol Cu 63.546 g Cu
x
 4.61x10 2 g Cu
1
1 mole Cu