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Quantum Numbers | AP Chemistry
Electron Energy
• Electrons gain/lose energy in
discrete quantities
o The same way that you
can ascend a flight of
stairs in minimum
increments of one stair,
an electron can gain/lose
energy in minimum
increments of 1 quantum
Identifying Electrons
• Each of an atom’s electrons can
be uniquely identified by 4
quantum numbers
• The Pauli exclusion principle
tells us that no two electrons in
an atom may share the same 4
quantum numbers
• The first quantum number is the
principal quantum number, n
o It indicates the shell in
which an electron is
found
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Atomic Shells of Potassium
The designated electron sits in the 3rd shell from
the nucleus. Its principal quantum number, n,
will be 3.
•
For main group elements, an
element’s row on the periodic
table tells us how many electron
shells that element has
o i.e. potassium has 4
shells, and it sits in the 4th
row of the periodic table
•
Electrons in the outermost shell
are known as valence electrons
The second quantum number is
the azimuthal quantum number, ℓ
o It indicates the electron’s
subshell
There are 4 possible subshells
with which you should be
familiar, and each is given a
corresponding number:
o s (numbered as 0)
o p (numbered as 1)
o d (numbered as 2)
o f (numbered as 3)
Each of an atom’s shells (n)
contains subshells from 0 n-1
o i.e. the 3rd shell contains
subshells numbered 0, 1,
and 2
aka the s, p, and d
subshells
o So, the designated
electron from the
previous illustration will
have an azimuthal
quantum number of 0, 1,
or 2, but not 3
The third quantum number is the
magnetic quantum number, mℓ
o It indicates the electron’s
orbital
Each subshell contains orbitals
numbered from -ℓ +ℓ
o i.e. the p-subshell (ℓ=1)
contains orbitals
numbered -1, 0, and 1
Thus, an electron
in a p-subshell
will be in one of
those 3 orbitals
The fourth quantum number is
the electron spin quantum
number, ms
o For any electron, it must
be +½ or –½
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© 2017 J Co Review, Inc., Accessed by Guest on 05-16-2017
Quantum Numbers | AP Chemistry
•
2 electrons in the same shell (n),
subshell (ℓ), and orbital (mℓ) will
have the same initial 3 quantum
numbers
o But their ms quantum
numbers will necessarily
be different; one is -½
and the other is +½
o The reason Na becomes
so stable when it loses an
electron is because it
loses its only 3rd-shell
electron
This leaves it with
a full valence
shell
Mapping the Electrons of Na
• As an example, take a look at the
following map of sodium’s
electrons
• Keep our rules in mind:
o n = 1 the element’s
row on the periodic table
o 0 ≤ ℓ ≤ n-1
o -ℓ ≤ mℓ ≤ ℓ
o ms = +½ or -½
• Typically, we don’t bother
writing ms as +½ or -½
o Rather, we symbolize that
two electrons have
opposite electron spins
via up-and-down arrows
(shown below)
•
Though sodium has many
orbitals in its 3rd shell, most of
them are unoccupied
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© 2017 J Co Review, Inc., Accessed by Guest on 05-16-2017